././@PaxHeader 0000000 0000000 0000000 00000000034 00000000000 010212 x ustar 00 28 mtime=1682599655.3394356
sgp4-2.22/ 0000755 0001751 0000173 00000000000 14422467347 011732 5 ustar 00runner docker ././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/LICENSE 0000644 0001751 0000173 00000002076 14422467341 012736 0 ustar 00runner docker The MIT License (MIT)
Copyright © 2012–2016 Brandon Rhodes
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/MANIFEST.in 0000644 0001751 0000173 00000000161 14422467341 013460 0 ustar 00runner docker include LICENSE
include extension/SGP4.h
include sgp4/SGP4-VER.TLE
include sgp4/sample*
include sgp4/tcppver.out
././@PaxHeader 0000000 0000000 0000000 00000000034 00000000000 010212 x ustar 00 28 mtime=1682599655.3394356
sgp4-2.22/PKG-INFO 0000644 0001751 0000173 00000074373 14422467347 013045 0 ustar 00runner docker Metadata-Version: 2.1
Name: sgp4
Version: 2.22
Summary: Track Earth satellites given TLE data, using up-to-date 2020 SGP4 routines.
Home-page: https://github.com/brandon-rhodes/python-sgp4
Author: Brandon Rhodes
Author-email: brandon@rhodesmill.org
License: MIT
Classifier: Development Status :: 5 - Production/Stable
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: MIT License
Classifier: Programming Language :: Python :: 2
Classifier: Programming Language :: Python :: 2.6
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.3
Classifier: Programming Language :: Python :: 3.4
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
Classifier: Programming Language :: Python :: 3.9
Classifier: Topic :: Scientific/Engineering :: Astronomy
License-File: LICENSE
This package compiles the official C++ code from `Revisiting Spacetrack
Report #3 `_ (AIAA
2006-6753) and uses it to compute the positions of satellites in Earth
orbit. Orbital elements can be read from either a legacy TLE file or
from a modern OMM element set, both of which you can fetch from a site
like `CelesTrak `_.
If your machine can’t install or compile the C++ code, then this package
falls back to using a slower pure-Python implementation of SGP4. Tests
make sure that its positions **agree to within 0.1 mm** with the
standard version of the algorithm — an error far less than the
1–3 km/day by which satellites themselves deviate from the ideal orbits
described in TLE files.
An accelerated routine is available that, given a series of times and of
satellites, computes a whole array of output positions using a fast C++
loop. See the “Array Acceleration” section below.
Note that the SGP4 propagator returns raw *x,y,z* Cartesian coordinates
in a “True Equator Mean Equinox” (TEME) reference frame that’s centered
on the Earth but does not rotate with it — an “Earth centered inertial”
(ECI) reference frame. The SGP4 propagator itself does not implement
the math to convert these positions into more official ECI frames like
J2000 or the ICRS, nor into any Earth-centered Earth-fixed (ECEF) frames
like the ITRS, nor into latitudes and longitudes through an Earth
ellipsoid like WGS84. For conversions into these other coordinate
frames, look for a comprehensive astronomy library, like the `Skyfield
`_ library that is built atop this one
(see the `section on Earth satellites
`_ in its
documentation).
Usage
-----
You will probably first want to to check whether your machine has
successfully installed the fast SGP4 C++ code, or is using the slow
Python version (in which case this value will be false):
>>> from sgp4.api import accelerated
>>> print(accelerated)
True
This library uses the same function names as the official C++ code, to
help users who are already familiar with SGP4 in other languages. Here
is how to compute the x,y,z position and velocity for the International
Space Station at 12:50:19 on 29 June 2000:
>>> from sgp4.api import Satrec
>>>
>>> s = '1 25544U 98067A 19343.69339541 .00001764 00000-0 38792-4 0 9991'
>>> t = '2 25544 51.6439 211.2001 0007417 17.6667 85.6398 15.50103472202482'
>>> satellite = Satrec.twoline2rv(s, t)
>>>
>>> jd, fr = 2458827, 0.362605
>>> e, r, v = satellite.sgp4(jd, fr)
>>> e
0
>>> print(r) # True Equator Mean Equinox position (km)
(-6102.44..., -986.33..., -2820.31...)
>>> print(v) # True Equator Mean Equinox velocity (km/s)
(-1.45..., -5.52..., 5.10...)
As input, you can provide either:
* A simple floating-point Julian Date for ``jd`` and the value 0.0 for
``fr``, if you are happy with the precision of a 64-bit floating point
number. Note that modern Julian Dates are greater than 2,450,000
which means that nearly half of the precision of a 64-bit float will
be consumed by the whole part that specifies the day. The remaining
digits will provide a precision for the fraction of around 20.1 µs.
This should be no problem for the accuracy of your result — satellite
positions usually off by a few kilometers anyway, far less than a
satellite moves in 20.1 µs — but if you run a solver that dives down
into the microseconds while searching for a rising or setting time,
the solver might be bothered by the 20.1 µs plateau between each jump
in the satellite’s position.
* Or, you can provide a coarse date ``jd`` plus a very precise fraction
``fr`` that supplies the rest of the value. The Julian Date for which
the satellite position is computed is the sum of the two values. One
common practice is to provide the whole number as ``jd`` and the
fraction as ``fr``; another is to have ``jd`` carry the fraction 0.5
since UTC midnight occurs halfway through each Julian Date. Either
way, splitting the value allows a solver to run all the way down into
the nanoseconds and still see SGP4 respond smoothly to tiny date
adjustments with tiny changes in the resulting satellite position.
Here is how to intrepret the results:
* ``e`` will be a non-zero error code if the satellite position could
not be computed for the given date. You can ``from sgp4.api import
SGP4_ERRORS`` to access a dictionary mapping error codes to error
messages explaining what each code means.
* ``r`` measures the satellite position in **kilometers** from the
center of the earth in the idiosyncratic True Equator Mean Equinox
coordinate frame used by SGP4.
* ``v`` velocity is the rate at which the position is changing,
expressed in **kilometers per second**.
If your application does not natively handle Julian dates, you can
compute ``jd`` and ``fr`` from calendar dates using ``jday()``.
>>> from sgp4.api import jday
>>> jd, fr = jday(2019, 12, 9, 12, 0, 0)
>>> jd
2458826.5
>>> fr
0.5
Double-checking your TLE lines
------------------------------
Because TLE is an old punch-card fixed-width format, it’s very sensitive
to whether exactly the right number of spaces are positioned in exactly
the right columns. If you suspect that your satellite elements aren’t
getting loaded correctly, try calling the slow pure-Python version of
``twoline2rv()``, which performs extra checks that the fast C++ doesn’t:
>>> from sgp4.earth_gravity import wgs72
>>> from sgp4.io import twoline2rv
>>> assert twoline2rv(s, t, wgs72)
Any TLE formatting errors will be raised as a ``ValueError``.
Using OMM elements instead of TLE
---------------------------------
The industry is migrating away from the original TLE format, because it
will soon run out of satellite numbers.
* Some TLE files now use a new “Alpha-5” convention that expands the
range of satellite numbers by using an initial letter; for example,
“E8493” means satellite 148493. This library supports the Alpha-5
convention and should return the correct integer in Python.
* Some authorities are now distributing satellite elements in an “OMM”
Orbit Mean Elements Message format that replaces the TLE format. You
can learn about OMM in Dr. T.S. Kelso’s `“A New Way to Obtain GP Data”
`_ at
the CelesTrak site.
You can already try out experimental support for OMM:
>>> from sgp4 import omm
Reading OMM data takes two steps, because OMM supports several different
text formats. First, parse the input text to recover the field names
and values that it stores; second, build a Python satellite object from
those field values. For example, to load OMM from XML:
>>> with open('sample_omm.xml') as f:
... fields = next(omm.parse_xml(f))
>>> sat = Satrec()
>>> omm.initialize(sat, fields)
Or, to load OMM from CSV:
>>> with open('sample_omm.csv') as f:
... fields = next(omm.parse_csv(f))
>>> sat = Satrec()
>>> omm.initialize(sat, fields)
Either way, the satellite object should wind up properly initialized and
ready to start producing positions.
If you are interested in saving satellite parameters using the new OMM
format, then read the section on “Export” below.
Epoch
-----
Over a given satellite’s lifetime, dozens or hundreds of different TLE
records will be produced as its orbit evolves. Each TLE record
specifies the “epoch date” for which it is most accurate. Typically a
TLE is only useful for a couple of weeks to either side of its epoch
date, beyond which its predictions become unreliable.
Satellite objects natively provide their epoch as a two-digit year and
then a fractional number of days into the year:
>>> satellite.epochyr
19
>>> satellite.epochdays
343.69339541
Because Sputnik was launched in 1957, satellite element sets will never
refer to an earlier year, so years 57 through 99 mean 1957–1999 while 0
through 56 mean 2000–2056. The TLE format will presumably be obsolete
in 2057 and have to be upgraded to 4-digit years.
To turn the number of days and its fraction into a calendar date and
time, use the ``days2mdhms()`` function.
>>> from sgp4.api import days2mdhms
>>> month, day, hour, minute, second = days2mdhms(19, 343.69339541)
>>> month
12
>>> day
9
>>> hour
16
>>> minute
38
>>> second
29.363424
The SGP4 library also translates those two numbers into a Julian date
and fractional Julian date, since Julian dates are more commonly used in
astronomy.
>>> satellite.jdsatepoch
2458826.5
>>> satellite.jdsatepochF
0.69339541
Finally, a convenience function is available in the library if you need
the epoch date and time as Python ``datetime``.
>>> from sgp4.conveniences import sat_epoch_datetime
>>> sat_epoch_datetime(satellite)
datetime.datetime(2019, 12, 9, 16, 38, 29, 363423, tzinfo=UTC)
Array Acceleration
------------------
To avoid the expense of running a Python loop when you have many dates
and times for which you want a position, you can pass your Julian dates
as arrays. The array routine is only faster if your machine has
successfully installed or compiled the SGP4 C++ code, so you might want
to check first:
>>> from sgp4.api import accelerated
>>> print(accelerated)
True
To call the array routine, make NumPy arrays for ``jd`` and ``fr`` that
are the same length:
>>> import numpy as np
>>> np.set_printoptions(precision=2)
>>> jd = np.array((2458826, 2458826, 2458826, 2458826))
>>> fr = np.array((0.0001, 0.0002, 0.0003, 0.0004))
>>> e, r, v = satellite.sgp4_array(jd, fr)
>>> print(e)
[0 0 0 0]
>>> print(r)
[[-3431.31 2620.15 -5252.97]
[-3478.86 2575.14 -5243.87]
[-3526.09 2529.89 -5234.28]
[-3572.98 2484.41 -5224.19]]
>>> print(v)
[[-5.52 -5.19 1.02]
[-5.49 -5.22 1.08]
[-5.45 -5.25 1.14]
[-5.41 -5.28 1.2 ]]
To avoid the expense of Python loops when you have many satellites and
dates, build a ``SatrecArray`` from several individual satellites. Its
``sgp4()`` method will expect both ``jd`` and ``fr`` to be NumPy arrays,
so if you only have one date, be sure to provide NumPy arrays of length
one. Here is a sample computation for 2 satellites and 4 dates:
>>> u = '1 20580U 90037B 19342.88042116 .00000361 00000-0 11007-4 0 9996'
>>> w = '2 20580 28.4682 146.6676 0002639 185.9222 322.7238 15.09309432427086'
>>> satellite2 = Satrec.twoline2rv(u, w)
>>> from sgp4.api import SatrecArray
>>> a = SatrecArray([satellite, satellite2])
>>> e, r, v = a.sgp4(jd, fr)
>>> np.set_printoptions(precision=2)
>>> print(e)
[[0 0 0 0]
[0 0 0 0]]
>>> print(r)
[[[-3431.31 2620.15 -5252.97]
[-3478.86 2575.14 -5243.87]
[-3526.09 2529.89 -5234.28]
[-3572.98 2484.41 -5224.19]]
[[ 5781.85 2564. -2798.22]
[ 5749.36 2618.59 -2814.63]
[ 5716.35 2672.94 -2830.78]
[ 5682.83 2727.05 -2846.68]]]
>>> print(v)
[[[-5.52 -5.19 1.02]
[-5.49 -5.22 1.08]
[-5.45 -5.25 1.14]
[-5.41 -5.28 1.2 ]]
[[-3.73 6.33 -1.91]
[-3.79 6.3 -1.88]
[-3.85 6.28 -1.85]
[-3.91 6.25 -1.83]]]
Export
------
If you have a ``Satrec`` you want to share with friends or persist to a
file, there’s an export routine that will turn it back into a TLE:
>>> from sgp4 import exporter
>>> line1, line2 = exporter.export_tle(satellite)
>>> line1
'1 25544U 98067A 19343.69339541 .00001764 00000-0 38792-4 0 9991'
>>> line2
'2 25544 51.6439 211.2001 0007417 17.6667 85.6398 15.50103472202482'
Happily, these are exactly the two TLE lines that we used to create this
satellite object:
>>> (s == line1) and (t == line2)
True
Another export routine is available that produces the fields defined by
the new OMM format (see the “OMM” section above):
>>> from pprint import pprint
>>> fields = exporter.export_omm(satellite, 'ISS (ZARYA)')
>>> pprint(fields)
{'ARG_OF_PERICENTER': 17.6667,
'BSTAR': 3.8792e-05,
'CENTER_NAME': 'EARTH',
'CLASSIFICATION_TYPE': 'U',
'ECCENTRICITY': 0.0007417,
'ELEMENT_SET_NO': 999,
'EPHEMERIS_TYPE': 0,
'EPOCH': '2019-12-09T16:38:29.363423',
'INCLINATION': 51.6439,
'MEAN_ANOMALY': 85.6398,
'MEAN_ELEMENT_THEORY': 'SGP4',
'MEAN_MOTION': 15.501034720000002,
'MEAN_MOTION_DDOT': 0.0,
'MEAN_MOTION_DOT': 1.764e-05,
'NORAD_CAT_ID': 25544,
'OBJECT_ID': '1998-067A',
'OBJECT_NAME': 'ISS (ZARYA)',
'RA_OF_ASC_NODE': 211.2001,
'REF_FRAME': 'TEME',
'REV_AT_EPOCH': 20248,
'TIME_SYSTEM': 'UTC'}
Gravity
-------
The SGP4 algorithm operates atop a set of constants specifying how
strong the Earth’s gravity is. The most recent official paper on SGP4
(see below) specifies that “We use WGS-72 as the default value”, so this
Python module uses the same default. But in case you want to use either
the old legacy version of the WGS-72 constants, or else the non-standard
but more modern WGS-84 constants, the ``twoline2rv()`` constructor takes
an optional argument:
>>> from sgp4.api import WGS72OLD, WGS72, WGS84
>>> satellite3 = Satrec.twoline2rv(s, t, WGS84)
You will in general get less accurate results if you choose WGS-84.
Even though it reflects more recent and accurate measures of the Earth,
satellite TLEs across the industry are most likely generated with WGS-72
as their basis. The positions you generate will better agree with the
real positions of each satellite if you use the same underlying gravity
constants as were used to generate the TLE.
Providing your own elements
---------------------------
If instead of parsing a TLE you want to specify orbital elements
directly, you can pass them as floating point numbers to a satellite
object’s ``sgp4init()`` method. For example, here’s how to build the
same International Space Station orbit that we loaded from a TLE in the
first code example above:
>>> satellite2 = Satrec()
>>> satellite2.sgp4init(
... WGS72, # gravity model
... 'i', # 'a' = old AFSPC mode, 'i' = improved mode
... 25544, # satnum: Satellite number
... 25545.69339541, # epoch: days since 1949 December 31 00:00 UT
... 3.8792e-05, # bstar: drag coefficient (1/earth radii)
... 0.0, # ndot: ballistic coefficient (radians/minute^2)
... 0.0, # nddot: mean motion 2nd derivative (radians/minute^3)
... 0.0007417, # ecco: eccentricity
... 0.3083420829620822, # argpo: argument of perigee (radians)
... 0.9013560935706996, # inclo: inclination (radians)
... 1.4946964807494398, # mo: mean anomaly (radians)
... 0.06763602333248933, # no_kozai: mean motion (radians/minute)
... 3.686137125541276, # nodeo: R.A. of ascending node (radians)
... )
These numbers don’t look the same as the numbers in the TLE, because the
underlying ``sgp4init()`` routine uses different units: radians rather
than degrees. But this is the same orbit and will produce the same
positions.
Note that ``ndot`` and ``nddot`` are ignored by the SGP4 propagator, so
you can leave them ``0.0`` without any effect on the resulting satellite
positions. But they do at least get saved to the satellite object, and
written out if you write the parameters to a TLE or OMM file (see the
“Export” section, above).
To compute the “epoch” argument, take the epoch’s Julian date and
subtract 2433281.5 days.
While the underlying ``sgp4init()`` routine leaves the attributes
``epochyr``, ``epochdays``, ``jdsatepoch``, and ``jdsatepochF`` unset,
this library goes ahead and sets them anyway for you, using the epoch
you provided.
See the next section for the complete list of attributes that are
available from the satellite record once it has been initialized.
Attributes
----------
There are several dozen ``Satrec`` attributes that expose data from the
underlying C++ SGP4 record. They fall into the following categories.
*Identification*
These are copied directly from the TLE record but aren’t used by the
propagation math.
| ``satnum_str`` — Satellite number, as a 5-character string.
| ``satnum`` — Satellite number, converted to an integer.
| ``classification`` — ``'U'``, ``'C'``, or ``'S'``
indicating the element set is Unclassified, Classified, or Secret.
| ``ephtype`` — Integer “ephemeris type”, used internally by space
agencies to mark element sets that are not ready for publication;
this field should always be ``0`` in published TLEs.
| ``elnum`` — Element set number.
| ``revnum`` — Satellite’s revolution number at the moment of the epoch,
presumably counting from 1 following launch.
*Orbital Elements*
These are the orbital parameters, copied verbatim from the text of the
TLE record. They describe the orbit at the moment of the TLE’s epoch
and so remain constant even as the satellite record is used over and
over again to propagate positions for different times.
| ``epochyr`` — Epoch date: the last two digits of the year.
| ``epochdays`` — Epoch date: the number of days into the year,
including a decimal fraction for the UTC time of day.
| ``ndot`` — First time derivative of the mean motion
(loaded from the TLE, but otherwise ignored).
| ``nddot`` — Second time derivative of the mean motion
(loaded from the TLE, but otherwise ignored).
| ``bstar`` — Ballistic drag coefficient B* (1/earth radii).
| ``inclo`` — Inclination (radians).
| ``nodeo`` — Right ascension of ascending node (radians).
| ``ecco`` — Eccentricity.
| ``argpo`` — Argument of perigee (radians).
| ``mo`` — Mean anomaly (radians).
| ``no_kozai`` — Mean motion (radians/minute).
| ``no`` — Alias for ``no_kozai``, for compatibility with old code.
You can also access the epoch as a Julian date:
| ``jdsatepoch`` — Whole part of the epoch’s Julian date.
| ``jdsatepochF`` — Fractional part of the epoch’s Julian date.
*Computed Orbit Properties*
These are computed when the satellite is first loaded,
as a convenience for callers who might be interested in them.
They aren’t used by the SGP4 propagator itself.
| ``a`` — Semi-major axis (earth radii).
| ``altp`` — Altitude of the satellite at perigee
(earth radii, assuming a spherical Earth).
| ``alta`` — Altitude of the satellite at apogee
(earth radii, assuming a spherical Earth).
| ``argpdot`` — Rate at which the argument of perigee is changing
(radians/minute).
| ``gsto`` — Greenwich Sidereal Time at the satellite’s epoch (radians).
| ``mdot`` — Rate at which the mean anomaly is changing (radians/minute)
| ``nodedot`` — Rate at which the right ascension of the ascending node
is changing (radians/minute).
*Propagator Mode*
| ``operationmode`` — A single character that directs SGP4
to either operate in its modern ``'i'`` improved mode
or in its legacy ``'a'`` AFSPC mode.
| ``method`` — A single character, chosen automatically
when the orbital elements were loaded, that indicates whether SGP4
has chosen to use its built-in ``'n'`` Near Earth
or ``'d'`` Deep Space mode for this satellite.
*Result of Most Recent Propagation*
| ``t`` —
The time you gave when you most recently asked SGP4
to compute this satellite’s position,
measured in minutes before (negative) or after (positive)
the satellite’s epoch.
| ``error`` —
Error code produced by the most recent SGP4 propagation
you performed with this element set.
The possible ``error`` codes are:
0. No error.
1. Mean eccentricity is outside the range 0 ≤ e < 1.
2. Mean motion has fallen below zero.
3. Perturbed eccentricity is outside the range 0 ≤ e ≤ 1.
4. Length of the orbit’s semi-latus rectum has fallen below zero.
5. (No longer used.)
6. Orbit has decayed: the computed position is underground.
(The position is still returned, in case the vector is helpful
to software that might be searching for the moment of re-entry.)
*Mean Elements From Most Recent Propagation*
Partway through each propagation, the SGP4 routine saves a set of
“singly averaged mean elements” that describe the orbit’s shape at the
moment for which a position is being computed. They are averaged with
respect to the mean anomaly and include the effects of secular gravity,
atmospheric drag, and — in Deep Space mode — of those pertubations from
the Sun and Moon that SGP4 averages over an entire revolution of each of
those bodies. They omit both the shorter-term and longer-term periodic
pertubations from the Sun and Moon that SGP4 applies right before
computing each position.
| ``am`` — Average semi-major axis (earth radii).
| ``em`` — Average eccentricity.
| ``im`` — Average inclination (radians).
| ``Om`` — Average right ascension of ascending node (radians).
| ``om`` — Average argument of perigee (radians).
| ``mm`` — Average mean anomaly (radians).
| ``nm`` — Average mean motion (radians/minute).
*Gravity Model Parameters*
When the satellite record is initialized, your choice of gravity model
results in a slate of eight constants being copied in:
| ``tumin`` — Minutes in one “time unit”.
| ``xke`` — The reciprocal of ``tumin``.
| ``mu`` — Earth’s gravitational parameter (km³/s²).
| ``radiusearthkm`` — Radius of the earth (km).
| ``j2``, ``j3``, ``j4`` — Un-normalized zonal harmonic values J₂, J₃, and J₄.
| ``j3oj2`` — The ratio J₃/J₂.
Printing satellite attributes
-----------------------------
If you want to print out a satellite, this library provides a convenient
“attribute dump” routine that takes a satellite and generates lines that
list its attributes::
from sys import stdout
from sgp4.conveniences import dump_satrec
stdout.writelines(dump_satrec(satellite))
If you want to compare two satellites, then simply pass a second
argument; the second satellite’s attributes will be printed in a second
column next to those of the first. ::
stdout.writelines(dump_satrec(satellite, satellite2))
Validation against the official algorithm
-----------------------------------------
This implementation passes all of the automated tests in the August 2010
release of the reference implementation of SGP4 by Vallado et al., who
originally published their revision of SGP4 in 2006:
Vallado, David A., Paul Crawford, Richard Hujsak, and T.S. Kelso,
“Revisiting Spacetrack Report #3,” presented at the AIAA/AAS
Astrodynamics Specialist Conference, Keystone, CO, 2006 August
21–24.
If you would like to review the paper, it is `available online
`_. You can
always download the latest version of their code for comparison against
this Python module (or other implementations) at `AIAA-2006-6753.zip
`_.
For developers
--------------
Developers can check out this full project from GitHub:
https://github.com/brandon-rhodes/python-sgp4
To run its unit tests, install Python 2, Python 3, and the ``tox``
testing tool. The tests runing in Python 2 will exercise the fallback
pure-Python version of the routines, while Python 3 exercises the fast
new C++ accelerated code::
cd python-sgp4
tox
Legacy API
----------
Before this library pivoted to wrapping Vallado's official C++ code and
was operating in pure Python only, it had a slightly quirkier API, which
is still supported for compatibility with older clients. You can learn
about it by reading the documentation from version 1.4 or earlier:
https://pypi.org/project/sgp4/1.4/
Changelog
---------
2023-04-27 — 2.22
* Added a ``satnum_str`` attribute, exposing the fact that the C++ now
stores the satellite number as a string; and check that ``satnum`` is
never greater than 339999.
* Fixed the units of the ``nddot`` attribute when the value is loaded
from an OMM record. (Since the TLE computation itself ignores this
attribute, this did not affect any satellite positions.)
* Enhanced the fallback Python version of ``twoline2rv()`` to verify
that TLE lines are ASCII, and added documentation using it to
double-check TLEs that might suffer from non-ASCII characters.
* If the user doesn’t set a satellite’s ``classification``, it now
defaults to ``'U'`` for ‘unclassified’.
2022-04-06 — 2.21
* Added ``dump_satrec()`` to the ``sgp4.conveniences`` module.
* Fixed the ``Satrec`` attribute ``.error``, which was previously
building a nonsense integer from the wrong data in memory.
* Removed ``.whichconst`` from Python ``Satrec``, to help users avoid
writing code that will break when the C++ extension is available.
2021-07-01 — 2.20
* Taught ``sgp4init()`` to round both ``epochdays`` and ``jdsatepochF``
to the same 8 decimal places used for the date fraction in a TLE, if
the user-supplied ``epoch`` itself has 8 or fewer digits behind the
decimal point. This should make it easier to build satellites that
round-trip to TLE format with perfect accuracy.
* Fixed how ``export_tle()`` formats the BSTAR field when its value, if
written in scientific notation, has a positive exponent.
* Fixed the ``epochyr`` assigned by ``sgp4init()`` so years before 2000
have two digits instead of three (for example, so that 1980 produces
an ``epochyr`` of 80 instead of 980).
2021-04-22 — 2.19
* Extended the documentation on the Python Package Index and in the
module docstring so it lists every ``Satrec`` attribute that this
library exposes; even the more obscure ones might be useful to folks
working to analyze satellite orbits.
2021-03-08 — 2.18
* If a TLE satellite number lacks the required 5 digits,
``twoline2rv()`` now gives the underlying C++ library a little help so
it can still parse the classification and international designator
correctly.
* The ``Satrec`` attributes ``jdsatepoch``, ``jdsatepochF``,
``epochyr``, and ``epochdays`` are now writeable, so users can adjust
their values manually — which should make up for the fact that the
``sgp4init()`` method can’t set them with full floating point
precision.
| 2021-02-17 — 2.17 — Fixed where in the output array the ``sgp4_array()`` method writes NaN values when an SGP4 propagation fails.
| 2021-02-12 — 2.16 — Fixed ``days2mdhms()`` rounding to always match TLE epoch.
| 2021-01-08 — 2.15 — Fixed parsing of the ``satnum`` TLE field in the Python fallback code, when the field has a leading space; added OMM export routine.
| 2020-12-16 — 2.14 — New data formats: added OMM message support for both XML and CSV, and added support for the new Alpha-5 extension to TLE files.
| 2020-10-14 — 2.13 — Enhanced ``sgp4init()`` with custom code that also sets the ``epochdays`` and ``epochyr`` satellite attributes.
| 2020-05-28 — 2.12 — Moved the decision of whether to set the locale during ``twoline2rv()`` from import time to runtime, for users who change locales after their application is up and running.
| 2020-05-24 — 2.11 — Fixed a regression in how dates are split into hours, minutes, and seconds that would sometimes produce a time whose second=60, crashing the pure-Python version of the library.
| 2020-05-22 — 2.10 — Switch the locale temporarily to ``C`` during the C++ accelerated ``twoline2rv()``, since it does not protect its ``sscanf()`` calls from locales that, like German, expect comma decimal points instead of the period decimal points always used in a TLE.
| 2020-05-21 — 2.9 — Added ``sat_epoch_datetime()``, expanded documentation around converting a satellite epoch to a date and time, and started rounding the epoch to exactly the digits provided in the TLE; and removed the ``Satrec.epoch`` attribute from Python fallback code to better match the C++ version.
| 2020-05-07 — 2.8 — New function ``jday_datetime()`` is now available in the ``sgp4.conveniences`` module, thanks to Egemen Imre.
| 2020-04-24 — 2.7 — New method ``sgp4init()`` (thank you, Chris Lewicki!) is available.
| 2020-04-20 — 2.6 — New routine ``export_tle()`` (thank you, Egemen Imre!) is available. Improved how the accelerated C++ backend parses the ``intldesg`` string and the ``revnum`` integer.
| 2020-03-22 — 2.5 — Gave the new accelerated ``twoline2rv()`` an optional argument that lets the user choose a non-standard set of gravity constants.
| 2020-02-25 — 2.4 — Improved the ``jday()`` docstring; made the old legacy Python resilient if the day of the month is out-of-range (past the end of the month) in a TLE; and Mark Rutten fixed the C++ so it compiles on Windows!
| 2020-02-04 — 2.3 — Removed experimental code that caused performance problems for users with Numba installed.
| 2020-02-02 — 2.2 — A second release on Palindrome Day: fix the Satrec ``.epochyr`` attribute so it behaves the same way in Python as it does in the official C library, where it is only the last 2 digits of the year; and make ``.no`` available in the Python fallback case as well.
| 2020-02-02 — 2.1 — Add vectorized array method to Satrec object; add ``.no`` attribute to new Satrec object to support old code that has not migrated to the new name ``.no_kozai``; gave Python wrapper classes ``__slots__`` to avoid the expense of a per-object attribute dictionary.
| 2020-01-30 — 2.0 — Rewrite API to use genuine Vallado C++ code on those systems where it can be compiled; add accelerated vectorized array interface; make ``gstime()`` a public function; clarify format error message.
| 2015-01-15 — 1.4 — Display detailed help when TLE input does not match format.
| 2014-06-26 — 1.3 — Return ``(NaN,NaN,NaN)`` vectors on error and set ``.error_message``
| 2013-11-29 — 1.2 — Made ``epochyr`` 4 digits; add ``datetime`` for ``.epoch``
| 2012-11-22 — 1.1 — Python 3 compatibility; more documentation
| 2012-08-27 — 1.0 — Initial release
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/README.md 0000644 0001751 0000173 00000000414 14422467341 013202 0 ustar 00runner docker python-sgp4
===========
Python implementation of most recent version of the SGP4 satellite
tracking algorithm.
* Documentation: https://pypi.python.org/pypi/sgp4/
* Download: https://pypi.org/project/sgp4/#files
* Changelog: https://pypi.org/project/sgp4/#changelog
././@PaxHeader 0000000 0000000 0000000 00000000034 00000000000 010212 x ustar 00 28 mtime=1682599655.3354356
sgp4-2.22/extension/ 0000755 0001751 0000173 00000000000 14422467347 013746 5 ustar 00runner docker ././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/extension/SGP4.cpp 0000644 0001751 0000173 00000330070 14422467341 015164 0 ustar 00runner docker /* ----------------------------------------------------------------
*
* sgp4unit.cpp
*
* this file contains the sgp4 procedures for analytical propagation
* of a satellite. the code was originally released in the 1980 and 1986
* spacetrack papers. a detailed discussion of the theory and history
* may be found in the 2006 aiaa paper by vallado, crawford, hujsak,
* and kelso.
*
* companion code for
* fundamentals of astrodynamics and applications
* 2013
* by david vallado
*
* (w) 719-573-2600, email dvallado@agi.com, davallado@gmail.com
*
* current :
* 12 mar 20 david vallado
* chg satnum to string for alpha 5 or 9-digit
* changes :
* 7 dec 15 david vallado
* fix jd, jdfrac
* 3 nov 14 david vallado
* update to msvs2013 c++
* 30 aug 10 david vallado
* delete unused variables in initl
* replace pow integer 2, 3 with multiplies for speed
* 3 nov 08 david vallado
* put returns in for error codes
* 29 sep 08 david vallado
* fix atime for faster operation in dspace
* add operationmode for afspc (a) or improved (i)
* performance mode
* 16 jun 08 david vallado
* update small eccentricity check
* 16 nov 07 david vallado
* misc fixes for better compliance
* 20 apr 07 david vallado
* misc fixes for constants
* 11 aug 06 david vallado
* chg lyddane choice back to strn3, constants, misc doc
* 15 dec 05 david vallado
* misc fixes
* 26 jul 05 david vallado
* fixes for paper
* note that each fix is preceded by a
* comment with "sgp4fix" and an explanation of
* what was changed
* 10 aug 04 david vallado
* 2nd printing baseline working
* 14 may 01 david vallado
* 2nd edition baseline
* 80 norad
* original baseline
* ---------------------------------------------------------------- */
#include "SGP4.h"
#define pi 3.14159265358979323846
// define global variables here, not in .h
// use extern in main
char help = 'n';
FILE *dbgfile;
/* ----------- local functions - only ever used internally by sgp4 ---------- */
static void dpper
(
double e3, double ee2, double peo, double pgho, double pho,
double pinco, double plo, double se2, double se3, double sgh2,
double sgh3, double sgh4, double sh2, double sh3, double si2,
double si3, double sl2, double sl3, double sl4, double t,
double xgh2, double xgh3, double xgh4, double xh2, double xh3,
double xi2, double xi3, double xl2, double xl3, double xl4,
double zmol, double zmos, double inclo,
char init,
double& ep, double& inclp, double& nodep, double& argpp, double& mp,
char opsmode
);
static void dscom
(
double epoch, double ep, double argpp, double tc, double inclp,
double nodep, double np,
double& snodm, double& cnodm, double& sinim, double& cosim, double& sinomm,
double& cosomm, double& day, double& e3, double& ee2, double& em,
double& emsq, double& gam, double& peo, double& pgho, double& pho,
double& pinco, double& plo, double& rtemsq, double& se2, double& se3,
double& sgh2, double& sgh3, double& sgh4, double& sh2, double& sh3,
double& si2, double& si3, double& sl2, double& sl3, double& sl4,
double& s1, double& s2, double& s3, double& s4, double& s5,
double& s6, double& s7, double& ss1, double& ss2, double& ss3,
double& ss4, double& ss5, double& ss6, double& ss7, double& sz1,
double& sz2, double& sz3, double& sz11, double& sz12, double& sz13,
double& sz21, double& sz22, double& sz23, double& sz31, double& sz32,
double& sz33, double& xgh2, double& xgh3, double& xgh4, double& xh2,
double& xh3, double& xi2, double& xi3, double& xl2, double& xl3,
double& xl4, double& nm, double& z1, double& z2, double& z3,
double& z11, double& z12, double& z13, double& z21, double& z22,
double& z23, double& z31, double& z32, double& z33, double& zmol,
double& zmos
);
static void dsinit
(
//sgp4fix no longer needed pass in xke
//gravconsttype whichconst,
double xke,
double cosim, double emsq, double argpo, double s1, double s2,
double s3, double s4, double s5, double sinim, double ss1,
double ss2, double ss3, double ss4, double ss5, double sz1,
double sz3, double sz11, double sz13, double sz21, double sz23,
double sz31, double sz33, double t, double tc, double gsto,
double mo, double mdot, double no, double nodeo, double nodedot,
double xpidot, double z1, double z3, double z11, double z13,
double z21, double z23, double z31, double z33, double ecco,
double eccsq, double& em, double& argpm, double& inclm, double& mm,
double& nm, double& nodem,
int& irez,
double& atime, double& d2201, double& d2211, double& d3210, double& d3222,
double& d4410, double& d4422, double& d5220, double& d5232, double& d5421,
double& d5433, double& dedt, double& didt, double& dmdt, double& dndt,
double& dnodt, double& domdt, double& del1, double& del2, double& del3,
double& xfact, double& xlamo, double& xli, double& xni
);
static void dspace
(
int irez,
double d2201, double d2211, double d3210, double d3222, double d4410,
double d4422, double d5220, double d5232, double d5421, double d5433,
double dedt, double del1, double del2, double del3, double didt,
double dmdt, double dnodt, double domdt, double argpo, double argpdot,
double t, double tc, double gsto, double xfact, double xlamo,
double no,
double& atime, double& em, double& argpm, double& inclm, double& xli,
double& mm, double& xni, double& nodem, double& dndt, double& nm
);
static void initl
(
// not needeed. included in satrec if needed later
// int satn,
// sgp4fix assin xke and j2
// gravconsttype whichconst,
double xke, double j2,
double ecco, double epoch, double inclo, double& no,
char& method,
double& ainv, double& ao, double& con41, double& con42, double& cosio,
double& cosio2, double& eccsq, double& omeosq, double& posq,
double& rp, double& rteosq, double& sinio, double& gsto, char opsmode
);
namespace SGP4Funcs
{
/* -----------------------------------------------------------------------------
*
* procedure dpper
*
* this procedure provides deep space long period periodic contributions
* to the mean elements. by design, these periodics are zero at epoch.
* this used to be dscom which included initialization, but it's really a
* recurring function.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* e3 -
* ee2 -
* peo -
* pgho -
* pho -
* pinco -
* plo -
* se2 , se3 , sgh2, sgh3, sgh4, sh2, sh3, si2, si3, sl2, sl3, sl4 -
* t -
* xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
* zmol -
* zmos -
* ep - eccentricity 0.0 - 1.0
* inclo - inclination - needed for lyddane modification
* nodep - right ascension of ascending node
* argpp - argument of perigee
* mp - mean anomaly
*
* outputs :
* ep - eccentricity 0.0 - 1.0
* inclp - inclination
* nodep - right ascension of ascending node
* argpp - argument of perigee
* mp - mean anomaly
*
* locals :
* alfdp -
* betdp -
* cosip , sinip , cosop , sinop ,
* dalf -
* dbet -
* dls -
* f2, f3 -
* pe -
* pgh -
* ph -
* pinc -
* pl -
* sel , ses , sghl , sghs , shl , shs , sil , sinzf , sis ,
* sll , sls
* xls -
* xnoh -
* zf -
* zm -
*
* coupling :
* none.
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
static void dpper
(
double e3, double ee2, double peo, double pgho, double pho,
double pinco, double plo, double se2, double se3, double sgh2,
double sgh3, double sgh4, double sh2, double sh3, double si2,
double si3, double sl2, double sl3, double sl4, double t,
double xgh2, double xgh3, double xgh4, double xh2, double xh3,
double xi2, double xi3, double xl2, double xl3, double xl4,
double zmol, double zmos, double inclo,
char init,
double& ep, double& inclp, double& nodep, double& argpp, double& mp,
char opsmode
)
{
/* --------------------- local variables ------------------------ */
const double twopi = 2.0 * pi;
double alfdp, betdp, cosip, cosop, dalf, dbet, dls,
f2, f3, pe, pgh, ph, pinc, pl,
sel, ses, sghl, sghs, shll, shs, sil,
sinip, sinop, sinzf, sis, sll, sls, xls,
xnoh, zf, zm, zel, zes, znl, zns;
/* ---------------------- constants ----------------------------- */
zns = 1.19459e-5;
zes = 0.01675;
znl = 1.5835218e-4;
zel = 0.05490;
/* --------------- calculate time varying periodics ----------- */
zm = zmos + zns * t;
// be sure that the initial call has time set to zero
if (init == 'y')
zm = zmos;
zf = zm + 2.0 * zes * sin(zm);
sinzf = sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * cos(zf);
ses = se2* f2 + se3 * f3;
sis = si2 * f2 + si3 * f3;
sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf;
sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf;
shs = sh2 * f2 + sh3 * f3;
zm = zmol + znl * t;
if (init == 'y')
zm = zmol;
zf = zm + 2.0 * zel * sin(zm);
sinzf = sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * cos(zf);
sel = ee2 * f2 + e3 * f3;
sil = xi2 * f2 + xi3 * f3;
sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf;
sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf;
shll = xh2 * f2 + xh3 * f3;
pe = ses + sel;
pinc = sis + sil;
pl = sls + sll;
pgh = sghs + sghl;
ph = shs + shll;
if (init == 'n')
{
pe = pe - peo;
pinc = pinc - pinco;
pl = pl - plo;
pgh = pgh - pgho;
ph = ph - pho;
inclp = inclp + pinc;
ep = ep + pe;
sinip = sin(inclp);
cosip = cos(inclp);
/* ----------------- apply periodics directly ------------ */
// sgp4fix for lyddane choice
// strn3 used original inclination - this is technically feasible
// gsfc used perturbed inclination - also technically feasible
// probably best to readjust the 0.2 limit value and limit discontinuity
// 0.2 rad = 11.45916 deg
// use next line for original strn3 approach and original inclination
// if (inclo >= 0.2)
// use next line for gsfc version and perturbed inclination
if (inclp >= 0.2)
{
ph = ph / sinip;
pgh = pgh - cosip * ph;
argpp = argpp + pgh;
nodep = nodep + ph;
mp = mp + pl;
}
else
{
/* ---- apply periodics with lyddane modification ---- */
sinop = sin(nodep);
cosop = cos(nodep);
alfdp = sinip * sinop;
betdp = sinip * cosop;
dalf = ph * cosop + pinc * cosip * sinop;
dbet = -ph * sinop + pinc * cosip * cosop;
alfdp = alfdp + dalf;
betdp = betdp + dbet;
nodep = fmod(nodep, twopi);
// sgp4fix for afspc written intrinsic functions
// nodep used without a trigonometric function ahead
if ((nodep < 0.0) && (opsmode == 'a'))
nodep = nodep + twopi;
xls = mp + argpp + cosip * nodep;
dls = pl + pgh - pinc * nodep * sinip;
xls = xls + dls;
xnoh = nodep;
nodep = atan2(alfdp, betdp);
// sgp4fix for afspc written intrinsic functions
// nodep used without a trigonometric function ahead
if ((nodep < 0.0) && (opsmode == 'a'))
nodep = nodep + twopi;
if (fabs(xnoh - nodep) > pi)
if (nodep < xnoh)
nodep = nodep + twopi;
else
nodep = nodep - twopi;
mp = mp + pl;
argpp = xls - mp - cosip * nodep;
}
} // if init == 'n'
//#include "debug1.cpp"
} // dpper
/*-----------------------------------------------------------------------------
*
* procedure dscom
*
* this procedure provides deep space common items used by both the secular
* and periodics subroutines. input is provided as shown. this routine
* used to be called dpper, but the functions inside weren't well organized.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* epoch -
* ep - eccentricity
* argpp - argument of perigee
* tc -
* inclp - inclination
* nodep - right ascension of ascending node
* np - mean motion
*
* outputs :
* sinim , cosim , sinomm , cosomm , snodm , cnodm
* day -
* e3 -
* ee2 -
* em - eccentricity
* emsq - eccentricity squared
* gam -
* peo -
* pgho -
* pho -
* pinco -
* plo -
* rtemsq -
* se2, se3 -
* sgh2, sgh3, sgh4 -
* sh2, sh3, si2, si3, sl2, sl3, sl4 -
* s1, s2, s3, s4, s5, s6, s7 -
* ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3 -
* sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33 -
* xgh2, xgh3, xgh4, xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
* nm - mean motion
* z1, z2, z3, z11, z12, z13, z21, z22, z23, z31, z32, z33 -
* zmol -
* zmos -
*
* locals :
* a1, a2, a3, a4, a5, a6, a7, a8, a9, a10 -
* betasq -
* cc -
* ctem, stem -
* x1, x2, x3, x4, x5, x6, x7, x8 -
* xnodce -
* xnoi -
* zcosg , zsing , zcosgl , zsingl , zcosh , zsinh , zcoshl , zsinhl ,
* zcosi , zsini , zcosil , zsinil ,
* zx -
* zy -
*
* coupling :
* none.
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
static void dscom
(
double epoch, double ep, double argpp, double tc, double inclp,
double nodep, double np,
double& snodm, double& cnodm, double& sinim, double& cosim, double& sinomm,
double& cosomm, double& day, double& e3, double& ee2, double& em,
double& emsq, double& gam, double& peo, double& pgho, double& pho,
double& pinco, double& plo, double& rtemsq, double& se2, double& se3,
double& sgh2, double& sgh3, double& sgh4, double& sh2, double& sh3,
double& si2, double& si3, double& sl2, double& sl3, double& sl4,
double& s1, double& s2, double& s3, double& s4, double& s5,
double& s6, double& s7, double& ss1, double& ss2, double& ss3,
double& ss4, double& ss5, double& ss6, double& ss7, double& sz1,
double& sz2, double& sz3, double& sz11, double& sz12, double& sz13,
double& sz21, double& sz22, double& sz23, double& sz31, double& sz32,
double& sz33, double& xgh2, double& xgh3, double& xgh4, double& xh2,
double& xh3, double& xi2, double& xi3, double& xl2, double& xl3,
double& xl4, double& nm, double& z1, double& z2, double& z3,
double& z11, double& z12, double& z13, double& z21, double& z22,
double& z23, double& z31, double& z32, double& z33, double& zmol,
double& zmos
)
{
/* -------------------------- constants ------------------------- */
const double zes = 0.01675;
const double zel = 0.05490;
const double c1ss = 2.9864797e-6;
const double c1l = 4.7968065e-7;
const double zsinis = 0.39785416;
const double zcosis = 0.91744867;
const double zcosgs = 0.1945905;
const double zsings = -0.98088458;
const double twopi = 2.0 * pi;
/* --------------------- local variables ------------------------ */
int lsflg;
double a1, a2, a3, a4, a5, a6, a7,
a8, a9, a10, betasq, cc, ctem, stem,
x1, x2, x3, x4, x5, x6, x7,
x8, xnodce, xnoi, zcosg, zcosgl, zcosh, zcoshl,
zcosi, zcosil, zsing, zsingl, zsinh, zsinhl, zsini,
zsinil, zx, zy;
nm = np;
em = ep;
snodm = sin(nodep);
cnodm = cos(nodep);
sinomm = sin(argpp);
cosomm = cos(argpp);
sinim = sin(inclp);
cosim = cos(inclp);
emsq = em * em;
betasq = 1.0 - emsq;
rtemsq = sqrt(betasq);
/* ----------------- initialize lunar solar terms --------------- */
peo = 0.0;
pinco = 0.0;
plo = 0.0;
pgho = 0.0;
pho = 0.0;
day = epoch + 18261.5 + tc / 1440.0;
xnodce = fmod(4.5236020 - 9.2422029e-4 * day, twopi);
stem = sin(xnodce);
ctem = cos(xnodce);
zcosil = 0.91375164 - 0.03568096 * ctem;
zsinil = sqrt(1.0 - zcosil * zcosil);
zsinhl = 0.089683511 * stem / zsinil;
zcoshl = sqrt(1.0 - zsinhl * zsinhl);
gam = 5.8351514 + 0.0019443680 * day;
zx = 0.39785416 * stem / zsinil;
zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
zx = atan2(zx, zy);
zx = gam + zx - xnodce;
zcosgl = cos(zx);
zsingl = sin(zx);
/* ------------------------- do solar terms --------------------- */
zcosg = zcosgs;
zsing = zsings;
zcosi = zcosis;
zsini = zsinis;
zcosh = cnodm;
zsinh = snodm;
cc = c1ss;
xnoi = 1.0 / nm;
for (lsflg = 1; lsflg <= 2; lsflg++)
{
a1 = zcosg * zcosh + zsing * zcosi * zsinh;
a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
a8 = zsing * zsini;
a9 = zsing * zsinh + zcosg * zcosi * zcosh;
a10 = zcosg * zsini;
a2 = cosim * a7 + sinim * a8;
a4 = cosim * a9 + sinim * a10;
a5 = -sinim * a7 + cosim * a8;
a6 = -sinim * a9 + cosim * a10;
x1 = a1 * cosomm + a2 * sinomm;
x2 = a3 * cosomm + a4 * sinomm;
x3 = -a1 * sinomm + a2 * cosomm;
x4 = -a3 * sinomm + a4 * cosomm;
x5 = a5 * sinomm;
x6 = a6 * sinomm;
x7 = a5 * cosomm;
x8 = a6 * cosomm;
z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * emsq;
z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * emsq;
z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * emsq;
z11 = -6.0 * a1 * a5 + emsq * (-24.0 * x1 * x7 - 6.0 * x3 * x5);
z12 = -6.0 * (a1 * a6 + a3 * a5) + emsq *
(-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
z13 = -6.0 * a3 * a6 + emsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
z21 = 6.0 * a2 * a5 + emsq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
z22 = 6.0 * (a4 * a5 + a2 * a6) + emsq *
(24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
z23 = 6.0 * a4 * a6 + emsq * (24.0 * x2 * x6 - 6.0 * x4 * x8);
z1 = z1 + z1 + betasq * z31;
z2 = z2 + z2 + betasq * z32;
z3 = z3 + z3 + betasq * z33;
s3 = cc * xnoi;
s2 = -0.5 * s3 / rtemsq;
s4 = s3 * rtemsq;
s1 = -15.0 * em * s4;
s5 = x1 * x3 + x2 * x4;
s6 = x2 * x3 + x1 * x4;
s7 = x2 * x4 - x1 * x3;
/* ----------------------- do lunar terms ------------------- */
if (lsflg == 1)
{
ss1 = s1;
ss2 = s2;
ss3 = s3;
ss4 = s4;
ss5 = s5;
ss6 = s6;
ss7 = s7;
sz1 = z1;
sz2 = z2;
sz3 = z3;
sz11 = z11;
sz12 = z12;
sz13 = z13;
sz21 = z21;
sz22 = z22;
sz23 = z23;
sz31 = z31;
sz32 = z32;
sz33 = z33;
zcosg = zcosgl;
zsing = zsingl;
zcosi = zcosil;
zsini = zsinil;
zcosh = zcoshl * cnodm + zsinhl * snodm;
zsinh = snodm * zcoshl - cnodm * zsinhl;
cc = c1l;
}
}
zmol = fmod(4.7199672 + 0.22997150 * day - gam, twopi);
zmos = fmod(6.2565837 + 0.017201977 * day, twopi);
/* ------------------------ do solar terms ---------------------- */
se2 = 2.0 * ss1 * ss6;
se3 = 2.0 * ss1 * ss7;
si2 = 2.0 * ss2 * sz12;
si3 = 2.0 * ss2 * (sz13 - sz11);
sl2 = -2.0 * ss3 * sz2;
sl3 = -2.0 * ss3 * (sz3 - sz1);
sl4 = -2.0 * ss3 * (-21.0 - 9.0 * emsq) * zes;
sgh2 = 2.0 * ss4 * sz32;
sgh3 = 2.0 * ss4 * (sz33 - sz31);
sgh4 = -18.0 * ss4 * zes;
sh2 = -2.0 * ss2 * sz22;
sh3 = -2.0 * ss2 * (sz23 - sz21);
/* ------------------------ do lunar terms ---------------------- */
ee2 = 2.0 * s1 * s6;
e3 = 2.0 * s1 * s7;
xi2 = 2.0 * s2 * z12;
xi3 = 2.0 * s2 * (z13 - z11);
xl2 = -2.0 * s3 * z2;
xl3 = -2.0 * s3 * (z3 - z1);
xl4 = -2.0 * s3 * (-21.0 - 9.0 * emsq) * zel;
xgh2 = 2.0 * s4 * z32;
xgh3 = 2.0 * s4 * (z33 - z31);
xgh4 = -18.0 * s4 * zel;
xh2 = -2.0 * s2 * z22;
xh3 = -2.0 * s2 * (z23 - z21);
//#include "debug2.cpp"
} // dscom
/*-----------------------------------------------------------------------------
*
* procedure dsinit
*
* this procedure provides deep space contributions to mean motion dot due
* to geopotential resonance with half day and one day orbits.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* xke - reciprocal of tumin
* cosim, sinim-
* emsq - eccentricity squared
* argpo - argument of perigee
* s1, s2, s3, s4, s5 -
* ss1, ss2, ss3, ss4, ss5 -
* sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33 -
* t - time
* tc -
* gsto - greenwich sidereal time rad
* mo - mean anomaly
* mdot - mean anomaly dot (rate)
* no - mean motion
* nodeo - right ascension of ascending node
* nodedot - right ascension of ascending node dot (rate)
* xpidot -
* z1, z3, z11, z13, z21, z23, z31, z33 -
* eccm - eccentricity
* argpm - argument of perigee
* inclm - inclination
* mm - mean anomaly
* xn - mean motion
* nodem - right ascension of ascending node
*
* outputs :
* em - eccentricity
* argpm - argument of perigee
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* nodem - right ascension of ascending node
* irez - flag for resonance 0-none, 1-one day, 2-half day
* atime -
* d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -
* dedt -
* didt -
* dmdt -
* dndt -
* dnodt -
* domdt -
* del1, del2, del3 -
* ses , sghl , sghs , sgs , shl , shs , sis , sls
* theta -
* xfact -
* xlamo -
* xli -
* xni
*
* locals :
* ainv2 -
* aonv -
* cosisq -
* eoc -
* f220, f221, f311, f321, f322, f330, f441, f442, f522, f523, f542, f543 -
* g200, g201, g211, g300, g310, g322, g410, g422, g520, g521, g532, g533 -
* sini2 -
* temp -
* temp1 -
* theta -
* xno2 -
*
* coupling :
* getgravconst- no longer used
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
static void dsinit
(
// sgp4fix just send in xke as a constant and eliminate getgravconst call
// gravconsttype whichconst,
double xke,
double cosim, double emsq, double argpo, double s1, double s2,
double s3, double s4, double s5, double sinim, double ss1,
double ss2, double ss3, double ss4, double ss5, double sz1,
double sz3, double sz11, double sz13, double sz21, double sz23,
double sz31, double sz33, double t, double tc, double gsto,
double mo, double mdot, double no, double nodeo, double nodedot,
double xpidot, double z1, double z3, double z11, double z13,
double z21, double z23, double z31, double z33, double ecco,
double eccsq, double& em, double& argpm, double& inclm, double& mm,
double& nm, double& nodem,
int& irez,
double& atime, double& d2201, double& d2211, double& d3210, double& d3222,
double& d4410, double& d4422, double& d5220, double& d5232, double& d5421,
double& d5433, double& dedt, double& didt, double& dmdt, double& dndt,
double& dnodt, double& domdt, double& del1, double& del2, double& del3,
double& xfact, double& xlamo, double& xli, double& xni
)
{
/* --------------------- local variables ------------------------ */
const double twopi = 2.0 * pi;
double ainv2, aonv = 0.0, cosisq, eoc, f220, f221, f311,
f321, f322, f330, f441, f442, f522, f523,
f542, f543, g200, g201, g211, g300, g310,
g322, g410, g422, g520, g521, g532, g533,
ses, sgs, sghl, sghs, shs, shll, sis,
sini2, sls, temp, temp1, theta, xno2, q22,
q31, q33, root22, root44, root54, rptim, root32,
root52, x2o3, znl, emo, zns, emsqo;
q22 = 1.7891679e-6;
q31 = 2.1460748e-6;
q33 = 2.2123015e-7;
root22 = 1.7891679e-6;
root44 = 7.3636953e-9;
root54 = 2.1765803e-9;
rptim = 4.37526908801129966e-3; // this equates to 7.29211514668855e-5 rad/sec
root32 = 3.7393792e-7;
root52 = 1.1428639e-7;
x2o3 = 2.0 / 3.0;
znl = 1.5835218e-4;
zns = 1.19459e-5;
// sgp4fix identify constants and allow alternate values
// just xke is used here so pass it in rather than have multiple calls
// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
/* -------------------- deep space initialization ------------ */
irez = 0;
if ((nm < 0.0052359877) && (nm > 0.0034906585))
irez = 1;
if ((nm >= 8.26e-3) && (nm <= 9.24e-3) && (em >= 0.5))
irez = 2;
/* ------------------------ do solar terms ------------------- */
ses = ss1 * zns * ss5;
sis = ss2 * zns * (sz11 + sz13);
sls = -zns * ss3 * (sz1 + sz3 - 14.0 - 6.0 * emsq);
sghs = ss4 * zns * (sz31 + sz33 - 6.0);
shs = -zns * ss2 * (sz21 + sz23);
// sgp4fix for 180 deg incl
if ((inclm < 5.2359877e-2) || (inclm > pi - 5.2359877e-2))
shs = 0.0;
if (sinim != 0.0)
shs = shs / sinim;
sgs = sghs - cosim * shs;
/* ------------------------- do lunar terms ------------------ */
dedt = ses + s1 * znl * s5;
didt = sis + s2 * znl * (z11 + z13);
dmdt = sls - znl * s3 * (z1 + z3 - 14.0 - 6.0 * emsq);
sghl = s4 * znl * (z31 + z33 - 6.0);
shll = -znl * s2 * (z21 + z23);
// sgp4fix for 180 deg incl
if ((inclm < 5.2359877e-2) || (inclm > pi - 5.2359877e-2))
shll = 0.0;
domdt = sgs + sghl;
dnodt = shs;
if (sinim != 0.0)
{
domdt = domdt - cosim / sinim * shll;
dnodt = dnodt + shll / sinim;
}
/* ----------- calculate deep space resonance effects -------- */
dndt = 0.0;
theta = fmod(gsto + tc * rptim, twopi);
em = em + dedt * t;
inclm = inclm + didt * t;
argpm = argpm + domdt * t;
nodem = nodem + dnodt * t;
mm = mm + dmdt * t;
// sgp4fix for negative inclinations
// the following if statement should be commented out
//if (inclm < 0.0)
// {
// inclm = -inclm;
// argpm = argpm - pi;
// nodem = nodem + pi;
// }
/* -------------- initialize the resonance terms ------------- */
if (irez != 0)
{
aonv = pow(nm / xke, x2o3);
/* ---------- geopotential resonance for 12 hour orbits ------ */
if (irez == 2)
{
cosisq = cosim * cosim;
emo = em;
em = ecco;
emsqo = emsq;
emsq = eccsq;
eoc = em * emsq;
g201 = -0.306 - (em - 0.64) * 0.440;
if (em <= 0.65)
{
g211 = 3.616 - 13.2470 * em + 16.2900 * emsq;
g310 = -19.302 + 117.3900 * em - 228.4190 * emsq + 156.5910 * eoc;
g322 = -18.9068 + 109.7927 * em - 214.6334 * emsq + 146.5816 * eoc;
g410 = -41.122 + 242.6940 * em - 471.0940 * emsq + 313.9530 * eoc;
g422 = -146.407 + 841.8800 * em - 1629.014 * emsq + 1083.4350 * eoc;
g520 = -532.114 + 3017.977 * em - 5740.032 * emsq + 3708.2760 * eoc;
}
else
{
g211 = -72.099 + 331.819 * em - 508.738 * emsq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * em - 2415.925 * emsq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * em - 2366.899 * emsq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * em - 7193.992 * emsq + 3651.957 * eoc;
g422 = -3581.690 + 16178.110 * em - 24462.770 * emsq + 12422.520 * eoc;
if (em > 0.715)
g520 = -5149.66 + 29936.92 * em - 54087.36 * emsq + 31324.56 * eoc;
else
g520 = 1464.74 - 4664.75 * em + 3763.64 * emsq;
}
if (em < 0.7)
{
g533 = -919.22770 + 4988.6100 * em - 9064.7700 * emsq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * em - 8491.4146 * emsq + 5337.524 * eoc;
g532 = -853.66600 + 4690.2500 * em - 8624.7700 * emsq + 5341.4 * eoc;
}
else
{
g533 = -37995.780 + 161616.52 * em - 229838.20 * emsq + 109377.94 * eoc;
g521 = -51752.104 + 218913.95 * em - 309468.16 * emsq + 146349.42 * eoc;
g532 = -40023.880 + 170470.89 * em - 242699.48 * emsq + 115605.82 * eoc;
}
sini2 = sinim * sinim;
f220 = 0.75 * (1.0 + 2.0 * cosim + cosisq);
f221 = 1.5 * sini2;
f321 = 1.875 * sinim * (1.0 - 2.0 * cosim - 3.0 * cosisq);
f322 = -1.875 * sinim * (1.0 + 2.0 * cosim - 3.0 * cosisq);
f441 = 35.0 * sini2 * f220;
f442 = 39.3750 * sini2 * sini2;
f522 = 9.84375 * sinim * (sini2 * (1.0 - 2.0 * cosim - 5.0 * cosisq) +
0.33333333 * (-2.0 + 4.0 * cosim + 6.0 * cosisq));
f523 = sinim * (4.92187512 * sini2 * (-2.0 - 4.0 * cosim +
10.0 * cosisq) + 6.56250012 * (1.0 + 2.0 * cosim - 3.0 * cosisq));
f542 = 29.53125 * sinim * (2.0 - 8.0 * cosim + cosisq *
(-12.0 + 8.0 * cosim + 10.0 * cosisq));
f543 = 29.53125 * sinim * (-2.0 - 8.0 * cosim + cosisq *
(12.0 + 8.0 * cosim - 10.0 * cosisq));
xno2 = nm * nm;
ainv2 = aonv * aonv;
temp1 = 3.0 * xno2 * ainv2;
temp = temp1 * root22;
d2201 = temp * f220 * g201;
d2211 = temp * f221 * g211;
temp1 = temp1 * aonv;
temp = temp1 * root32;
d3210 = temp * f321 * g310;
d3222 = temp * f322 * g322;
temp1 = temp1 * aonv;
temp = 2.0 * temp1 * root44;
d4410 = temp * f441 * g410;
d4422 = temp * f442 * g422;
temp1 = temp1 * aonv;
temp = temp1 * root52;
d5220 = temp * f522 * g520;
d5232 = temp * f523 * g532;
temp = 2.0 * temp1 * root54;
d5421 = temp * f542 * g521;
d5433 = temp * f543 * g533;
xlamo = fmod(mo + nodeo + nodeo - theta - theta, twopi);
xfact = mdot + dmdt + 2.0 * (nodedot + dnodt - rptim) - no;
em = emo;
emsq = emsqo;
}
/* ---------------- synchronous resonance terms -------------- */
if (irez == 1)
{
g200 = 1.0 + emsq * (-2.5 + 0.8125 * emsq);
g310 = 1.0 + 2.0 * emsq;
g300 = 1.0 + emsq * (-6.0 + 6.60937 * emsq);
f220 = 0.75 * (1.0 + cosim) * (1.0 + cosim);
f311 = 0.9375 * sinim * sinim * (1.0 + 3.0 * cosim) - 0.75 * (1.0 + cosim);
f330 = 1.0 + cosim;
f330 = 1.875 * f330 * f330 * f330;
del1 = 3.0 * nm * nm * aonv * aonv;
del2 = 2.0 * del1 * f220 * g200 * q22;
del3 = 3.0 * del1 * f330 * g300 * q33 * aonv;
del1 = del1 * f311 * g310 * q31 * aonv;
xlamo = fmod(mo + nodeo + argpo - theta, twopi);
xfact = mdot + xpidot - rptim + dmdt + domdt + dnodt - no;
}
/* ------------ for sgp4, initialize the integrator ---------- */
xli = xlamo;
xni = no;
atime = 0.0;
nm = no + dndt;
}
//#include "debug3.cpp"
} // dsinit
/*-----------------------------------------------------------------------------
*
* procedure dspace
*
* this procedure provides deep space contributions to mean elements for
* perturbing third body. these effects have been averaged over one
* revolution of the sun and moon. for earth resonance effects, the
* effects have been averaged over no revolutions of the satellite.
* (mean motion)
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -
* dedt -
* del1, del2, del3 -
* didt -
* dmdt -
* dnodt -
* domdt -
* irez - flag for resonance 0-none, 1-one day, 2-half day
* argpo - argument of perigee
* argpdot - argument of perigee dot (rate)
* t - time
* tc -
* gsto - gst
* xfact -
* xlamo -
* no - mean motion
* atime -
* em - eccentricity
* ft -
* argpm - argument of perigee
* inclm - inclination
* xli -
* mm - mean anomaly
* xni - mean motion
* nodem - right ascension of ascending node
*
* outputs :
* atime -
* em - eccentricity
* argpm - argument of perigee
* inclm - inclination
* xli -
* mm - mean anomaly
* xni -
* nodem - right ascension of ascending node
* dndt -
* nm - mean motion
*
* locals :
* delt -
* ft -
* theta -
* x2li -
* x2omi -
* xl -
* xldot -
* xnddt -
* xndt -
* xomi -
*
* coupling :
* none -
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
static void dspace
(
int irez,
double d2201, double d2211, double d3210, double d3222, double d4410,
double d4422, double d5220, double d5232, double d5421, double d5433,
double dedt, double del1, double del2, double del3, double didt,
double dmdt, double dnodt, double domdt, double argpo, double argpdot,
double t, double tc, double gsto, double xfact, double xlamo,
double no,
double& atime, double& em, double& argpm, double& inclm, double& xli,
double& mm, double& xni, double& nodem, double& dndt, double& nm
)
{
const double twopi = 2.0 * pi;
int iretn, iret;
double delt, ft, theta, x2li, x2omi, xl, xldot, xnddt, xndt, xomi, g22, g32,
g44, g52, g54, fasx2, fasx4, fasx6, rptim, step2, stepn, stepp;
fasx2 = 0.13130908;
fasx4 = 2.8843198;
fasx6 = 0.37448087;
g22 = 5.7686396;
g32 = 0.95240898;
g44 = 1.8014998;
g52 = 1.0508330;
g54 = 4.4108898;
rptim = 4.37526908801129966e-3; // this equates to 7.29211514668855e-5 rad/sec
stepp = 720.0;
stepn = -720.0;
step2 = 259200.0;
/* ----------- calculate deep space resonance effects ----------- */
dndt = 0.0;
theta = fmod(gsto + tc * rptim, twopi);
em = em + dedt * t;
inclm = inclm + didt * t;
argpm = argpm + domdt * t;
nodem = nodem + dnodt * t;
mm = mm + dmdt * t;
// sgp4fix for negative inclinations
// the following if statement should be commented out
// if (inclm < 0.0)
// {
// inclm = -inclm;
// argpm = argpm - pi;
// nodem = nodem + pi;
// }
/* - update resonances : numerical (euler-maclaurin) integration - */
/* ------------------------- epoch restart ---------------------- */
// sgp4fix for propagator problems
// the following integration works for negative time steps and periods
// the specific changes are unknown because the original code was so convoluted
// sgp4fix take out atime = 0.0 and fix for faster operation
ft = 0.0;
if (irez != 0)
{
// sgp4fix streamline check
if ((atime == 0.0) || (t * atime <= 0.0) || (fabs(t) < fabs(atime)))
{
atime = 0.0;
xni = no;
xli = xlamo;
}
// sgp4fix move check outside loop
if (t > 0.0)
delt = stepp;
else
delt = stepn;
iretn = 381; // added for do loop
iret = 0; // added for loop
while (iretn == 381)
{
/* ------------------- dot terms calculated ------------- */
/* ----------- near - synchronous resonance terms ------- */
if (irez != 2)
{
xndt = del1 * sin(xli - fasx2) + del2 * sin(2.0 * (xli - fasx4)) +
del3 * sin(3.0 * (xli - fasx6));
xldot = xni + xfact;
xnddt = del1 * cos(xli - fasx2) +
2.0 * del2 * cos(2.0 * (xli - fasx4)) +
3.0 * del3 * cos(3.0 * (xli - fasx6));
xnddt = xnddt * xldot;
}
else
{
/* --------- near - half-day resonance terms -------- */
xomi = argpo + argpdot * atime;
x2omi = xomi + xomi;
x2li = xli + xli;
xndt = d2201 * sin(x2omi + xli - g22) + d2211 * sin(xli - g22) +
d3210 * sin(xomi + xli - g32) + d3222 * sin(-xomi + xli - g32) +
d4410 * sin(x2omi + x2li - g44) + d4422 * sin(x2li - g44) +
d5220 * sin(xomi + xli - g52) + d5232 * sin(-xomi + xli - g52) +
d5421 * sin(xomi + x2li - g54) + d5433 * sin(-xomi + x2li - g54);
xldot = xni + xfact;
xnddt = d2201 * cos(x2omi + xli - g22) + d2211 * cos(xli - g22) +
d3210 * cos(xomi + xli - g32) + d3222 * cos(-xomi + xli - g32) +
d5220 * cos(xomi + xli - g52) + d5232 * cos(-xomi + xli - g52) +
2.0 * (d4410 * cos(x2omi + x2li - g44) +
d4422 * cos(x2li - g44) + d5421 * cos(xomi + x2li - g54) +
d5433 * cos(-xomi + x2li - g54));
xnddt = xnddt * xldot;
}
/* ----------------------- integrator ------------------- */
// sgp4fix move end checks to end of routine
if (fabs(t - atime) >= stepp)
{
iret = 0;
iretn = 381;
}
else // exit here
{
ft = t - atime;
iretn = 0;
}
if (iretn == 381)
{
xli = xli + xldot * delt + xndt * step2;
xni = xni + xndt * delt + xnddt * step2;
atime = atime + delt;
}
} // while iretn = 381
nm = xni + xndt * ft + xnddt * ft * ft * 0.5;
xl = xli + xldot * ft + xndt * ft * ft * 0.5;
if (irez != 1)
{
mm = xl - 2.0 * nodem + 2.0 * theta;
dndt = nm - no;
}
else
{
mm = xl - nodem - argpm + theta;
dndt = nm - no;
}
nm = no + dndt;
}
//#include "debug4.cpp"
} // dsspace
/*-----------------------------------------------------------------------------
*
* procedure initl
*
* this procedure initializes the spg4 propagator. all the initialization is
* consolidated here instead of having multiple loops inside other routines.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* satn - satellite number - not needed, placed in satrec
* xke - reciprocal of tumin
* j2 - j2 zonal harmonic
* ecco - eccentricity 0.0 - 1.0
* epoch - epoch time in days from jan 0, 1950. 0 hr
* inclo - inclination of satellite
* no - mean motion of satellite
*
* outputs :
* ainv - 1.0 / a
* ao - semi major axis
* con41 -
* con42 - 1.0 - 5.0 cos(i)
* cosio - cosine of inclination
* cosio2 - cosio squared
* eccsq - eccentricity squared
* method - flag for deep space 'd', 'n'
* omeosq - 1.0 - ecco * ecco
* posq - semi-parameter squared
* rp - radius of perigee
* rteosq - square root of (1.0 - ecco*ecco)
* sinio - sine of inclination
* gsto - gst at time of observation rad
* no - mean motion of satellite
*
* locals :
* ak -
* d1 -
* del -
* adel -
* po -
*
* coupling :
* getgravconst- no longer used
* gstime - find greenwich sidereal time from the julian date
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
static void initl
(
// sgp4fix satn not needed. include in satrec in case needed later
// int satn,
// sgp4fix just pass in xke and j2
// gravconsttype whichconst,
double xke, double j2,
double ecco, double epoch, double inclo, double no_kozai, char opsmode,
char& method, double& ainv, double& ao, double& con41, double& con42, double& cosio,
double& cosio2, double& eccsq, double& omeosq, double& posq,
double& rp, double& rteosq, double& sinio, double& gsto, double& no_unkozai
)
{
/* --------------------- local variables ------------------------ */
double ak, d1, del, adel, po, x2o3;
// sgp4fix use old way of finding gst
double ds70;
double ts70, tfrac, c1, thgr70, fk5r, c1p2p;
const double twopi = 2.0 * pi;
/* ----------------------- earth constants ---------------------- */
// sgp4fix identify constants and allow alternate values
// only xke and j2 are used here so pass them in directly
// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
x2o3 = 2.0 / 3.0;
/* ------------- calculate auxillary epoch quantities ---------- */
eccsq = ecco * ecco;
omeosq = 1.0 - eccsq;
rteosq = sqrt(omeosq);
cosio = cos(inclo);
cosio2 = cosio * cosio;
/* ------------------ un-kozai the mean motion ----------------- */
ak = pow(xke / no_kozai, x2o3);
d1 = 0.75 * j2 * (3.0 * cosio2 - 1.0) / (rteosq * omeosq);
del = d1 / (ak * ak);
adel = ak * (1.0 - del * del - del *
(1.0 / 3.0 + 134.0 * del * del / 81.0));
del = d1 / (adel * adel);
no_unkozai = no_kozai / (1.0 + del);
ao = pow(xke / (no_unkozai), x2o3);
sinio = sin(inclo);
po = ao * omeosq;
con42 = 1.0 - 5.0 * cosio2;
con41 = -con42 - cosio2 - cosio2;
ainv = 1.0 / ao;
posq = po * po;
rp = ao * (1.0 - ecco);
method = 'n';
// sgp4fix modern approach to finding sidereal time
// if (opsmode == 'a')
// {
// sgp4fix use old way of finding gst
// count integer number of days from 0 jan 1970
ts70 = epoch - 7305.0;
ds70 = floor(ts70 + 1.0e-8);
tfrac = ts70 - ds70;
// find greenwich location at epoch
c1 = 1.72027916940703639e-2;
thgr70 = 1.7321343856509374;
fk5r = 5.07551419432269442e-15;
c1p2p = c1 + twopi;
double gsto1 = fmod(thgr70 + c1*ds70 + c1p2p*tfrac + ts70*ts70*fk5r, twopi);
if (gsto1 < 0.0)
gsto1 = gsto1 + twopi;
// }
// else
gsto = gstime_SGP4(epoch + 2433281.5);
//#include "debug5.cpp"
} // initl
/*-----------------------------------------------------------------------------
*
* procedure sgp4init
*
* this procedure initializes variables for sgp4.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* opsmode - mode of operation afspc or improved 'a', 'i'
* whichconst - which set of constants to use 72, 84
* satn - satellite number
* bstar - sgp4 type drag coefficient kg/m2er
* ecco - eccentricity
* epoch - epoch time in days from jan 0, 1950. 0 hr
* argpo - argument of perigee (output if ds)
* inclo - inclination
* mo - mean anomaly (output if ds)
* no - mean motion
* nodeo - right ascension of ascending node
*
* outputs :
* satrec - common values for subsequent calls
* return code - non-zero on error.
* 1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
* 2 - mean motion less than 0.0
* 3 - pert elements, ecc < 0.0 or ecc > 1.0
* 4 - semi-latus rectum < 0.0
* 5 - epoch elements are sub-orbital
* 6 - satellite has decayed
*
* locals :
* cnodm , snodm , cosim , sinim , cosomm , sinomm
* cc1sq , cc2 , cc3
* coef , coef1
* cosio4 -
* day -
* dndt -
* em - eccentricity
* emsq - eccentricity squared
* eeta -
* etasq -
* gam -
* argpm - argument of perigee
* nodem -
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* perige - perigee
* pinvsq -
* psisq -
* qzms24 -
* rtemsq -
* s1, s2, s3, s4, s5, s6, s7 -
* sfour -
* ss1, ss2, ss3, ss4, ss5, ss6, ss7 -
* sz1, sz2, sz3
* sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33 -
* tc -
* temp -
* temp1, temp2, temp3 -
* tsi -
* xpidot -
* xhdot1 -
* z1, z2, z3 -
* z11, z12, z13, z21, z22, z23, z31, z32, z33 -
*
* coupling :
* getgravconst-
* initl -
* dscom -
* dpper -
* dsinit -
* sgp4 -
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
bool sgp4init
(
gravconsttype whichconst, char opsmode, const char satn[5], const double epoch,
const double xbstar, const double xndot, const double xnddot, const double xecco, const double xargpo,
const double xinclo, const double xmo, const double xno_kozai,
const double xnodeo, elsetrec& satrec
)
{
/* --------------------- local variables ------------------------ */
double ao, ainv, con42, cosio, sinio, cosio2, eccsq,
omeosq, posq, rp, rteosq,
cnodm, snodm, cosim, sinim, cosomm, sinomm, cc1sq,
cc2, cc3, coef, coef1, cosio4, day, dndt,
em, emsq, eeta, etasq, gam, argpm, nodem,
inclm, mm, nm, perige, pinvsq, psisq, qzms24,
rtemsq, s1, s2, s3, s4, s5, s6,
s7, sfour, ss1, ss2, ss3, ss4, ss5,
ss6, ss7, sz1, sz2, sz3, sz11, sz12,
sz13, sz21, sz22, sz23, sz31, sz32, sz33,
tc, temp, temp1, temp2, temp3, tsi, xpidot,
xhdot1, z1, z2, z3, z11, z12, z13,
z21, z22, z23, z31, z32, z33,
qzms2t, ss, x2o3, r[3], v[3],
delmotemp, qzms2ttemp, qzms24temp;
/* ------------------------ initialization --------------------- */
// sgp4fix divisor for divide by zero check on inclination
// the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
// 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency
const double temp4 = 1.5e-12;
/* ----------- set all near earth variables to zero ------------ */
satrec.isimp = 0; satrec.method = 'n'; satrec.aycof = 0.0;
satrec.con41 = 0.0; satrec.cc1 = 0.0; satrec.cc4 = 0.0;
satrec.cc5 = 0.0; satrec.d2 = 0.0; satrec.d3 = 0.0;
satrec.d4 = 0.0; satrec.delmo = 0.0; satrec.eta = 0.0;
satrec.argpdot = 0.0; satrec.omgcof = 0.0; satrec.sinmao = 0.0;
satrec.t = 0.0; satrec.t2cof = 0.0; satrec.t3cof = 0.0;
satrec.t4cof = 0.0; satrec.t5cof = 0.0; satrec.x1mth2 = 0.0;
satrec.x7thm1 = 0.0; satrec.mdot = 0.0; satrec.nodedot = 0.0;
satrec.xlcof = 0.0; satrec.xmcof = 0.0; satrec.nodecf = 0.0;
/* ----------- set all deep space variables to zero ------------ */
satrec.irez = 0; satrec.d2201 = 0.0; satrec.d2211 = 0.0;
satrec.d3210 = 0.0; satrec.d3222 = 0.0; satrec.d4410 = 0.0;
satrec.d4422 = 0.0; satrec.d5220 = 0.0; satrec.d5232 = 0.0;
satrec.d5421 = 0.0; satrec.d5433 = 0.0; satrec.dedt = 0.0;
satrec.del1 = 0.0; satrec.del2 = 0.0; satrec.del3 = 0.0;
satrec.didt = 0.0; satrec.dmdt = 0.0; satrec.dnodt = 0.0;
satrec.domdt = 0.0; satrec.e3 = 0.0; satrec.ee2 = 0.0;
satrec.peo = 0.0; satrec.pgho = 0.0; satrec.pho = 0.0;
satrec.pinco = 0.0; satrec.plo = 0.0; satrec.se2 = 0.0;
satrec.se3 = 0.0; satrec.sgh2 = 0.0; satrec.sgh3 = 0.0;
satrec.sgh4 = 0.0; satrec.sh2 = 0.0; satrec.sh3 = 0.0;
satrec.si2 = 0.0; satrec.si3 = 0.0; satrec.sl2 = 0.0;
satrec.sl3 = 0.0; satrec.sl4 = 0.0; satrec.gsto = 0.0;
satrec.xfact = 0.0; satrec.xgh2 = 0.0; satrec.xgh3 = 0.0;
satrec.xgh4 = 0.0; satrec.xh2 = 0.0; satrec.xh3 = 0.0;
satrec.xi2 = 0.0; satrec.xi3 = 0.0; satrec.xl2 = 0.0;
satrec.xl3 = 0.0; satrec.xl4 = 0.0; satrec.xlamo = 0.0;
satrec.zmol = 0.0; satrec.zmos = 0.0; satrec.atime = 0.0;
satrec.xli = 0.0; satrec.xni = 0.0;
/* ------------------------ earth constants ----------------------- */
// sgp4fix identify constants and allow alternate values
// this is now the only call for the constants
getgravconst(whichconst, satrec.tumin, satrec.mus, satrec.radiusearthkm, satrec.xke,
satrec.j2, satrec.j3, satrec.j4, satrec.j3oj2);
//-------------------------------------------------------------------------
satrec.error = 0;
satrec.operationmode = opsmode;
// new alpha5 or 9-digit number
#ifdef _MSC_VER
strcpy_s(satrec.satnum, 6 * sizeof(char), satn);
#else
strcpy(satrec.satnum, satn);
#endif
// sgp4fix - note the following variables are also passed directly via satrec.
// it is possible to streamline the sgp4init call by deleting the "x"
// variables, but the user would need to set the satrec.* values first. we
// include the additional assignments in case twoline2rv is not used.
satrec.bstar = xbstar;
// sgp4fix allow additional parameters in the struct
satrec.ndot = xndot;
satrec.nddot = xnddot;
satrec.ecco = xecco;
satrec.argpo = xargpo;
satrec.inclo = xinclo;
satrec.mo = xmo;
// sgp4fix rename variables to clarify which mean motion is intended
satrec.no_kozai = xno_kozai;
satrec.nodeo = xnodeo;
// single averaged mean elements
satrec.am = satrec.em = satrec.im = satrec.Om = satrec.mm = satrec.nm = 0.0;
/* ------------------------ earth constants ----------------------- */
// sgp4fix identify constants and allow alternate values no longer needed
// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
ss = 78.0 / satrec.radiusearthkm + 1.0;
// sgp4fix use multiply for speed instead of pow
qzms2ttemp = (120.0 - 78.0) / satrec.radiusearthkm;
qzms2t = qzms2ttemp * qzms2ttemp * qzms2ttemp * qzms2ttemp;
x2o3 = 2.0 / 3.0;
satrec.init = 'y';
satrec.t = 0.0;
// sgp4fix remove satn as it is not needed in initl
initl
(satrec.xke, satrec.j2, satrec.ecco, epoch, satrec.inclo, satrec.no_kozai, satrec.operationmode,
satrec.method, ainv, ao, satrec.con41, con42, cosio, cosio2, eccsq, omeosq,
posq, rp, rteosq, sinio, satrec.gsto, satrec.no_unkozai);
satrec.a = pow(satrec.no_unkozai * satrec.tumin, (-2.0 / 3.0));
satrec.alta = satrec.a * (1.0 + satrec.ecco) - 1.0;
satrec.altp = satrec.a * (1.0 - satrec.ecco) - 1.0;
satrec.error = 0;
// sgp4fix remove this check as it is unnecessary
// the mrt check in sgp4 handles decaying satellite cases even if the starting
// condition is below the surface of te earth
// if (rp < 1.0)
// {
// printf("# *** satn%d epoch elts sub-orbital ***\n", satn);
// satrec.error = 5;
// }
if ((omeosq >= 0.0) || (satrec.no_unkozai >= 0.0))
{
satrec.isimp = 0;
if (rp < (220.0 / satrec.radiusearthkm + 1.0))
satrec.isimp = 1;
sfour = ss;
qzms24 = qzms2t;
perige = (rp - 1.0) * satrec.radiusearthkm;
/* - for perigees below 156 km, s and qoms2t are altered - */
if (perige < 156.0)
{
sfour = perige - 78.0;
if (perige < 98.0)
sfour = 20.0;
// sgp4fix use multiply for speed instead of pow
qzms24temp = (120.0 - sfour) / satrec.radiusearthkm;
qzms24 = qzms24temp * qzms24temp * qzms24temp * qzms24temp;
sfour = sfour / satrec.radiusearthkm + 1.0;
}
pinvsq = 1.0 / posq;
tsi = 1.0 / (ao - sfour);
satrec.eta = ao * satrec.ecco * tsi;
etasq = satrec.eta * satrec.eta;
eeta = satrec.ecco * satrec.eta;
psisq = fabs(1.0 - etasq);
coef = qzms24 * pow(tsi, 4.0);
coef1 = coef / pow(psisq, 3.5);
cc2 = coef1 * satrec.no_unkozai * (ao * (1.0 + 1.5 * etasq + eeta *
(4.0 + etasq)) + 0.375 * satrec.j2 * tsi / psisq * satrec.con41 *
(8.0 + 3.0 * etasq * (8.0 + etasq)));
satrec.cc1 = satrec.bstar * cc2;
cc3 = 0.0;
if (satrec.ecco > 1.0e-4)
cc3 = -2.0 * coef * tsi * satrec.j3oj2 * satrec.no_unkozai * sinio / satrec.ecco;
satrec.x1mth2 = 1.0 - cosio2;
satrec.cc4 = 2.0* satrec.no_unkozai * coef1 * ao * omeosq *
(satrec.eta * (2.0 + 0.5 * etasq) + satrec.ecco *
(0.5 + 2.0 * etasq) - satrec.j2 * tsi / (ao * psisq) *
(-3.0 * satrec.con41 * (1.0 - 2.0 * eeta + etasq *
(1.5 - 0.5 * eeta)) + 0.75 * satrec.x1mth2 *
(2.0 * etasq - eeta * (1.0 + etasq)) * cos(2.0 * satrec.argpo)));
satrec.cc5 = 2.0 * coef1 * ao * omeosq * (1.0 + 2.75 *
(etasq + eeta) + eeta * etasq);
cosio4 = cosio2 * cosio2;
temp1 = 1.5 * satrec.j2 * pinvsq * satrec.no_unkozai;
temp2 = 0.5 * temp1 * satrec.j2 * pinvsq;
temp3 = -0.46875 * satrec.j4 * pinvsq * pinvsq * satrec.no_unkozai;
satrec.mdot = satrec.no_unkozai + 0.5 * temp1 * rteosq * satrec.con41 + 0.0625 *
temp2 * rteosq * (13.0 - 78.0 * cosio2 + 137.0 * cosio4);
satrec.argpdot = -0.5 * temp1 * con42 + 0.0625 * temp2 *
(7.0 - 114.0 * cosio2 + 395.0 * cosio4) +
temp3 * (3.0 - 36.0 * cosio2 + 49.0 * cosio4);
xhdot1 = -temp1 * cosio;
satrec.nodedot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * cosio2) +
2.0 * temp3 * (3.0 - 7.0 * cosio2)) * cosio;
xpidot = satrec.argpdot + satrec.nodedot;
satrec.omgcof = satrec.bstar * cc3 * cos(satrec.argpo);
satrec.xmcof = 0.0;
if (satrec.ecco > 1.0e-4)
satrec.xmcof = -x2o3 * coef * satrec.bstar / eeta;
satrec.nodecf = 3.5 * omeosq * xhdot1 * satrec.cc1;
satrec.t2cof = 1.5 * satrec.cc1;
// sgp4fix for divide by zero with xinco = 180 deg
if (fabs(cosio + 1.0) > 1.5e-12)
satrec.xlcof = -0.25 * satrec.j3oj2 * sinio * (3.0 + 5.0 * cosio) / (1.0 + cosio);
else
satrec.xlcof = -0.25 * satrec.j3oj2 * sinio * (3.0 + 5.0 * cosio) / temp4;
satrec.aycof = -0.5 * satrec.j3oj2 * sinio;
// sgp4fix use multiply for speed instead of pow
delmotemp = 1.0 + satrec.eta * cos(satrec.mo);
satrec.delmo = delmotemp * delmotemp * delmotemp;
satrec.sinmao = sin(satrec.mo);
satrec.x7thm1 = 7.0 * cosio2 - 1.0;
/* --------------- deep space initialization ------------- */
if ((2 * pi / satrec.no_unkozai) >= 225.0)
{
satrec.method = 'd';
satrec.isimp = 1;
tc = 0.0;
inclm = satrec.inclo;
dscom
(
epoch, satrec.ecco, satrec.argpo, tc, satrec.inclo, satrec.nodeo,
satrec.no_unkozai, snodm, cnodm, sinim, cosim, sinomm, cosomm,
day, satrec.e3, satrec.ee2, em, emsq, gam,
satrec.peo, satrec.pgho, satrec.pho, satrec.pinco,
satrec.plo, rtemsq, satrec.se2, satrec.se3,
satrec.sgh2, satrec.sgh3, satrec.sgh4,
satrec.sh2, satrec.sh3, satrec.si2, satrec.si3,
satrec.sl2, satrec.sl3, satrec.sl4, s1, s2, s3, s4, s5,
s6, s7, ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3,
sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33,
satrec.xgh2, satrec.xgh3, satrec.xgh4, satrec.xh2,
satrec.xh3, satrec.xi2, satrec.xi3, satrec.xl2,
satrec.xl3, satrec.xl4, nm, z1, z2, z3, z11,
z12, z13, z21, z22, z23, z31, z32, z33,
satrec.zmol, satrec.zmos
);
dpper
(
satrec.e3, satrec.ee2, satrec.peo, satrec.pgho,
satrec.pho, satrec.pinco, satrec.plo, satrec.se2,
satrec.se3, satrec.sgh2, satrec.sgh3, satrec.sgh4,
satrec.sh2, satrec.sh3, satrec.si2, satrec.si3,
satrec.sl2, satrec.sl3, satrec.sl4, satrec.t,
satrec.xgh2, satrec.xgh3, satrec.xgh4, satrec.xh2,
satrec.xh3, satrec.xi2, satrec.xi3, satrec.xl2,
satrec.xl3, satrec.xl4, satrec.zmol, satrec.zmos, inclm, satrec.init,
satrec.ecco, satrec.inclo, satrec.nodeo, satrec.argpo, satrec.mo,
satrec.operationmode
);
argpm = 0.0;
nodem = 0.0;
mm = 0.0;
dsinit
(
satrec.xke,
cosim, emsq, satrec.argpo, s1, s2, s3, s4, s5, sinim, ss1, ss2, ss3, ss4,
ss5, sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33, satrec.t, tc,
satrec.gsto, satrec.mo, satrec.mdot, satrec.no_unkozai, satrec.nodeo,
satrec.nodedot, xpidot, z1, z3, z11, z13, z21, z23, z31, z33,
satrec.ecco, eccsq, em, argpm, inclm, mm, nm, nodem,
satrec.irez, satrec.atime,
satrec.d2201, satrec.d2211, satrec.d3210, satrec.d3222,
satrec.d4410, satrec.d4422, satrec.d5220, satrec.d5232,
satrec.d5421, satrec.d5433, satrec.dedt, satrec.didt,
satrec.dmdt, dndt, satrec.dnodt, satrec.domdt,
satrec.del1, satrec.del2, satrec.del3, satrec.xfact,
satrec.xlamo, satrec.xli, satrec.xni
);
}
/* ----------- set variables if not deep space ----------- */
if (satrec.isimp != 1)
{
cc1sq = satrec.cc1 * satrec.cc1;
satrec.d2 = 4.0 * ao * tsi * cc1sq;
temp = satrec.d2 * tsi * satrec.cc1 / 3.0;
satrec.d3 = (17.0 * ao + sfour) * temp;
satrec.d4 = 0.5 * temp * ao * tsi * (221.0 * ao + 31.0 * sfour) *
satrec.cc1;
satrec.t3cof = satrec.d2 + 2.0 * cc1sq;
satrec.t4cof = 0.25 * (3.0 * satrec.d3 + satrec.cc1 *
(12.0 * satrec.d2 + 10.0 * cc1sq));
satrec.t5cof = 0.2 * (3.0 * satrec.d4 +
12.0 * satrec.cc1 * satrec.d3 +
6.0 * satrec.d2 * satrec.d2 +
15.0 * cc1sq * (2.0 * satrec.d2 + cc1sq));
}
} // if omeosq = 0 ...
/* finally propogate to zero epoch to initialize all others. */
// sgp4fix take out check to let satellites process until they are actually below earth surface
// if(satrec.error == 0)
sgp4(satrec, 0.0, r, v);
satrec.init = 'n';
//#include "debug6.cpp"
//sgp4fix return boolean. satrec.error contains any error codes
return true;
} // sgp4init
/*-----------------------------------------------------------------------------
*
* procedure sgp4
*
* this procedure is the sgp4 prediction model from space command. this is an
* updated and combined version of sgp4 and sdp4, which were originally
* published separately in spacetrack report #3. this version follows the
* methodology from the aiaa paper (2006) describing the history and
* development of the code.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* satrec - initialised structure from sgp4init() call.
* tsince - time since epoch (minutes)
*
* outputs :
* r - position vector km
* v - velocity km/sec
* return code - non-zero on error.
* 1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
* 2 - mean motion less than 0.0
* 3 - pert elements, ecc < 0.0 or ecc > 1.0
* 4 - semi-latus rectum < 0.0
* 5 - epoch elements are sub-orbital
* 6 - satellite has decayed
*
* locals :
* am -
* axnl, aynl -
* betal -
* cosim , sinim , cosomm , sinomm , cnod , snod , cos2u ,
* sin2u , coseo1 , sineo1 , cosi , sini , cosip , sinip ,
* cosisq , cossu , sinsu , cosu , sinu
* delm -
* delomg -
* dndt -
* eccm -
* emsq -
* ecose -
* el2 -
* eo1 -
* eccp -
* esine -
* argpm -
* argpp -
* omgadf -c
* pl -
* r -
* rtemsq -
* rdotl -
* rl -
* rvdot -
* rvdotl -
* su -
* t2 , t3 , t4 , tc
* tem5, temp , temp1 , temp2 , tempa , tempe , templ
* u , ux , uy , uz , vx , vy , vz
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* nodem - right asc of ascending node
* xinc -
* xincp -
* xl -
* xlm -
* mp -
* xmdf -
* xmx -
* xmy -
* nodedf -
* xnode -
* nodep -
* np -
*
* coupling :
* getgravconst- no longer used. Variables are conatined within satrec
* dpper
* dpspace
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
bool sgp4
(
elsetrec& satrec, double tsince,
double r[3], double v[3]
)
{
double am, axnl, aynl, betal, cosim, cnod,
cos2u, coseo1, cosi, cosip, cosisq, cossu, cosu,
delm, delomg, em, emsq, ecose, el2, eo1,
ep, esine, argpm, argpp, argpdf, pl, mrt = 0.0,
mvt, rdotl, rl, rvdot, rvdotl, sinim,
sin2u, sineo1, sini, sinip, sinsu, sinu,
snod, su, t2, t3, t4, tem5, temp,
temp1, temp2, tempa, tempe, templ, u, ux,
uy, uz, vx, vy, vz, inclm, mm,
nm, nodem, xinc, xincp, xl, xlm, mp,
xmdf, xmx, xmy, nodedf, xnode, nodep, tc, dndt,
twopi, x2o3, vkmpersec, delmtemp;
int ktr;
/* ------------------ set mathematical constants --------------- */
// sgp4fix divisor for divide by zero check on inclination
// the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
// 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency
const double temp4 = 1.5e-12;
twopi = 2.0 * pi;
x2o3 = 2.0 / 3.0;
// sgp4fix identify constants and allow alternate values
// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
vkmpersec = satrec.radiusearthkm * satrec.xke / 60.0;
/* --------------------- clear sgp4 error flag ----------------- */
satrec.t = tsince;
satrec.error = 0;
/* ------- update for secular gravity and atmospheric drag ----- */
xmdf = satrec.mo + satrec.mdot * satrec.t;
argpdf = satrec.argpo + satrec.argpdot * satrec.t;
nodedf = satrec.nodeo + satrec.nodedot * satrec.t;
argpm = argpdf;
mm = xmdf;
t2 = satrec.t * satrec.t;
nodem = nodedf + satrec.nodecf * t2;
tempa = 1.0 - satrec.cc1 * satrec.t;
tempe = satrec.bstar * satrec.cc4 * satrec.t;
templ = satrec.t2cof * t2;
if (satrec.isimp != 1)
{
delomg = satrec.omgcof * satrec.t;
// sgp4fix use mutliply for speed instead of pow
delmtemp = 1.0 + satrec.eta * cos(xmdf);
delm = satrec.xmcof *
(delmtemp * delmtemp * delmtemp -
satrec.delmo);
temp = delomg + delm;
mm = xmdf + temp;
argpm = argpdf - temp;
t3 = t2 * satrec.t;
t4 = t3 * satrec.t;
tempa = tempa - satrec.d2 * t2 - satrec.d3 * t3 -
satrec.d4 * t4;
tempe = tempe + satrec.bstar * satrec.cc5 * (sin(mm) -
satrec.sinmao);
templ = templ + satrec.t3cof * t3 + t4 * (satrec.t4cof +
satrec.t * satrec.t5cof);
}
nm = satrec.no_unkozai;
em = satrec.ecco;
inclm = satrec.inclo;
if (satrec.method == 'd')
{
tc = satrec.t;
dspace
(
satrec.irez,
satrec.d2201, satrec.d2211, satrec.d3210,
satrec.d3222, satrec.d4410, satrec.d4422,
satrec.d5220, satrec.d5232, satrec.d5421,
satrec.d5433, satrec.dedt, satrec.del1,
satrec.del2, satrec.del3, satrec.didt,
satrec.dmdt, satrec.dnodt, satrec.domdt,
satrec.argpo, satrec.argpdot, satrec.t, tc,
satrec.gsto, satrec.xfact, satrec.xlamo,
satrec.no_unkozai, satrec.atime,
em, argpm, inclm, satrec.xli, mm, satrec.xni,
nodem, dndt, nm
);
} // if method = d
if (nm <= 0.0)
{
// printf("# error nm %f\n", nm);
satrec.error = 2;
// sgp4fix add return
return false;
}
am = pow((satrec.xke / nm), x2o3) * tempa * tempa;
nm = satrec.xke / pow(am, 1.5);
em = em - tempe;
// fix tolerance for error recognition
// sgp4fix am is fixed from the previous nm check
if ((em >= 1.0) || (em < -0.001)/* || (am < 0.95)*/)
{
// printf("# error em %f\n", em);
satrec.error = 1;
// sgp4fix to return if there is an error in eccentricity
return false;
}
// sgp4fix fix tolerance to avoid a divide by zero
if (em < 1.0e-6)
em = 1.0e-6;
mm = mm + satrec.no_unkozai * templ;
xlm = mm + argpm + nodem;
emsq = em * em;
temp = 1.0 - emsq;
nodem = fmod(nodem, twopi);
argpm = fmod(argpm, twopi);
xlm = fmod(xlm, twopi);
mm = fmod(xlm - argpm - nodem, twopi);
// sgp4fix recover singly averaged mean elements
satrec.am = am;
satrec.em = em;
satrec.im = inclm;
satrec.Om = nodem;
satrec.om = argpm;
satrec.mm = mm;
satrec.nm = nm;
/* ----------------- compute extra mean quantities ------------- */
sinim = sin(inclm);
cosim = cos(inclm);
/* -------------------- add lunar-solar periodics -------------- */
ep = em;
xincp = inclm;
argpp = argpm;
nodep = nodem;
mp = mm;
sinip = sinim;
cosip = cosim;
if (satrec.method == 'd')
{
dpper
(
satrec.e3, satrec.ee2, satrec.peo,
satrec.pgho, satrec.pho, satrec.pinco,
satrec.plo, satrec.se2, satrec.se3,
satrec.sgh2, satrec.sgh3, satrec.sgh4,
satrec.sh2, satrec.sh3, satrec.si2,
satrec.si3, satrec.sl2, satrec.sl3,
satrec.sl4, satrec.t, satrec.xgh2,
satrec.xgh3, satrec.xgh4, satrec.xh2,
satrec.xh3, satrec.xi2, satrec.xi3,
satrec.xl2, satrec.xl3, satrec.xl4,
satrec.zmol, satrec.zmos, satrec.inclo,
'n', ep, xincp, nodep, argpp, mp, satrec.operationmode
);
if (xincp < 0.0)
{
xincp = -xincp;
nodep = nodep + pi;
argpp = argpp - pi;
}
if ((ep < 0.0) || (ep > 1.0))
{
// printf("# error ep %f\n", ep);
satrec.error = 3;
// sgp4fix add return
return false;
}
} // if method = d
/* -------------------- long period periodics ------------------ */
if (satrec.method == 'd')
{
sinip = sin(xincp);
cosip = cos(xincp);
satrec.aycof = -0.5*satrec.j3oj2*sinip;
// sgp4fix for divide by zero for xincp = 180 deg
if (fabs(cosip + 1.0) > 1.5e-12)
satrec.xlcof = -0.25 * satrec.j3oj2 * sinip * (3.0 + 5.0 * cosip) / (1.0 + cosip);
else
satrec.xlcof = -0.25 * satrec.j3oj2 * sinip * (3.0 + 5.0 * cosip) / temp4;
}
axnl = ep * cos(argpp);
temp = 1.0 / (am * (1.0 - ep * ep));
aynl = ep* sin(argpp) + temp * satrec.aycof;
xl = mp + argpp + nodep + temp * satrec.xlcof * axnl;
/* --------------------- solve kepler's equation --------------- */
u = fmod(xl - nodep, twopi);
eo1 = u;
tem5 = 9999.9;
ktr = 1;
// sgp4fix for kepler iteration
// the following iteration needs better limits on corrections
while ((fabs(tem5) >= 1.0e-12) && (ktr <= 10))
{
sineo1 = sin(eo1);
coseo1 = cos(eo1);
tem5 = 1.0 - coseo1 * axnl - sineo1 * aynl;
tem5 = (u - aynl * coseo1 + axnl * sineo1 - eo1) / tem5;
if (fabs(tem5) >= 0.95)
tem5 = tem5 > 0.0 ? 0.95 : -0.95;
eo1 = eo1 + tem5;
ktr = ktr + 1;
}
/* ------------- short period preliminary quantities ----------- */
ecose = axnl*coseo1 + aynl*sineo1;
esine = axnl*sineo1 - aynl*coseo1;
el2 = axnl*axnl + aynl*aynl;
pl = am*(1.0 - el2);
if (pl < 0.0)
{
// printf("# error pl %f\n", pl);
satrec.error = 4;
// sgp4fix add return
return false;
}
else
{
rl = am * (1.0 - ecose);
rdotl = sqrt(am) * esine / rl;
rvdotl = sqrt(pl) / rl;
betal = sqrt(1.0 - el2);
temp = esine / (1.0 + betal);
sinu = am / rl * (sineo1 - aynl - axnl * temp);
cosu = am / rl * (coseo1 - axnl + aynl * temp);
su = atan2(sinu, cosu);
sin2u = (cosu + cosu) * sinu;
cos2u = 1.0 - 2.0 * sinu * sinu;
temp = 1.0 / pl;
temp1 = 0.5 * satrec.j2 * temp;
temp2 = temp1 * temp;
/* -------------- update for short period periodics ------------ */
if (satrec.method == 'd')
{
cosisq = cosip * cosip;
satrec.con41 = 3.0*cosisq - 1.0;
satrec.x1mth2 = 1.0 - cosisq;
satrec.x7thm1 = 7.0*cosisq - 1.0;
}
mrt = rl * (1.0 - 1.5 * temp2 * betal * satrec.con41) +
0.5 * temp1 * satrec.x1mth2 * cos2u;
su = su - 0.25 * temp2 * satrec.x7thm1 * sin2u;
xnode = nodep + 1.5 * temp2 * cosip * sin2u;
xinc = xincp + 1.5 * temp2 * cosip * sinip * cos2u;
mvt = rdotl - nm * temp1 * satrec.x1mth2 * sin2u / satrec.xke;
rvdot = rvdotl + nm * temp1 * (satrec.x1mth2 * cos2u +
1.5 * satrec.con41) / satrec.xke;
/* --------------------- orientation vectors ------------------- */
sinsu = sin(su);
cossu = cos(su);
snod = sin(xnode);
cnod = cos(xnode);
sini = sin(xinc);
cosi = cos(xinc);
xmx = -snod * cosi;
xmy = cnod * cosi;
ux = xmx * sinsu + cnod * cossu;
uy = xmy * sinsu + snod * cossu;
uz = sini * sinsu;
vx = xmx * cossu - cnod * sinsu;
vy = xmy * cossu - snod * sinsu;
vz = sini * cossu;
/* --------- position and velocity (in km and km/sec) ---------- */
r[0] = (mrt * ux)* satrec.radiusearthkm;
r[1] = (mrt * uy)* satrec.radiusearthkm;
r[2] = (mrt * uz)* satrec.radiusearthkm;
v[0] = (mvt * ux + rvdot * vx) * vkmpersec;
v[1] = (mvt * uy + rvdot * vy) * vkmpersec;
v[2] = (mvt * uz + rvdot * vz) * vkmpersec;
} // if pl > 0
// sgp4fix for decaying satellites
if (mrt < 1.0)
{
// printf("# decay condition %11.6f \n",mrt);
satrec.error = 6;
return false;
}
//#include "debug7.cpp"
return true;
} // sgp4
/* -----------------------------------------------------------------------------
*
* function getgravconst
*
* this function gets constants for the propagator. note that mu is identified to
* facilitiate comparisons with newer models. the common useage is wgs72.
*
* author : david vallado 719-573-2600 21 jul 2006
*
* inputs :
* whichconst - which set of constants to use wgs72old, wgs72, wgs84
*
* outputs :
* tumin - minutes in one time unit
* mu - earth gravitational parameter
* radiusearthkm - radius of the earth in km
* xke - reciprocal of tumin
* j2, j3, j4 - un-normalized zonal harmonic values
* j3oj2 - j3 divided by j2
*
* locals :
*
* coupling :
* none
*
* references :
* norad spacetrack report #3
* vallado, crawford, hujsak, kelso 2006
--------------------------------------------------------------------------- */
void getgravconst
(
gravconsttype whichconst,
double& tumin,
double& mus,
double& radiusearthkm,
double& xke,
double& j2,
double& j3,
double& j4,
double& j3oj2
)
{
switch (whichconst)
{
// -- wgs-72 low precision str#3 constants --
case wgs72old:
mus = 398600.79964; // in km3 / s2
radiusearthkm = 6378.135; // km
xke = 0.0743669161; // reciprocal of tumin
tumin = 1.0 / xke;
j2 = 0.001082616;
j3 = -0.00000253881;
j4 = -0.00000165597;
j3oj2 = j3 / j2;
break;
// ------------ wgs-72 constants ------------
case wgs72:
mus = 398600.8; // in km3 / s2
radiusearthkm = 6378.135; // km
xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm / mus);
tumin = 1.0 / xke;
j2 = 0.001082616;
j3 = -0.00000253881;
j4 = -0.00000165597;
j3oj2 = j3 / j2;
break;
case wgs84:
// ------------ wgs-84 constants ------------
mus = 398600.5; // in km3 / s2
radiusearthkm = 6378.137; // km
xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm / mus);
tumin = 1.0 / xke;
j2 = 0.00108262998905;
j3 = -0.00000253215306;
j4 = -0.00000161098761;
j3oj2 = j3 / j2;
break;
default:
fprintf(stderr, "unknown gravity option (%d)\n", whichconst);
break;
}
} // getgravconst
// older sgp4io methods
/* -----------------------------------------------------------------------------
*
* function twoline2rv
*
* this function converts the two line element set character string data to
* variables and initializes the sgp4 variables. several intermediate varaibles
* and quantities are determined. note that the result is a structure so multiple
* satellites can be processed simaltaneously without having to reinitialize. the
* verification mode is an important option that permits quick checks of any
* changes to the underlying technical theory. this option works using a
* modified tle file in which the start, stop, and delta time values are
* included at the end of the second line of data. this only works with the
* verification mode. the catalog mode simply propagates from -1440 to 1440 min
* from epoch and is useful when performing entire catalog runs.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs :
* longstr1 - first line of the tle
* longstr2 - second line of the tle
* typerun - type of run verification 'v', catalog 'c',
* manual 'm'
* typeinput - type of manual input mfe 'm', epoch 'e', dayofyr 'd'
* opsmode - mode of operation afspc or improved 'a', 'i'
* whichconst - which set of constants to use 72, 84
*
* outputs :
* satrec - structure containing all the sgp4 satellite information
*
* coupling :
* getgravconst-
* days2mdhms - conversion of days to month, day, hour, minute, second
* jday - convert day month year hour minute second into julian date
* sgp4init - initialize the sgp4 variables
*
* references :
* norad spacetrack report #3
* vallado, crawford, hujsak, kelso 2006
--------------------------------------------------------------------------- */
void twoline2rv
(
char longstr1[130], char longstr2[130],
char typerun, char typeinput, char opsmode,
gravconsttype whichconst,
double& startmfe, double& stopmfe, double& deltamin,
elsetrec& satrec
)
{
const double deg2rad = pi / 180.0; // 0.0174532925199433
const double xpdotp = 1440.0 / (2.0 *pi); // 229.1831180523293
double sec;
double startsec, stopsec, startdayofyr, stopdayofyr, jdstart, jdstop, jdstartF, jdstopF;
int startyear, stopyear, startmon, stopmon, startday, stopday,
starthr, stophr, startmin, stopmin;
int cardnumb, j;
// sgp4fix include in satrec
// long revnum = 0, elnum = 0;
// char classification, intldesg[11];
int year = 0;
int mon, day, hr, minute, nexp, ibexp;
// sgp4fix no longer needed
// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
satrec.error = 0;
// set the implied decimal points since doing a formated read
// fixes for bad input data values (missing, ...)
for (j = 10; j <= 15; j++)
if (longstr1[j] == ' ')
longstr1[j] = '_';
if (longstr1[44] != ' ')
longstr1[43] = longstr1[44];
longstr1[44] = '.';
if (longstr1[7] == ' ')
longstr1[7] = 'U';
if (longstr1[9] == ' ')
longstr1[9] = '.';
for (j = 45; j <= 49; j++)
if (longstr1[j] == ' ')
longstr1[j] = '0';
if (longstr1[51] == ' ')
longstr1[51] = '0';
if (longstr1[53] != ' ')
longstr1[52] = longstr1[53];
longstr1[53] = '.';
longstr2[25] = '.';
for (j = 26; j <= 32; j++)
if (longstr2[j] == ' ')
longstr2[j] = '0';
if (longstr1[62] == ' ')
longstr1[62] = '0';
if (longstr1[68] == ' ')
longstr1[68] = '0';
#ifdef _MSC_VER // chk if compiling in MSVS c++
sscanf_s(longstr1, "%2d %5s %1c %10s %2d %12lf %11lf %7lf %2d %7lf %2d %2d %6ld ",
&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.classification, sizeof(char), &satrec.intldesg, 11 * sizeof(char), &satrec.epochyr,
&satrec.epochdays, &satrec.ndot, &satrec.nddot, &nexp, &satrec.bstar, &ibexp, &satrec.ephtype, &satrec.elnum);
#else
sscanf(longstr1, "%2d %5s %1c %10s %2d %12lf %11lf %7lf %2d %7lf %2d %2d %6ld ",
&cardnumb, &satrec.satnum, &satrec.classification, &satrec.intldesg, &satrec.epochyr,
&satrec.epochdays, &satrec.ndot, &satrec.nddot, &nexp, &satrec.bstar,
&ibexp, &satrec.ephtype, &satrec.elnum);
#endif
if (typerun == 'v') // run for specified times from the file
{
if (longstr2[52] == ' ')
{
#ifdef _MSC_VER
sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld %lf %lf %lf \n",
&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#else
sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld %lf %lf %lf \n",
&cardnumb, &satrec.satnum, &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#endif
}
else
{
#ifdef _MSC_VER
sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld %lf %lf %lf \n",
&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#else
sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld %lf %lf %lf \n",
&cardnumb, &satrec.satnum, &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#endif
}
}
else // simply run -1 day to +1 day or user input times
{
if (longstr2[52] == ' ')
{
#ifdef _MSC_VER
sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld \n",
&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum);
#else
sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld \n",
&cardnumb, &satrec.satnum, &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum);
#endif
}
else
{
#ifdef _MSC_VER
sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld \n",
&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum);
#else
sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld \n",
&cardnumb, &satrec.satnum, &satrec.inclo,
&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
&satrec.revnum);
#endif
}
}
// ---- find no, ndot, nddot ----
satrec.no_kozai = satrec.no_kozai / xpdotp; //* rad/min
satrec.nddot = satrec.nddot * pow(10.0, nexp);
satrec.bstar = satrec.bstar * pow(10.0, ibexp);
// ---- convert to sgp4 units ----
// satrec.a = pow( satrec.no_kozai*tumin , (-2.0/3.0) );
satrec.ndot = satrec.ndot / (xpdotp*1440.0); //* ? * minperday
satrec.nddot = satrec.nddot / (xpdotp*1440.0 * 1440);
// ---- find standard orbital elements ----
satrec.inclo = satrec.inclo * deg2rad;
satrec.nodeo = satrec.nodeo * deg2rad;
satrec.argpo = satrec.argpo * deg2rad;
satrec.mo = satrec.mo * deg2rad;
// sgp4fix not needed here
// satrec.alta = satrec.a*(1.0 + satrec.ecco) - 1.0;
// satrec.altp = satrec.a*(1.0 - satrec.ecco) - 1.0;
// ----------------------------------------------------------------
// find sgp4epoch time of element set
// remember that sgp4 uses units of days from 0 jan 1950 (sgp4epoch)
// and minutes from the epoch (time)
// ----------------------------------------------------------------
// ---------------- temp fix for years from 1957-2056 -------------------
// --------- correct fix will occur when year is 4-digit in tle ---------
if (satrec.epochyr < 57)
year = satrec.epochyr + 2000;
else
year = satrec.epochyr + 1900;
days2mdhms_SGP4(year, satrec.epochdays, mon, day, hr, minute, sec);
jday_SGP4(year, mon, day, hr, minute, sec, satrec.jdsatepoch, satrec.jdsatepochF);
// ---- input start stop times manually
if ((typerun != 'v') && (typerun != 'c'))
{
// ------------- enter start/stop ymd hms values --------------------
if (typeinput == 'e')
{
printf("input start prop year mon day hr min sec \n");
// make sure there is no space at the end of the format specifiers in scanf!
#ifdef _MSC_VER
scanf_s("%i %i %i %i %i %lf", &startyear, &startmon, &startday, &starthr, &startmin, &startsec);
#else
scanf("%i %i %i %i %i %lf", &startyear, &startmon, &startday, &starthr, &startmin, &startsec);
#endif
fflush(stdin);
jday_SGP4(startyear, startmon, startday, starthr, startmin, startsec, jdstart, jdstartF);
printf("input stop prop year mon day hr min sec \n");
#ifdef _MSC_VER
scanf_s("%i %i %i %i %i %lf", &stopyear, &stopmon, &stopday, &stophr, &stopmin, &stopsec);
#else
scanf("%i %i %i %i %i %lf", &stopyear, &stopmon, &stopday, &stophr, &stopmin, &stopsec);
#endif
fflush(stdin);
jday_SGP4(stopyear, stopmon, stopday, stophr, stopmin, stopsec, jdstop, jdstopF);
startmfe = (jdstart - satrec.jdsatepoch) * 1440.0 + (jdstartF - satrec.jdsatepochF) * 1440.0;
stopmfe = (jdstop - satrec.jdsatepoch) * 1440.0 + (jdstopF - satrec.jdsatepochF) * 1440.0;
printf("input time step in minutes \n");
#ifdef _MSC_VER
scanf_s("%lf", &deltamin);
#else
scanf("%lf", &deltamin);
#endif
}
// -------- enter start/stop year and days of year values -----------
if (typeinput == 'd')
{
printf("input start year dayofyr \n");
#ifdef _MSC_VER
scanf_s("%i %lf", &startyear, &startdayofyr);
#else
scanf("%i %lf", &startyear, &startdayofyr);
#endif
printf("input stop year dayofyr \n");
#ifdef _MSC_VER
scanf_s("%i %lf", &stopyear, &stopdayofyr);
#else
scanf("%i %lf", &stopyear, &stopdayofyr);
#endif
days2mdhms_SGP4(startyear, startdayofyr, mon, day, hr, minute, sec);
jday_SGP4(startyear, mon, day, hr, minute, sec, jdstart, jdstartF);
days2mdhms_SGP4(stopyear, stopdayofyr, mon, day, hr, minute, sec);
jday_SGP4(stopyear, mon, day, hr, minute, sec, jdstop, jdstopF);
startmfe = (jdstart - satrec.jdsatepoch) * 1440.0 + (jdstartF - satrec.jdsatepochF) * 1440.0;
stopmfe = (jdstop - satrec.jdsatepoch) * 1440.0 + (jdstopF - satrec.jdsatepochF) * 1440.0;
printf("input time step in minutes \n");
#ifdef _MSC_VER
scanf_s("%lf", &deltamin);
#else
scanf("%lf", &deltamin);
#endif
}
// ------------------ enter start/stop mfe values -------------------
if (typeinput == 'm')
{
#ifdef _MSC_VER
printf("input start min from epoch \n");
scanf_s("%lf", &startmfe);
printf("input stop min from epoch \n");
scanf_s("%lf", &stopmfe);
printf("input time step in minutes \n");
scanf_s("%lf", &deltamin);
#else
printf("input start min from epoch \n");
scanf("%lf", &startmfe);
printf("input stop min from epoch \n");
scanf("%lf", &stopmfe);
printf("input time step in minutes \n");
scanf("%lf", &deltamin);
#endif
}
}
// ------------ perform complete catalog evaluation, -+ 1 day -----------
if (typerun == 'c')
{
startmfe = -1440.0;
stopmfe = 1440.0;
deltamin = 10.0;
}
// ---------------- initialize the orbit at sgp4epoch -------------------
sgp4init(whichconst, opsmode, satrec.satnum, (satrec.jdsatepoch + satrec.jdsatepochF) - 2433281.5, satrec.bstar,
satrec.ndot, satrec.nddot, satrec.ecco, satrec.argpo, satrec.inclo, satrec.mo, satrec.no_kozai,
satrec.nodeo, satrec);
} // twoline2rv
// older sgp4ext methods
/* -----------------------------------------------------------------------------
*
* function gstime_SGP4
*
* this function finds the greenwich sidereal time.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* jdut1 - julian date in ut1 days from 4713 bc
*
* outputs :
* gstime - greenwich sidereal time 0 to 2pi rad
*
* locals :
* temp - temporary variable for doubles rad
* tut1 - julian centuries from the
* jan 1, 2000 12 h epoch (ut1)
*
* coupling :
* none
*
* references :
* vallado 2013, 187, eq 3-45
* --------------------------------------------------------------------------- */
double gstime_SGP4
(
double jdut1
)
{
const double twopi = 2.0 * pi;
const double deg2rad = pi / 180.0;
double temp, tut1;
tut1 = (jdut1 - 2451545.0) / 36525.0;
temp = -6.2e-6* tut1 * tut1 * tut1 + 0.093104 * tut1 * tut1 +
(876600.0 * 3600 + 8640184.812866) * tut1 + 67310.54841; // sec
temp = fmod(temp * deg2rad / 240.0, twopi); //360/86400 = 1/240, to deg, to rad
// ------------------------ check quadrants ---------------------
if (temp < 0.0)
temp += twopi;
return temp;
} // gstime
double sgn_SGP4
(
double x
)
{
if (x < 0.0)
{
return -1.0;
}
else
{
return 1.0;
}
} // sgn
/* -----------------------------------------------------------------------------
*
* function mag_SGP4
*
* this procedure finds the magnitude of a vector.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec - vector
*
* outputs :
* mag - answer
*
* locals :
* none.
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
double mag_SGP4
(
double x[3]
)
{
return sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
} // mag
/* -----------------------------------------------------------------------------
*
* procedure cross_SGP4
*
* this procedure crosses two vectors.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* outvec - vector result of a x b
*
* locals :
* none.
*
* coupling :
* mag magnitude of a vector
---------------------------------------------------------------------------- */
void cross_SGP4
(
double vec1[3], double vec2[3], double outvec[3]
)
{
outvec[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1];
outvec[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2];
outvec[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0];
} // end cross
/* -----------------------------------------------------------------------------
*
* function dot_SGP4
*
* this function finds the dot product of two vectors.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* dot - result
*
* locals :
* none.
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
double dot_SGP4
(
double x[3], double y[3]
)
{
return (x[0] * y[0] + x[1] * y[1] + x[2] * y[2]);
} // dot
/* -----------------------------------------------------------------------------
*
* procedure angle_SGP4
*
* this procedure calculates the angle between two vectors. the output is
* set to 999999.1 to indicate an undefined value. be sure to check for
* this at the output phase.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* theta - angle between the two vectors -pi to pi
*
* locals :
* temp - temporary real variable
*
* coupling :
* dot dot product of two vectors
* --------------------------------------------------------------------------- */
double angle_SGP4
(
double vec1[3],
double vec2[3]
)
{
double small, undefined, magv1, magv2, temp;
small = 0.00000001;
undefined = 999999.1;
magv1 = mag_SGP4(vec1);
magv2 = mag_SGP4(vec2);
if (magv1*magv2 > small*small)
{
temp = dot_SGP4(vec1, vec2) / (magv1*magv2);
if (fabs(temp) > 1.0)
temp = sgn_SGP4(temp) * 1.0;
return acos(temp);
}
else
return undefined;
} // angle
/* -----------------------------------------------------------------------------
*
* function asinh_SGP4
*
* this function evaluates the inverse hyperbolic sine function.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* xval - angle value any real
*
* outputs :
* arcsinh - result any real
*
* locals :
* none.
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
double asinh_SGP4
(
double xval
)
{
return log(xval + sqrt(xval*xval + 1.0));
} // asinh
/* -----------------------------------------------------------------------------
*
* function newtonnu_SGP4
*
* this function solves keplers equation when the true anomaly is known.
* the mean and eccentric, parabolic, or hyperbolic anomaly is also found.
* the parabolic limit at 168 is arbitrary. the hyperbolic anomaly is also
* limited. the hyperbolic sine is used because it's not double valued.
*
* author : david vallado 719-573-2600 27 may 2002
*
* revisions
* vallado - fix small 24 sep 2002
*
* inputs description range / units
* ecc - eccentricity 0.0 to
* nu - true anomaly -2pi to 2pi rad
*
* outputs :
* e0 - eccentric anomaly 0.0 to 2pi rad 153.02
* m - mean anomaly 0.0 to 2pi rad 151.7425
*
* locals :
* e1 - eccentric anomaly, next value rad
* sine - sine of e
* cose - cosine of e
* ktr - index
*
* coupling :
* asinh - arc hyperbolic sine
*
* references :
* vallado 2013, 77, alg 5
* --------------------------------------------------------------------------- */
void newtonnu_SGP4
(
double ecc, double nu,
double& e0, double& m
)
{
double small, sine, cose;
// --------------------- implementation ---------------------
e0 = 999999.9;
m = 999999.9;
small = 0.00000001;
// --------------------------- circular ------------------------
if (fabs(ecc) < small)
{
m = nu;
e0 = nu;
}
else
// ---------------------- elliptical -----------------------
if (ecc < 1.0 - small)
{
sine = (sqrt(1.0 - ecc*ecc) * sin(nu)) / (1.0 + ecc*cos(nu));
cose = (ecc + cos(nu)) / (1.0 + ecc*cos(nu));
e0 = atan2(sine, cose);
m = e0 - ecc*sin(e0);
}
else
// -------------------- hyperbolic --------------------
if (ecc > 1.0 + small)
{
if ((ecc > 1.0) && (fabs(nu) + 0.00001 < pi - acos(1.0 / ecc)))
{
sine = (sqrt(ecc*ecc - 1.0) * sin(nu)) / (1.0 + ecc*cos(nu));
e0 = asinh_SGP4(sine);
m = ecc*sinh(e0) - e0;
}
}
else
// ----------------- parabolic ---------------------
if (fabs(nu) < 168.0*pi / 180.0)
{
e0 = tan(nu*0.5);
m = e0 + (e0*e0*e0) / 3.0;
}
if (ecc < 1.0)
{
m = fmod(m, 2.0 *pi);
if (m < 0.0)
m = m + 2.0 *pi;
e0 = fmod(e0, 2.0 *pi);
}
} // newtonnu
/* -----------------------------------------------------------------------------
*
* function rv2coe_SGP4
*
* this function finds the classical orbital elements given the geocentric
* equatorial position and velocity vectors.
*
* author : david vallado 719-573-2600 21 jun 2002
*
* revisions
* vallado - fix special cases 5 sep 2002
* vallado - delete extra check in inclination code 16 oct 2002
* vallado - add constant file use 29 jun 2003
* vallado - add mu 2 apr 2007
*
* inputs description range / units
* r - ijk position vector km
* v - ijk velocity vector km / s
* mu - gravitational parameter km3 / s2
*
* outputs :
* p - semilatus rectum km
* a - semimajor axis km
* ecc - eccentricity
* incl - inclination 0.0 to pi rad
* omega - right ascension of ascending node 0.0 to 2pi rad
* argp - argument of perigee 0.0 to 2pi rad
* nu - true anomaly 0.0 to 2pi rad
* m - mean anomaly 0.0 to 2pi rad
* arglat - argument of latitude (ci) 0.0 to 2pi rad
* truelon - true longitude (ce) 0.0 to 2pi rad
* lonper - longitude of periapsis (ee) 0.0 to 2pi rad
*
* locals :
* hbar - angular momentum h vector km2 / s
* ebar - eccentricity e vector
* nbar - line of nodes n vector
* c1 - v**2 - u/r
* rdotv - r dot v
* hk - hk unit vector
* sme - specfic mechanical energy km2 / s2
* i - index
* e - eccentric, parabolic,
* hyperbolic anomaly rad
* temp - temporary variable
* typeorbit - type of orbit ee, ei, ce, ci
*
* coupling :
* mag - magnitude of a vector
* cross - cross product of two vectors
* angle - find the angle between two vectors
* newtonnu - find the mean anomaly
*
* references :
* vallado 2013, 113, alg 9, ex 2-5
* --------------------------------------------------------------------------- */
void rv2coe_SGP4
(
double r[3], double v[3], double mus,
double& p, double& a, double& ecc, double& incl, double& omega, double& argp,
double& nu, double& m, double& arglat, double& truelon, double& lonper
)
{
double undefined, small, hbar[3], nbar[3], magr, magv, magn, ebar[3], sme,
rdotv, infinite, temp, c1, hk, twopi, magh, halfpi, e;
int i;
// switch this to an integer msvs seems to have probelms with this and strncpy_s
//char typeorbit[2];
int typeorbit;
// here
// typeorbit = 1 = 'ei'
// typeorbit = 2 = 'ce'
// typeorbit = 3 = 'ci'
// typeorbit = 4 = 'ee'
twopi = 2.0 * pi;
halfpi = 0.5 * pi;
small = 0.00000001;
undefined = 999999.1;
infinite = 999999.9;
// ------------------------- implementation -----------------
magr = mag_SGP4(r);
magv = mag_SGP4(v);
// ------------------ find h n and e vectors ----------------
cross_SGP4(r, v, hbar);
magh = mag_SGP4(hbar);
if (magh > small)
{
nbar[0] = -hbar[1];
nbar[1] = hbar[0];
nbar[2] = 0.0;
magn = mag_SGP4(nbar);
c1 = magv*magv - mus / magr;
rdotv = dot_SGP4(r, v);
for (i = 0; i <= 2; i++)
ebar[i] = (c1*r[i] - rdotv*v[i]) / mus;
ecc = mag_SGP4(ebar);
// ------------ find a e and semi-latus rectum ----------
sme = (magv*magv*0.5) - (mus / magr);
if (fabs(sme) > small)
a = -mus / (2.0 *sme);
else
a = infinite;
p = magh*magh / mus;
// ----------------- find inclination -------------------
hk = hbar[2] / magh;
incl = acos(hk);
// -------- determine type of orbit for later use --------
// ------ elliptical, parabolic, hyperbolic inclined -------
//#ifdef _MSC_VER // chk if compiling under MSVS
// strcpy_s(typeorbit, 2 * sizeof(char), "ei");
//#else
// strcpy(typeorbit, "ei");
//#endif
typeorbit = 1;
if (ecc < small)
{
// ---------------- circular equatorial ---------------
if ((incl < small) | (fabs(incl - pi) < small))
{
//#ifdef _MSC_VER
// strcpy_s(typeorbit, sizeof(typeorbit), "ce");
//#else
// strcpy(typeorbit, "ce");
//#endif
typeorbit = 2;
}
else
{
// -------------- circular inclined ---------------
//#ifdef _MSC_VER
// strcpy_s(typeorbit, sizeof(typeorbit), "ci");
//#else
// strcpy(typeorbit, "ci");
//#endif
typeorbit = 3;
}
}
else
{
// - elliptical, parabolic, hyperbolic equatorial --
if ((incl < small) | (fabs(incl - pi) < small)){
//#ifdef _MSC_VER
// strcpy_s(typeorbit, sizeof(typeorbit), "ee");
//#else
// strcpy(typeorbit, "ee");
//#endif
typeorbit = 4;
}
}
// ---------- find right ascension of the ascending node ------------
if (magn > small)
{
temp = nbar[0] / magn;
if (fabs(temp) > 1.0)
temp = sgn_SGP4(temp);
omega = acos(temp);
if (nbar[1] < 0.0)
omega = twopi - omega;
}
else
omega = undefined;
// ---------------- find argument of perigee ---------------
//if (strcmp(typeorbit, "ei") == 0)
if (typeorbit == 1)
{
argp = angle_SGP4(nbar, ebar);
if (ebar[2] < 0.0)
argp = twopi - argp;
}
else
argp = undefined;
// ------------ find true anomaly at epoch -------------
//if (typeorbit[0] == 'e')
if ((typeorbit == 1) || (typeorbit == 4))
{
nu = angle_SGP4(ebar, r);
if (rdotv < 0.0)
nu = twopi - nu;
}
else
nu = undefined;
// ---- find argument of latitude - circular inclined -----
//if (strcmp(typeorbit, "ci") == 0)
if (typeorbit == 3)
{
arglat = angle_SGP4(nbar, r);
if (r[2] < 0.0)
arglat = twopi - arglat;
m = arglat;
}
else
arglat = undefined;
// -- find longitude of perigee - elliptical equatorial ----
//if ((ecc>small) && (strcmp(typeorbit, "ee") == 0))
if ((ecc>small) && (typeorbit == 4))
{
temp = ebar[0] / ecc;
if (fabs(temp) > 1.0)
temp = sgn_SGP4(temp);
lonper = acos(temp);
if (ebar[1] < 0.0)
lonper = twopi - lonper;
if (incl > halfpi)
lonper = twopi - lonper;
}
else
lonper = undefined;
// -------- find true longitude - circular equatorial ------
//if ((magr>small) && (strcmp(typeorbit, "ce") == 0))
if ((magr > small) && (typeorbit == 2))
{
temp = r[0] / magr;
if (fabs(temp) > 1.0)
temp = sgn_SGP4(temp);
truelon = acos(temp);
if (r[1] < 0.0)
truelon = twopi - truelon;
if (incl > halfpi)
truelon = twopi - truelon;
m = truelon;
}
else
truelon = undefined;
// ------------ find mean anomaly for all orbits -----------
//if (typeorbit[0] == 'e')
if ((typeorbit == 1) || (typeorbit == 4))
newtonnu_SGP4(ecc, nu, e, m);
}
else
{
p = undefined;
a = undefined;
ecc = undefined;
incl = undefined;
omega = undefined;
argp = undefined;
nu = undefined;
m = undefined;
arglat = undefined;
truelon = undefined;
lonper = undefined;
}
} // rv2coe
/* -----------------------------------------------------------------------------
*
* procedure jday_SGP4
*
* this procedure finds the julian date given the year, month, day, and time.
* the julian date is defined by each elapsed day since noon, jan 1, 4713 bc.
*
* algorithm : calculate the answer in one step for efficiency
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* year - year 1900 .. 2100
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - universal time hour 0 .. 23
* min - universal time min 0 .. 59
* sec - universal time sec 0.0 .. 59.999
*
* outputs :
* jd - julian date days from 4713 bc
* jdfrac - julian date fraction into day days from 4713 bc
*
* locals :
* none.
*
* coupling :
* none.
*
* references :
* vallado 2013, 183, alg 14, ex 3-4
* --------------------------------------------------------------------------- */
void jday_SGP4
(
int year, int mon, int day, int hr, int minute, double sec,
double& jd, double& jdFrac
)
{
jd = 367.0 * year -
floor((7 * (year + floor((mon + 9) / 12.0))) * 0.25) +
floor(275 * mon / 9.0) +
day + 1721013.5; // use - 678987.0 to go to mjd directly
jdFrac = (sec + minute * 60.0 + hr * 3600.0) / 86400.0;
// check that the day and fractional day are correct
if (fabs(jdFrac) > 1.0)
{
double dtt = floor(jdFrac);
jd = jd + dtt;
jdFrac = jdFrac - dtt;
}
// - 0.5*sgn(100.0*year + mon - 190002.5) + 0.5;
} // jday
/* -----------------------------------------------------------------------------
*
* procedure days2mdhms_SGP4
*
* this procedure converts the day of the year, days, to the equivalent month
* day, hour, minute and second.
*
* algorithm : set up array for the number of days per month
* find leap year - use 1900 because 2000 is a leap year
* loop through a temp value while the value is < the days
* perform int conversions to the correct day and month
* convert remainder into h m s using type conversions
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* year - year 1900 .. 2100
* days - julian day of the year 1.0 .. 366.0
*
* outputs :
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - hour 0 .. 23
* min - minute 0 .. 59
* sec - second 0.0 .. 59.999
*
* locals :
* dayofyr - day of year
* temp - temporary extended values
* inttemp - temporary int value
* i - index
* lmonth[13] - int array containing the number of days per month
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
void days2mdhms_SGP4
(
int year, double days,
int& mon, int& day, int& hr, int& minute, double& sec
)
{
int i, inttemp, dayofyr;
double temp;
int lmonth[] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
dayofyr = (int)floor(days);
/* ----------------- find month and day of month ---------------- */
if ((year % 4) == 0)
lmonth[2] = 29;
i = 1;
inttemp = 0;
while ((dayofyr > inttemp + lmonth[i]) && (i < 12))
{
inttemp = inttemp + lmonth[i];
i++;
}
mon = i;
day = dayofyr - inttemp;
/* ----------------- find hours minutes and seconds ------------- */
temp = (days - dayofyr) * 24.0;
hr = (int)floor(temp);
temp = (temp - hr) * 60.0;
minute = (int)floor(temp);
sec = (temp - minute) * 60.0;
} // days2mdhms
/* -----------------------------------------------------------------------------
*
* procedure invjday_SGP4
*
* this procedure finds the year, month, day, hour, minute and second
* given the julian date. tu can be ut1, tdt, tdb, etc.
*
* algorithm : set up starting values
* find leap year - use 1900 because 2000 is a leap year
* find the elapsed days through the year in a loop
* call routine to find each individual value
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* jd - julian date days from 4713 bc
* jdfrac - julian date fraction into day days from 4713 bc
*
* outputs :
* year - year 1900 .. 2100
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - hour 0 .. 23
* min - minute 0 .. 59
* sec - second 0.0 .. 59.999
*
* locals :
* days - day of year plus fractional
* portion of a day days
* tu - julian centuries from 0 h
* jan 0, 1900
* temp - temporary double values
* leapyrs - number of leap years from 1900
*
* coupling :
* days2mdhms - finds month, day, hour, minute and second given days and year
*
* references :
* vallado 2013, 203, alg 22, ex 3-13
* --------------------------------------------------------------------------- */
void invjday_SGP4
(
double jd, double jdfrac,
int& year, int& mon, int& day,
int& hr, int& minute, double& sec
)
{
int leapyrs;
double dt, days, tu, temp;
// check jdfrac for multiple days
if (fabs(jdfrac) >= 1.0)
{
jd = jd + floor(jdfrac);
jdfrac = jdfrac - floor(jdfrac);
}
// check for fraction of a day included in the jd
dt = jd - floor(jd) - 0.5;
if (fabs(dt) > 0.00000001)
{
jd = jd - dt;
jdfrac = jdfrac + dt;
}
/* --------------- find year and days of the year --------------- */
temp = jd - 2415019.5;
tu = temp / 365.25;
year = 1900 + (int)floor(tu);
leapyrs = (int)floor((year - 1901) * 0.25);
days = floor(temp - ((year - 1900) * 365.0 + leapyrs));
/* ------------ check for case of beginning of a year ----------- */
if (days + jdfrac < 1.0)
{
year = year - 1;
leapyrs = (int)floor((year - 1901) * 0.25);
days = floor(temp - ((year - 1900) * 365.0 + leapyrs));
}
/* ----------------- find remaining data ------------------------- */
days2mdhms_SGP4(year, days + jdfrac, mon, day, hr, minute, sec);
} // invjday
} // namespace SGP4Funcs
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/extension/SGP4.h 0000644 0001751 0000173 00000015256 14422467341 014637 0 ustar 00runner docker #ifndef _SGP4h_
#define _SGP4h_
/* ----------------------------------------------------------------
*
* SGP4.h
*
* this file contains the sgp4 procedures for analytical propagation
* of a satellite. the code was originally released in the 1980 and 1986
* spacetrack papers. a detailed discussion of the theory and history
* may be found in the 2006 aiaa paper by vallado, crawford, hujsak,
* and kelso.
*
* current :
* 12 mar 20 david vallado
* chg satnum to string for alpha 5 or 9-digit
* changes :
* 7 dec 15 david vallado
* fix jd, jdfrac
* 3 nov 14 david vallado
* update to msvs2013 c++
* 30 Dec 11 david vallado
* consolidate updated code version
* 30 Aug 10 david vallado
* delete unused variables in initl
* replace pow inetger 2, 3 with multiplies for speed
* 3 Nov 08 david vallado
* put returns in for error codes
* 29 sep 08 david vallado
* fix atime for faster operation in dspace
* add operationmode for afspc (a) or improved (i)
* performance mode
* 20 apr 07 david vallado
* misc fixes for constants
* 11 aug 06 david vallado
* chg lyddane choice back to strn3, constants, misc doc
* 15 dec 05 david vallado
* misc fixes
* 26 jul 05 david vallado
* fixes for paper
* note that each fix is preceded by a
* comment with "sgp4fix" and an explanation of
* what was changed
* 10 aug 04 david vallado
* 2nd printing baseline working
* 14 may 01 david vallado
* 2nd edition baseline
* 80 norad
* original baseline
* ---------------------------------------------------------------- */
#pragma once
#include
#include
#include
#include
#define SGP4Version "SGP4 Version 2020-07-13"
// -------------------------- structure declarations ----------------------------
typedef enum
{
wgs72old,
wgs72,
wgs84
} gravconsttype;
typedef struct elsetrec
{
char satnum[6];
int epochyr, epochtynumrev;
int error;
char operationmode;
char init, method;
/* Near Earth */
int isimp;
double aycof , con41 , cc1 , cc4 , cc5 , d2 , d3 , d4 ,
delmo , eta , argpdot, omgcof , sinmao , t , t2cof, t3cof ,
t4cof , t5cof , x1mth2 , x7thm1 , mdot , nodedot, xlcof , xmcof ,
nodecf;
/* Deep Space */
int irez;
double d2201 , d2211 , d3210 , d3222 , d4410 , d4422 , d5220 , d5232 ,
d5421 , d5433 , dedt , del1 , del2 , del3 , didt , dmdt ,
dnodt , domdt , e3 , ee2 , peo , pgho , pho , pinco ,
plo , se2 , se3 , sgh2 , sgh3 , sgh4 , sh2 , sh3 ,
si2 , si3 , sl2 , sl3 , sl4 , gsto , xfact , xgh2 ,
xgh3 , xgh4 , xh2 , xh3 , xi2 , xi3 , xl2 , xl3 ,
xl4 , xlamo , zmol , zmos , atime , xli , xni;
double a, altp, alta, epochdays, jdsatepoch, jdsatepochF, nddot, ndot,
bstar, rcse, inclo, nodeo, ecco, argpo, mo, no_kozai;
// sgp4fix add new variables from tle
char classification, intldesg[11];
int ephtype;
long elnum , revnum;
// sgp4fix add unkozai'd variable
double no_unkozai;
// sgp4fix add singly averaged variables
double am , em , im , Om , om , mm , nm;
// sgp4fix add constant parameters to eliminate mutliple calls during execution
double tumin, mus, radiusearthkm, xke, j2, j3, j4, j3oj2;
// Additional elements to capture relevant TLE and object information:
long dia_mm; // RSO dia in mm
double period_sec; // Period in seconds
unsigned char active; // "Active S/C" flag (0=n, 1=y)
unsigned char not_orbital; // "Orbiting S/C" flag (0=n, 1=y)
double rcs_m2; // "RCS (m^2)" storage
} elsetrec;
namespace SGP4Funcs
{
// public class SGP4Class
// {
bool sgp4init
(
gravconsttype whichconst, char opsmode, const char satn[9], const double epoch,
const double xbstar, const double xndot, const double xnddot, const double xecco, const double xargpo,
const double xinclo, const double xmo, const double xno,
const double xnodeo, elsetrec& satrec
);
bool sgp4
(
// no longer need gravconsttype whichconst, all data contained in satrec
elsetrec& satrec, double tsince,
double r[3], double v[3]
);
void getgravconst
(
gravconsttype whichconst,
double& tumin,
double& mus,
double& radiusearthkm,
double& xke,
double& j2,
double& j3,
double& j4,
double& j3oj2
);
// older sgp4io methods
void twoline2rv
(
char longstr1[130], char longstr2[130],
char typerun, char typeinput, char opsmode,
gravconsttype whichconst,
double& startmfe, double& stopmfe, double& deltamin,
elsetrec& satrec
);
// older sgp4ext methods
double gstime_SGP4
(
double jdut1
);
double sgn_SGP4
(
double x
);
double mag_SGP4
(
double x[3]
);
void cross_SGP4
(
double vec1[3], double vec2[3], double outvec[3]
);
double dot_SGP4
(
double x[3], double y[3]
);
double angle_SGP4
(
double vec1[3],
double vec2[3]
);
void newtonnu_SGP4
(
double ecc, double nu,
double& e0, double& m
);
double asinh_SGP4
(
double xval
);
void rv2coe_SGP4
(
double r[3], double v[3], double mus,
double& p, double& a, double& ecc, double& incl, double& omega, double& argp,
double& nu, double& m, double& arglat, double& truelon, double& lonper
);
void jday_SGP4
(
int year, int mon, int day, int hr, int minute, double sec,
double& jd, double& jdFrac
);
void days2mdhms_SGP4
(
int year, double days,
int& mon, int& day, int& hr, int& minute, double& sec
);
void invjday_SGP4
(
double jd, double jdFrac,
int& year, int& mon, int& day,
int& hr, int& minute, double& sec
);
} // namespace
#endif
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/extension/wrapper.cpp 0000644 0001751 0000173 00000053325 14422467341 016134 0 ustar 00runner docker #define PY_SSIZE_T_CLEAN
#include
#include "SGP4.h"
#include "structmember.h"
/* Whether scanf() prefers commas as the decimal point: true means that
we cannot count on the current locale to interpret numbers correctly
when the Vallado C++ code calls `sscanf()`. */
static bool switch_locale;
/* Satrec object that wraps a single raw SGP4 struct, and a Satrec array
that can broadcast into NumPy arrays. */
typedef struct {
PyObject_HEAD
elsetrec satrec;
} SatrecObject;
typedef struct {
PyObject_VAR_HEAD
elsetrec satrec[0];
} SatrecArrayObject;
/* Support routine that is used to support NumPy array broadcasting for
both individual satellite objects and also arrays. */
static PyObject *
_vectorized_sgp4(PyObject *args, elsetrec *raw_satrec_array, int imax)
{
PyObject *jd_arg, *fr_arg, *e_arg, *r_arg, *v_arg;
Py_buffer jd_buf, fr_buf, e_buf, r_buf, v_buf;
PyObject *rv = NULL;
// To prepare for "cleanup:" below.
jd_buf.buf = fr_buf.buf = e_buf.buf = r_buf.buf = v_buf.buf = NULL;
if (!PyArg_ParseTuple(args, "OOOOO:sgp4",
&jd_arg, &fr_arg, &e_arg, &r_arg, &v_arg))
return NULL;
if (PyObject_GetBuffer(jd_arg, &jd_buf, PyBUF_SIMPLE)) goto cleanup;
if (PyObject_GetBuffer(fr_arg, &fr_buf, PyBUF_SIMPLE)) goto cleanup;
if (PyObject_GetBuffer(e_arg, &e_buf, PyBUF_WRITABLE)) goto cleanup;
if (PyObject_GetBuffer(r_arg, &r_buf, PyBUF_WRITABLE)) goto cleanup;
if (PyObject_GetBuffer(v_arg, &v_buf, PyBUF_WRITABLE)) goto cleanup;
if (jd_buf.len != fr_buf.len) {
PyErr_SetString(PyExc_ValueError, "jd and fr must have the same shape");
goto cleanup;
}
// This extra block allows the "goto" statements above to jump
// across these further variable declarations.
{
Py_ssize_t jmax = jd_buf.len / sizeof(double);
if ((r_buf.len != (Py_ssize_t) sizeof(double) * imax * jmax * 3) ||
(v_buf.len != (Py_ssize_t) sizeof(double) * imax * jmax * 3) ||
(e_buf.len != (Py_ssize_t) sizeof(uint8_t) * imax * jmax)) {
PyErr_SetString(PyExc_ValueError, "bad output array dimension");
goto cleanup;
}
double *jd = (double*) jd_buf.buf;
double *fr = (double*) fr_buf.buf;
double *r = (double*) r_buf.buf;
double *v = (double*) v_buf.buf;
uint8_t *e = (uint8_t*) e_buf.buf;
#pragma omp parallel for
for (Py_ssize_t i=0; i < imax; i++) {
elsetrec &satrec = raw_satrec_array[i];
for (Py_ssize_t j=0; j < jmax; j++) {
double t = (jd[j] - satrec.jdsatepoch) * 1440.0
+ (fr[j] - satrec.jdsatepochF) * 1440.0;
Py_ssize_t k1 = i * jmax + j;
Py_ssize_t k3 = 3 * k1;
SGP4Funcs::sgp4(satrec, t, r + k3, v + k3);
e[k1] = (uint8_t) satrec.error;
if (satrec.error && satrec.error < 6) {
r[k3] = r[k3+1] = r[k3+2] = v[k3] = v[k3+1] = v[k3+2] = NAN;
}
}
}
}
Py_INCREF(Py_None);
rv = Py_None;
cleanup:
if (jd_buf.buf) PyBuffer_Release(&jd_buf);
if (fr_buf.buf) PyBuffer_Release(&fr_buf);
if (r_buf.buf) PyBuffer_Release(&r_buf);
if (v_buf.buf) PyBuffer_Release(&v_buf);
if (e_buf.buf) PyBuffer_Release(&e_buf);
return rv;
}
/* Details of the "Satrec" satellite object. */
static PyObject *
Satrec_twoline2rv(PyTypeObject *cls, PyObject *args)
{
char *string1, *string2, line1[130], line2[130];
gravconsttype whichconst = wgs72;
double dummy;
if (!PyArg_ParseTuple(args,
"ss|i:twoline2rv",
&string1, &string2, &whichconst))
return NULL;
// Copy both lines, since twoline2rv() might write to both buffers.
strncpy(line1, string1, 130);
strncpy(line2, string2, 130);
// Truncate the line before any checksum characters, if present;
// otherwise the C++ scanf() interprets each checksum character as
// part of the preceding value.
line1[68] = '\0';
line2[68] = '\0';
/* Allocate the new object. */
SatrecObject *self = (SatrecObject*) cls->tp_alloc(cls, 0);
if (!self)
return NULL;
/* Correct for locales that use a comma as the decimal point, since
users report that the scanf() function on macOS is sensitive to
locale when parsing floats. This operation is not thread-safe,
but we have not released the GIL. */
float f;
sscanf("1,5", "%f", &f);
switch_locale = (f == 1.5);
char *old_locale = NULL;
if (switch_locale)
old_locale = setlocale(LC_NUMERIC, "C");
/* Leading spaces in a catalog number make scanf() in the official
code consume the Classification letter as part of the catalog
number. (The first character of the International Designator
then gets consumed as the Classification instead.) But no
parsing error is reported, which is bad for users, so let's avoid
the situation by adding leading zeros ourselves. */
for (int i=2; i<7; i++) {
if (line1[i] == ' ') line1[i] = '0';
if (line2[i] == ' ') line2[i] = '0';
}
/* Call the official routine. */
SGP4Funcs::twoline2rv(line1, line2, ' ', ' ', 'i', whichconst,
dummy, dummy, dummy, self->satrec);
/* Usability bonus: round the fractional day to exactly the eight
digits specified in the TLE. */
self->satrec.jdsatepochF = round(self->satrec.jdsatepochF * 1e8) / 1e8;
/* To avoid having scanf() interpret the "intldesg" as zero or as
several fields, the C++ library changes spaces to periods and
underscores. Let's convert them back to avoid surprising users
and to match our Python implementation. */
if (self->satrec.intldesg[0] == '.')
self->satrec.intldesg[0] = ' ';
for (int i=1; i<11; i++)
if (self->satrec.intldesg[i] == '_')
self->satrec.intldesg[i] = ' ';
/* Restore previous locale. */
if (switch_locale)
setlocale(LC_NUMERIC, old_locale);
return (PyObject*) self;
}
static PyObject *
Satrec_sgp4init(PyObject *self, PyObject *args)
{
char satnum_str[6];
int whichconst; /* "int" rather than "gravconsttype" so we know size */
int opsmode; /* "int" rather than "char" because "C" needs an int */
long int satnum;
double epoch, bstar, ndot, nddot;
double ecco, argpo, inclo, mo, no_kozai, nodeo;
if (!PyArg_ParseTuple(args, "iCldddddddddd:sgp4init", &whichconst,
&opsmode, &satnum, &epoch, &bstar, &ndot, &nddot,
&ecco, &argpo, &inclo, &mo, &no_kozai, &nodeo))
return NULL;
// See https://www.space-track.org/documentation#tle-alpha5
if (satnum < 100000) {
snprintf(satnum_str, 6, "%05ld", satnum);
} else if (satnum > 339999) {
PyErr_SetString(PyExc_ValueError, "satellite number cannot exceed "
"339999, whose Alpha 5 encoding is 'Z9999'");
return 0;
} else {
char c = 'A' + satnum / 10000 - 10;
if (c > 'I') c++;
if (c > 'O') c++;
satnum_str[0] = c;
snprintf(satnum_str + 1, 5, "%04ld", satnum % 10000);
}
elsetrec &satrec = ((SatrecObject*) self)->satrec;
SGP4Funcs::sgp4init((gravconsttype) whichconst, opsmode, satnum_str, epoch,
bstar, ndot, nddot, ecco, argpo, inclo, mo, no_kozai,
nodeo, satrec);
/* Populate date fields that SGP4Funcs::twoline2rv would set. */
double whole;
double fraction = modf(epoch, &whole);
double whole_jd = whole + 2433281.5;
/* Go out on a limb: if `epoch` has no decimal digits past the 8
decimal places stored in a TLE, then assume the user is trying
to specify an exact decimal fraction. */
double epoch8 = epoch * 1e8;
if (round(epoch8) == epoch8) {
fraction = round(fraction * 1e8) / 1e8;
}
satrec.jdsatepoch = whole_jd;
satrec.jdsatepochF = fraction;
int y, m, d, H, M;
double S, jan0jd, jan0fr /* always comes out 0.0 */;
SGP4Funcs::invjday_SGP4(2433281.5, whole, y, m, d, H, M, S);
SGP4Funcs::jday_SGP4(y, 1, 0, 0, 0, 0.0, jan0jd, jan0fr);
satrec.epochyr = y % 100;
satrec.epochdays = whole_jd - jan0jd + fraction;
satrec.classification = 'U'; /* default to Unclassified, not '\0' */
/* Return true, like sgp4init does; check satrec.error for an error code */
Py_INCREF(Py_None);
return Py_None;
}
static PyObject *
Satrec_sgp4_tsince(PyObject *self, PyObject *args)
{
double tsince, r[3], v[3];
if (!PyArg_ParseTuple(args, "d:sgp4_tsince", &tsince))
return NULL;
elsetrec &satrec = ((SatrecObject*) self)->satrec;
SGP4Funcs::sgp4(satrec, tsince, r, v);
if (satrec.error && satrec.error < 6)
r[0] = r[1] = r[2] = v[0] = v[1] = v[2] = NAN;
return Py_BuildValue("i(fff)(fff)", satrec.error,
r[0], r[1], r[2], v[0], v[1], v[2]);
}
static PyObject *
Satrec_sgp4(PyObject *self, PyObject *args)
{
double jd, fr, r[3], v[3];
if (!PyArg_ParseTuple(args, "dd:sgp4", &jd, &fr))
return NULL;
elsetrec &satrec = ((SatrecObject*) self)->satrec;
double tsince = (jd - satrec.jdsatepoch) * 1440.0
+ (fr - satrec.jdsatepochF) * 1440.0;
SGP4Funcs::sgp4(satrec, tsince, r, v);
if (satrec.error && satrec.error < 6)
r[0] = r[1] = r[2] = v[0] = v[1] = v[2] = NAN;
return Py_BuildValue("i(fff)(fff)", satrec.error,
r[0], r[1], r[2], v[0], v[1], v[2]);
}
static PyObject *
Satrec__sgp4(PyObject *self, PyObject *args)
{
SatrecObject *obj = (SatrecObject*) self;
elsetrec *raw_satrec_array = &(obj->satrec);
Py_ssize_t imax = 1;
return _vectorized_sgp4(args, raw_satrec_array, imax);
}
static PyMethodDef Satrec_methods[] = {
{"twoline2rv", (PyCFunction)Satrec_twoline2rv, METH_VARARGS | METH_CLASS,
PyDoc_STR("Initialize the record from two lines of TLE text and an optional gravity constant.")},
{"sgp4init", (PyCFunction)Satrec_sgp4init, METH_VARARGS,
PyDoc_STR("Initialize the record from orbital elements.")},
{"sgp4", (PyCFunction)Satrec_sgp4, METH_VARARGS,
PyDoc_STR("Given a modified julian date, return position and velocity.")},
{"_sgp4", (PyCFunction)Satrec__sgp4, METH_VARARGS,
PyDoc_STR("Given an array of modified julian dates, return position and velocity arrays.")},
{"sgp4_tsince", (PyCFunction)Satrec_sgp4_tsince, METH_VARARGS,
PyDoc_STR("Given minutes since epoch, return position and velocity.")},
{NULL, NULL}
};
#define O(member) offsetof(SatrecObject, satrec.member)
static PyMemberDef Satrec_members[] = {
/* Listed in the order they appear in a TLE record. */
{"operationmode", T_CHAR, O(operationmode), READONLY,
PyDoc_STR("Operation mode: 'a' legacy AFSPC, or 'i' improved.")},
{"jdsatepoch", T_DOUBLE, O(jdsatepoch), 0,
PyDoc_STR("Julian date of epoch, day number (see jdsatepochF).")},
{"jdsatepochF", T_DOUBLE, O(jdsatepochF), 0,
PyDoc_STR("Julian date of epoch, fraction of day (see jdsatepoch).")},
{"classification", T_CHAR, O(classification), 0,
"Usually U=Unclassified, C=Classified, or S=Secret."},
/* intldesg: inline character array; see Satrec_getset. */
{"epochyr", T_INT, O(epochyr), 0,
PyDoc_STR("Year of this element set's epoch (see epochdays). Not set by sgp4init().")},
{"epochdays", T_DOUBLE, O(epochdays), 0,
PyDoc_STR("Day of the year of this element set's epoch (see epochyr). Not set by sgp4init().")},
{"ndot", T_DOUBLE, O(ndot), READONLY,
PyDoc_STR("Ballistic Coefficient in radians/minute^2.")},
{"nddot", T_DOUBLE, O(nddot), READONLY,
PyDoc_STR("Second Derivative of Mean Motion in radians/minute^3.")},
{"bstar", T_DOUBLE, O(bstar), READONLY,
PyDoc_STR("Drag Term in inverse Earth radii.")},
{"ephtype", T_INT, O(ephtype), 0,
PyDoc_STR("Ephemeris type (should be 0 in published TLEs).")},
{"elnum", T_LONG, O(elnum), 0,
PyDoc_STR("Element set number.")},
{"inclo", T_DOUBLE, O(inclo), READONLY,
PyDoc_STR("Inclination in radians.")},
{"nodeo", T_DOUBLE, O(nodeo), READONLY,
PyDoc_STR("Right ascension of ascending node in radians.")},
{"ecco", T_DOUBLE, O(ecco), READONLY,
PyDoc_STR("Eccentricity.")},
{"argpo", T_DOUBLE, O(argpo), READONLY,
PyDoc_STR("Argument of perigee in radians.")},
{"mo", T_DOUBLE, O(mo), READONLY,
PyDoc_STR("Mean anomaly in radians.")},
{"no_kozai", T_DOUBLE, O(no_kozai), READONLY,
PyDoc_STR("Mean motion in radians per minute.")},
{"revnum", T_LONG, O(revnum), 0,
PyDoc_STR("Integer revolution number at the epoch.")},
/* For compatibility with the old struct members, also accept the
plain name "no". */
{"no", T_DOUBLE, O(no_kozai), READONLY,
PyDoc_STR("Alias for the more carefully named ``no_kozai``.")},
/* Derived values that do not appear explicitly in the TLE. */
{"method", T_CHAR, O(method), READONLY,
PyDoc_STR("Method, either 'n' near earth or 'd' deep space.")},
{"error", T_INT, O(error), READONLY,
PyDoc_STR("Error code (1-6) documented in sgp4()")},
{"a", T_DOUBLE, O(a), READONLY,
PyDoc_STR("semi-major axis")},
{"altp", T_DOUBLE, O(altp), READONLY,
PyDoc_STR("altitude of perigee")},
{"alta", T_DOUBLE, O(alta), READONLY,
PyDoc_STR("altitude of perigee")},
/* Single averaged mean elements */
{"am", T_DOUBLE, O(am), READONLY,
PyDoc_STR("am: Average semi-major axis")},
{"em", T_DOUBLE, O(em), READONLY,
PyDoc_STR("em: Average eccentricity")},
{"im", T_DOUBLE, O(im), READONLY,
PyDoc_STR("im: Average inclination")},
{"Om", T_DOUBLE, O(Om), READONLY,
PyDoc_STR("Om: Average right ascension of ascending node")},
{"om", T_DOUBLE, O(om), READONLY,
PyDoc_STR("om: Average argument of perigee")},
{"mm", T_DOUBLE, O(mm), READONLY,
PyDoc_STR("mm: Average mean anomaly")},
{"nm", T_DOUBLE, O(nm), READONLY,
PyDoc_STR("nm: Average mean motion")},
/* Gravity-constant dependent values (initialized by sgp4init() */
{"tumin", T_DOUBLE, O(tumin), READONLY,
PyDoc_STR("minutes in one time unit")},
{"mu", T_DOUBLE, O(mus), READONLY,
PyDoc_STR("Earth gravitational parameter")},
{"radiusearthkm", T_DOUBLE, O(radiusearthkm), READONLY,
PyDoc_STR("radius of the earth in km")},
{"xke", T_DOUBLE, O(xke), READONLY,
PyDoc_STR("reciprocal of tumin")},
{"j2", T_DOUBLE, O(j2), READONLY,
PyDoc_STR("un-normalized zonal harmonic j2 value")},
{"j3", T_DOUBLE, O(j3), READONLY,
PyDoc_STR("un-normalized zonal harmonic j3 value")},
{"j4", T_DOUBLE, O(j4), READONLY,
PyDoc_STR("un-normalized zonal harmonic j4 value")},
{"j3oj2", T_DOUBLE, O(j3oj2), READONLY,
PyDoc_STR("j3 divided by j2")},
/* Other convenience variables (some required by propagation.py) */
{"t", T_DOUBLE, O(t), READONLY,
PyDoc_STR("Last tsince input to sgp4()")},
{"mdot", T_DOUBLE, O(mdot), READONLY,
PyDoc_STR("mean anomaly dot (rate)")},
{"argpdot", T_DOUBLE, O(argpdot), READONLY,
PyDoc_STR("argument of perigee dot (rate)")},
{"nodedot", T_DOUBLE, O(nodedot), READONLY,
PyDoc_STR("right ascension of ascending node dot (rate)")},
{"gsto", T_DOUBLE, O(gsto), READONLY,
PyDoc_STR("gsto: greenwich sidereal time")},
{NULL}
};
#undef O
static PyObject *
get_intldesg(SatrecObject *self, void *closure)
{
int length = 0;
char *s = self->satrec.intldesg;
while (length <= 7 && s[length])
length++;
while (length && s[length-1] == ' ')
length--;
return PyUnicode_FromStringAndSize(s, length);
}
static int
set_intldesg(SatrecObject *self, PyObject *value, void *closure)
{
const char *s = PyUnicode_AsUTF8(value);
if (!s)
return -1;
strncpy(self->satrec.intldesg, s, 10);
self->satrec.intldesg[10] = '\0';
return 0;
}
/* The official TLE code has switched `satnum` to a string, but to avoid
a breaking change we make the string available as `satnum_str` and
still return an integer for `satnum`. */
static PyObject *
get_satnum(SatrecObject *self, void *closure)
{
char *s = self->satrec.satnum;
long n;
if (strlen(s) < 5 || s[0] <= '9')
n = atol(s);
else if (s[0] <= 'I')
n = (s[0] - 'A' + 10) * 10000 + atol(s + 1);
else if (s[0] <= 'O')
n = (s[0] - 'A' + 9) * 10000 + atol(s + 1);
else
n = (s[0] - 'A' + 8) * 10000 + atol(s + 1);
return PyLong_FromLong(n);
}
static PyObject *
get_satnum_str(SatrecObject *self, void *closure)
{
return PyUnicode_FromString(self->satrec.satnum);
}
static int
set_satnum_str(SatrecObject *self, PyObject *value, void *closure)
{
const char *s = PyUnicode_AsUTF8(value);
if (!s)
return -1;
strncpy(self->satrec.satnum, s, 5);
self->satrec.satnum[5] = '\0';
return 0;
}
static PyGetSetDef Satrec_getset[] = {
{"intldesg", (getter)get_intldesg, (setter)set_intldesg,
PyDoc_STR("International Designator: a string of up to 7 characters"
" from the first line of the TLE that typically provides"
" two digits for the launch year, a 3-digit launch number,"
" and one or two letters for which piece of the launch.")},
{"satnum", (getter)get_satnum, NULL,
PyDoc_STR("Satellite number from characters 3-7 of each TLE line,"
" as an integer.")},
{"satnum_str", (getter)get_satnum_str, (setter)set_satnum_str,
PyDoc_STR("Satellite number from characters 3-7 of each TLE line,"
" as a string.")},
{NULL},
};
static PyTypeObject SatrecType = {
PyVarObject_HEAD_INIT(NULL, 0)
/* See the module initialization function at the bottom of this file. */
};
/* Details of the SatrecArray. */
static Py_ssize_t
Satrec_len(PyObject *self) {
return ((SatrecArrayObject*)self)->ob_base.ob_size;
}
static PySequenceMethods SatrecArray_as_sequence = {
Satrec_len
};
static PyObject *
SatrecArray_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
PyObject *sequence;
if (!PyArg_ParseTuple(args, "O:SatrecArray", &sequence))
return NULL;
Py_ssize_t length = PySequence_Length(sequence);
if (length == -1)
return NULL;
return type->tp_alloc(type, length);
}
static int
SatrecArray_init(SatrecArrayObject *self, PyObject *args, PyObject *kwds)
{
PyObject *sequence;
if (!PyArg_ParseTuple(args, "O:SatrecArray", &sequence))
return -1;
Py_ssize_t length = PySequence_Length(sequence);
if (length == -1)
return -1;
for (Py_ssize_t i=0; isatrec[i] = ((SatrecObject *)item)->satrec;
Py_DECREF(item);
}
return 0;
}
static PyObject *
SatrecArray_sgp4(PyObject *self, PyObject *args)
{
SatrecArrayObject *satrec_array = (SatrecArrayObject*) self;
elsetrec *raw_satrec_array = &(satrec_array->satrec[0]);
Py_ssize_t imax = satrec_array->ob_base.ob_size;
return _vectorized_sgp4(args, raw_satrec_array, imax);
}
static PyMethodDef SatrecArray_methods[] = {
{"_sgp4", (PyCFunction)SatrecArray_sgp4, METH_VARARGS,
PyDoc_STR("Given array of minutes since epoch, write"
" positions, velocities, and errors to arrays.")},
{NULL, NULL}
};
static PyTypeObject SatrecArrayType = {
PyVarObject_HEAD_INIT(NULL, sizeof(elsetrec))
/* See the module initialization function at the bottom of this file. */
};
/* The module that ties it all together. */
static PyModuleDef module = {
PyModuleDef_HEAD_INIT,
"sgp4.vallado_cpp",
"Official C++ SGP4 implementation.",
-1
};
#include
PyMODINIT_FUNC
PyInit_vallado_cpp(void)
{
SatrecType.tp_name = "sgp4.vallado_cpp.Satrec";
SatrecType.tp_basicsize = sizeof(SatrecObject);
SatrecArrayType.tp_itemsize = 0;
SatrecType.tp_flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE;
SatrecType.tp_doc = "SGP4 satellite record.";
SatrecType.tp_methods = Satrec_methods;
SatrecType.tp_members = Satrec_members;
SatrecType.tp_getset = Satrec_getset;
SatrecType.tp_new = PyType_GenericNew;
if (PyType_Ready(&SatrecType) < 0)
return NULL;
SatrecArrayType.tp_name = "sgp4.vallado_cpp.SatrecArray";
SatrecArrayType.tp_basicsize = sizeof(SatrecArrayObject);
SatrecArrayType.tp_itemsize = sizeof(elsetrec);
SatrecArrayType.tp_as_sequence = &SatrecArray_as_sequence;
SatrecArrayType.tp_flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE;
SatrecArrayType.tp_doc = "SGP4 array of satellites.";
SatrecArrayType.tp_methods = SatrecArray_methods;
SatrecArrayType.tp_init = (initproc) SatrecArray_init;
SatrecArrayType.tp_new = SatrecArray_new;
if (PyType_Ready(&SatrecArrayType) < 0)
return NULL;
PyObject *m = PyModule_Create(&module);
if (m == NULL)
return NULL;
Py_INCREF(&SatrecType);
if (PyModule_AddObject(m, "Satrec", (PyObject *) &SatrecType) < 0) {
Py_DECREF(&SatrecType);
Py_DECREF(m);
return NULL;
}
Py_INCREF(&SatrecArrayType);
if (PyModule_AddObject(m, "SatrecArray", (PyObject *) &SatrecArrayType) < 0) {
Py_DECREF(&SatrecArrayType);
Py_DECREF(&SatrecType);
Py_DECREF(m);
return NULL;
}
if (PyModule_AddIntConstant(m, "WGS72", (int)wgs72) ||
PyModule_AddIntConstant(m, "WGS72OLD", (int)wgs72old) ||
PyModule_AddIntConstant(m, "WGS84", (int)wgs84))
return NULL;
return m;
}
././@PaxHeader 0000000 0000000 0000000 00000000034 00000000000 010212 x ustar 00 28 mtime=1682599655.3394356
sgp4-2.22/setup.cfg 0000644 0001751 0000173 00000000046 14422467347 013553 0 ustar 00runner docker [egg_info]
tag_build =
tag_date = 0
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/setup.py 0000644 0001751 0000173 00000004712 14422467341 013442 0 ustar 00runner docker import os
import sys
from distutils.core import setup, Extension
import sgp4
description, long_description = sgp4.__doc__.split('\n', 1)
# Force compilation on Travis CI + Python 3 to make sure it keeps working.
optional = True
if sys.version_info[0] != 2 and os.environ.get('TRAVIS') == 'true':
optional = False
# It is hard to write C extensions that support both Python 2 and 3, so
# we opt here to support the acceleration only for Python 3.
ext_modules = []
if sys.version_info[0] == 3:
ext_modules.append(Extension(
'sgp4.vallado_cpp',
optional=optional,
sources=[
'extension/SGP4.cpp',
'extension/wrapper.cpp',
],
# TODO: can we safely figure out how to use a pair of options
# like these, adapted to as many platforms as possible, to use
# multiple processors when available?
# extra_compile_args=['-fopenmp'],
# extra_link_args=['-fopenmp'],
extra_compile_args=['-ffloat-store'],
))
# Read the package's "__version__" without importing it.
path = 'sgp4/__init__.py'
with open(path, 'rb') as f:
text = f.read().decode('utf-8')
text = text.replace('-*- coding: utf-8 -*-', '') # for Python 2.7
namespace = {}
eval(compile(text, path, 'exec'), namespace)
setup(name = 'sgp4',
version = namespace['__version__'],
description = description,
long_description = long_description,
license = 'MIT',
author = 'Brandon Rhodes',
author_email = 'brandon@rhodesmill.org',
url = 'https://github.com/brandon-rhodes/python-sgp4',
classifiers = [
'Development Status :: 5 - Production/Stable',
'Intended Audience :: Science/Research',
'License :: OSI Approved :: MIT License',
'Programming Language :: Python :: 2',
'Programming Language :: Python :: 2.6',
'Programming Language :: Python :: 2.7',
'Programming Language :: Python :: 3',
'Programming Language :: Python :: 3.3',
'Programming Language :: Python :: 3.4',
'Programming Language :: Python :: 3.5',
'Programming Language :: Python :: 3.6',
'Programming Language :: Python :: 3.7',
'Programming Language :: Python :: 3.8',
'Programming Language :: Python :: 3.9',
'Topic :: Scientific/Engineering :: Astronomy',
],
packages = ['sgp4'],
package_data = {'sgp4': ['SGP4-VER.TLE', 'sample*', 'tcppver.out']},
ext_modules = ext_modules,
)
././@PaxHeader 0000000 0000000 0000000 00000000034 00000000000 010212 x ustar 00 28 mtime=1682599655.3394356
sgp4-2.22/sgp4/ 0000755 0001751 0000173 00000000000 14422467347 012607 5 ustar 00runner docker ././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/SGP4-VER.TLE 0000644 0001751 0000173 00000020650 14422467341 014321 0 ustar 00runner docker # ------------------ Verification test cases ----------------------
# # TEME example
1 00005U 58002B 00179.78495062 .00000023 00000-0 28098-4 0 4753
2 00005 34.2682 348.7242 1859667 331.7664 19.3264 10.82419157413667 0.00 4320.0 360.00
# ## fig show lyddane fix error with gsfc ver
1 04632U 70093B 04031.91070959 -.00000084 00000-0 10000-3 0 9955
2 04632 11.4628 273.1101 1450506 207.6000 143.9350 1.20231981 44145 -5184.0 -4896.0 120.00
# DELTA 1 DEB # near earth normal drag equation
# # perigee = 377.26km, so moderate drag case
1 06251U 62025E 06176.82412014 .00008885 00000-0 12808-3 0 3985
2 06251 58.0579 54.0425 0030035 139.1568 221.1854 15.56387291 6774 0.0 2880.0 120.00
# MOLNIYA 2-14 # 12h resonant ecc in 0.65 to 0.7 range
1 08195U 75081A 06176.33215444 .00000099 00000-0 11873-3 0 813
2 08195 64.1586 279.0717 6877146 264.7651 20.2257 2.00491383225656 0.0 2880.0 120.00
# MOLNIYA 1-36 ## fig 12h resonant ecc in 0.7 to 0.715 range
1 09880U 77021A 06176.56157475 .00000421 00000-0 10000-3 0 9814
2 09880 64.5968 349.3786 7069051 270.0229 16.3320 2.00813614112380 0.0 2880.0 120.00
# SMS 1 AKM # show the integrator problem with gsfc ver
1 09998U 74033F 05148.79417928 -.00000112 00000-0 00000+0 0 4480
2 09998 9.4958 313.1750 0270971 327.5225 30.8097 1.16186785 45878 -1440.0 -720.00 60.0
# # Original STR#3 SDP4 test
1 11801U 80230.29629788 .01431103 00000-0 14311-1 13
2 11801 46.7916 230.4354 7318036 47.4722 10.4117 2.28537848 13 0.0 1440.0 360.00
# EUTELSAT 1-F1 (ECS1)## fig lyddane choice in GSFC at 2080 min
1 14128U 83058A 06176.02844893 -.00000158 00000-0 10000-3 0 9627
2 14128 11.4384 35.2134 0011562 26.4582 333.5652 0.98870114 46093 0.0 2880.0 120.00
# SL-6 R/B(2) # Deep space, perigee = 82.48 (<98) for
# # s4 > 20 mod
1 16925U 86065D 06151.67415771 .02550794 -30915-6 18784-3 0 4486
2 16925 62.0906 295.0239 5596327 245.1593 47.9690 4.88511875148616 0.0 1440.0 120.00
# SL-12 R/B # Shows Lyddane choice at 1860 and 4700 min
1 20413U 83020D 05363.79166667 .00000000 00000-0 00000+0 0 7041
2 20413 12.3514 187.4253 7864447 196.3027 356.5478 0.24690082 7978 1440.0 4320.0 120.00
# MOLNIYA 1-83 # 12h resonant, ecc > 0.715 (negative BSTAR)
1 21897U 92011A 06176.02341244 -.00001273 00000-0 -13525-3 0 3044
2 21897 62.1749 198.0096 7421690 253.0462 20.1561 2.01269994104880 0.0 2880.0 120.00
# SL-6 R/B(2) # last tle given, decayed 2006-04-04, day 94
1 22312U 93002D 06094.46235912 .99999999 81888-5 49949-3 0 3953
2 22312 62.1486 77.4698 0308723 267.9229 88.7392 15.95744531 98783 54.2028672 1440.0 20.00
# SL-6 R/B(2) # 12h resonant ecc in the > 0.715 range
1 22674U 93035D 06176.55909107 .00002121 00000-0 29868-3 0 6569
2 22674 63.5035 354.4452 7541712 253.3264 18.7754 1.96679808 93877 0.0 2880.0 120.00
# ARIANE 44L+ R/B # Lyddane bug at <= 70 min for atan2(),
# # no quadrant fix
1 23177U 94040C 06175.45752052 .00000386 00000-0 76590-3 0 95
2 23177 7.0496 179.8238 7258491 296.0482 8.3061 2.25906668 97438 0.0 1440.0 120.00
# WIND # STR#3 Kepler failes past about 200 min
1 23333U 94071A 94305.49999999 -.00172956 26967-3 10000-3 0 15
2 23333 28.7490 2.3720 9728298 30.4360 1.3500 0.07309491 70 0.0 1600.0 120.00
# ARIANE 42P+3 R/B ## fig Lyddane bug at > 280.5 min for AcTan()
1 23599U 95029B 06171.76535463 .00085586 12891-6 12956-2 0 2905
2 23599 6.9327 0.2849 5782022 274.4436 25.2425 4.47796565123555 0.0 720.0 20.00
# ITALSAT 2 # 24h resonant GEO, inclination > 3 deg
1 24208U 96044A 06177.04061740 -.00000094 00000-0 10000-3 0 1600
2 24208 3.8536 80.0121 0026640 311.0977 48.3000 1.00778054 36119 0.0 1440.0 120.00
# AMC-4 ## fig low incl, show incl shift with
# ## gsfc version from 240 to 1440 min
1 25954U 99060A 04039.68057285 -.00000108 00000-0 00000-0 0 6847
2 25954 0.0004 243.8136 0001765 15.5294 22.7134 1.00271289 15615 -1440.0 1440.0 120.00
# INTELSAT 902 # negative incl at 9313 min then
# # 270 deg Lyddane bug at 37606 min
1 26900U 01039A 06106.74503247 .00000045 00000-0 10000-3 0 8290
2 26900 0.0164 266.5378 0003319 86.1794 182.2590 1.00273847 16981 9300.00 9400.00 60.00
# COSMOS 1024 DEB # 12h resonant ecc in 0.5 to 0.65 range
1 26975U 78066F 06174.85818871 .00000620 00000-0 10000-3 0 6809
2 26975 68.4714 236.1303 5602877 123.7484 302.5767 2.05657553 67521 0.0 2880.0 120.00
# CBERS 2 # Near Earth, ecc = 8.84E-5 (< 1.0e-4)
# # drop certain normal drag terms
1 28057U 03049A 06177.78615833 .00000060 00000-0 35940-4 0 1836
2 28057 98.4283 247.6961 0000884 88.1964 271.9322 14.35478080140550 0.0 2880.0 120.00
# NAVSTAR 53 (USA 175)# 12h non-resonant GPS (ecc < 0.5 ecc)
1 28129U 03058A 06175.57071136 -.00000104 00000-0 10000-3 0 459
2 28129 54.7298 324.8098 0048506 266.2640 93.1663 2.00562768 18443 0.0 1440.0 120.00
# COSMOS 2405 # Near Earth, perigee = 127.20 (< 156) s4 mod
1 28350U 04020A 06167.21788666 .16154492 76267-5 18678-3 0 8894
2 28350 64.9977 345.6130 0024870 260.7578 99.9590 16.47856722116490 0.0 2880.0 120.00
# H-2 R/B # Deep space, perigee = 135.75 (<156) s4 mod
1 28623U 05006B 06177.81079184 .00637644 69054-6 96390-3 0 6000
2 28623 28.5200 114.9834 6249053 170.2550 212.8965 3.79477162 12753 0.0 1440.0 120.00
# XM-3 # 24h resonant geo, incl < 3 deg goes
# # negative around 1130 min
1 28626U 05008A 06176.46683397 -.00000205 00000-0 10000-3 0 2190
2 28626 0.0019 286.9433 0000335 13.7918 55.6504 1.00270176 4891 0.0 1440.0 120.00
# MINOTAUR R/B # Sub-orbital case - Decayed 2005-11-29
# #(perigee = -51km), lost in 50 minutes
1 28872U 05037B 05333.02012661 .25992681 00000-0 24476-3 0 1534
2 28872 96.4736 157.9986 0303955 244.0492 110.6523 16.46015938 10708 0.0 60.0 5.00
# SL-14 DEB # Last stage of decay - lost in under 420 min
1 29141U 85108AA 06170.26783845 .99999999 00000-0 13519-0 0 718
2 29141 82.4288 273.4882 0015848 277.2124 83.9133 15.93343074 6828 0.0 440.0 20.00
# SL-12 DEB # Near Earth, perigee = 212.24 < 220
# # simplified drag eq
1 29238U 06022G 06177.28732010 .00766286 10823-4 13334-2 0 101
2 29238 51.5595 213.7903 0202579 95.2503 267.9010 15.73823839 1061 0.0 1440.0 120.00
# # Original STR#3 SGP4 test
1 88888U 80275.98708465 .00073094 13844-3 66816-4 0 87
2 88888 72.8435 115.9689 0086731 52.6988 110.5714 16.05824518 1058 0.0 1440.0 120.00
#
# # check error code 4
1 33333U 05037B 05333.02012661 .25992681 00000-0 24476-3 0 1534
2 33333 96.4736 157.9986 9950000 244.0492 110.6523 4.00004038 10708 0.0 150.0 5.00
# # try and check error code 2 but this
1 33334U 78066F 06174.85818871 .00000620 00000-0 10000-3 0 6809
2 33334 68.4714 236.1303 5602877 123.7484 302.5767 0.00001000 67521 0.0 1440.0 1.00
# # try to check error code 3 looks like ep never goes below zero, tied close to ecc
1 33335U 05008A 06176.46683397 -.00000205 00000-0 10000-3 0 2190
2 33335 0.0019 286.9433 0000004 13.7918 55.6504 1.00270176 4891 0.0 1440.0 20.00
# SL-12 R/B # Shows Lyddane choice at 1860 and 4700 min
1 20413U 83020D 05363.79166667 .00000000 00000-0 00000+0 0 7041
2 20413 12.3514 187.4253 7864447 196.3027 356.5478 0.24690082 7978 1844000.0 1845100.0 5.00
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/__init__.py 0000644 0001751 0000173 00000072546 14422467341 014730 0 ustar 00runner docker # -*- coding: utf-8 -*-
"""Track Earth satellites given TLE data, using up-to-date 2020 SGP4 routines.
This package compiles the official C++ code from `Revisiting Spacetrack
Report #3 `_ (AIAA
2006-6753) and uses it to compute the positions of satellites in Earth
orbit. Orbital elements can be read from either a legacy TLE file or
from a modern OMM element set, both of which you can fetch from a site
like `CelesTrak `_.
If your machine can’t install or compile the C++ code, then this package
falls back to using a slower pure-Python implementation of SGP4. Tests
make sure that its positions **agree to within 0.1 mm** with the
standard version of the algorithm — an error far less than the
1–3 km/day by which satellites themselves deviate from the ideal orbits
described in TLE files.
An accelerated routine is available that, given a series of times and of
satellites, computes a whole array of output positions using a fast C++
loop. See the “Array Acceleration” section below.
Note that the SGP4 propagator returns raw *x,y,z* Cartesian coordinates
in a “True Equator Mean Equinox” (TEME) reference frame that’s centered
on the Earth but does not rotate with it — an “Earth centered inertial”
(ECI) reference frame. The SGP4 propagator itself does not implement
the math to convert these positions into more official ECI frames like
J2000 or the ICRS, nor into any Earth-centered Earth-fixed (ECEF) frames
like the ITRS, nor into latitudes and longitudes through an Earth
ellipsoid like WGS84. For conversions into these other coordinate
frames, look for a comprehensive astronomy library, like the `Skyfield
`_ library that is built atop this one
(see the `section on Earth satellites
`_ in its
documentation).
Usage
-----
You will probably first want to to check whether your machine has
successfully installed the fast SGP4 C++ code, or is using the slow
Python version (in which case this value will be false):
>>> from sgp4.api import accelerated
>>> print(accelerated)
True
This library uses the same function names as the official C++ code, to
help users who are already familiar with SGP4 in other languages. Here
is how to compute the x,y,z position and velocity for the International
Space Station at 12:50:19 on 29 June 2000:
>>> from sgp4.api import Satrec
>>>
>>> s = '1 25544U 98067A 19343.69339541 .00001764 00000-0 38792-4 0 9991'
>>> t = '2 25544 51.6439 211.2001 0007417 17.6667 85.6398 15.50103472202482'
>>> satellite = Satrec.twoline2rv(s, t)
>>>
>>> jd, fr = 2458827, 0.362605
>>> e, r, v = satellite.sgp4(jd, fr)
>>> e
0
>>> print(r) # True Equator Mean Equinox position (km)
(-6102.44..., -986.33..., -2820.31...)
>>> print(v) # True Equator Mean Equinox velocity (km/s)
(-1.45..., -5.52..., 5.10...)
As input, you can provide either:
* A simple floating-point Julian Date for ``jd`` and the value 0.0 for
``fr``, if you are happy with the precision of a 64-bit floating point
number. Note that modern Julian Dates are greater than 2,450,000
which means that nearly half of the precision of a 64-bit float will
be consumed by the whole part that specifies the day. The remaining
digits will provide a precision for the fraction of around 20.1 µs.
This should be no problem for the accuracy of your result — satellite
positions usually off by a few kilometers anyway, far less than a
satellite moves in 20.1 µs — but if you run a solver that dives down
into the microseconds while searching for a rising or setting time,
the solver might be bothered by the 20.1 µs plateau between each jump
in the satellite’s position.
* Or, you can provide a coarse date ``jd`` plus a very precise fraction
``fr`` that supplies the rest of the value. The Julian Date for which
the satellite position is computed is the sum of the two values. One
common practice is to provide the whole number as ``jd`` and the
fraction as ``fr``; another is to have ``jd`` carry the fraction 0.5
since UTC midnight occurs halfway through each Julian Date. Either
way, splitting the value allows a solver to run all the way down into
the nanoseconds and still see SGP4 respond smoothly to tiny date
adjustments with tiny changes in the resulting satellite position.
Here is how to intrepret the results:
* ``e`` will be a non-zero error code if the satellite position could
not be computed for the given date. You can ``from sgp4.api import
SGP4_ERRORS`` to access a dictionary mapping error codes to error
messages explaining what each code means.
* ``r`` measures the satellite position in **kilometers** from the
center of the earth in the idiosyncratic True Equator Mean Equinox
coordinate frame used by SGP4.
* ``v`` velocity is the rate at which the position is changing,
expressed in **kilometers per second**.
If your application does not natively handle Julian dates, you can
compute ``jd`` and ``fr`` from calendar dates using ``jday()``.
>>> from sgp4.api import jday
>>> jd, fr = jday(2019, 12, 9, 12, 0, 0)
>>> jd
2458826.5
>>> fr
0.5
Double-checking your TLE lines
------------------------------
Because TLE is an old punch-card fixed-width format, it’s very sensitive
to whether exactly the right number of spaces are positioned in exactly
the right columns. If you suspect that your satellite elements aren’t
getting loaded correctly, try calling the slow pure-Python version of
``twoline2rv()``, which performs extra checks that the fast C++ doesn’t:
>>> from sgp4.earth_gravity import wgs72
>>> from sgp4.io import twoline2rv
>>> assert twoline2rv(s, t, wgs72)
Any TLE formatting errors will be raised as a ``ValueError``.
Using OMM elements instead of TLE
---------------------------------
The industry is migrating away from the original TLE format, because it
will soon run out of satellite numbers.
* Some TLE files now use a new “Alpha-5” convention that expands the
range of satellite numbers by using an initial letter; for example,
“E8493” means satellite 148493. This library supports the Alpha-5
convention and should return the correct integer in Python.
* Some authorities are now distributing satellite elements in an “OMM”
Orbit Mean Elements Message format that replaces the TLE format. You
can learn about OMM in Dr. T.S. Kelso’s `“A New Way to Obtain GP Data”
`_ at
the CelesTrak site.
You can already try out experimental support for OMM:
>>> from sgp4 import omm
Reading OMM data takes two steps, because OMM supports several different
text formats. First, parse the input text to recover the field names
and values that it stores; second, build a Python satellite object from
those field values. For example, to load OMM from XML:
>>> with open('sample_omm.xml') as f:
... fields = next(omm.parse_xml(f))
>>> sat = Satrec()
>>> omm.initialize(sat, fields)
Or, to load OMM from CSV:
>>> with open('sample_omm.csv') as f:
... fields = next(omm.parse_csv(f))
>>> sat = Satrec()
>>> omm.initialize(sat, fields)
Either way, the satellite object should wind up properly initialized and
ready to start producing positions.
If you are interested in saving satellite parameters using the new OMM
format, then read the section on “Export” below.
Epoch
-----
Over a given satellite’s lifetime, dozens or hundreds of different TLE
records will be produced as its orbit evolves. Each TLE record
specifies the “epoch date” for which it is most accurate. Typically a
TLE is only useful for a couple of weeks to either side of its epoch
date, beyond which its predictions become unreliable.
Satellite objects natively provide their epoch as a two-digit year and
then a fractional number of days into the year:
>>> satellite.epochyr
19
>>> satellite.epochdays
343.69339541
Because Sputnik was launched in 1957, satellite element sets will never
refer to an earlier year, so years 57 through 99 mean 1957–1999 while 0
through 56 mean 2000–2056. The TLE format will presumably be obsolete
in 2057 and have to be upgraded to 4-digit years.
To turn the number of days and its fraction into a calendar date and
time, use the ``days2mdhms()`` function.
>>> from sgp4.api import days2mdhms
>>> month, day, hour, minute, second = days2mdhms(19, 343.69339541)
>>> month
12
>>> day
9
>>> hour
16
>>> minute
38
>>> second
29.363424
The SGP4 library also translates those two numbers into a Julian date
and fractional Julian date, since Julian dates are more commonly used in
astronomy.
>>> satellite.jdsatepoch
2458826.5
>>> satellite.jdsatepochF
0.69339541
Finally, a convenience function is available in the library if you need
the epoch date and time as Python ``datetime``.
>>> from sgp4.conveniences import sat_epoch_datetime
>>> sat_epoch_datetime(satellite)
datetime.datetime(2019, 12, 9, 16, 38, 29, 363423, tzinfo=UTC)
Array Acceleration
------------------
To avoid the expense of running a Python loop when you have many dates
and times for which you want a position, you can pass your Julian dates
as arrays. The array routine is only faster if your machine has
successfully installed or compiled the SGP4 C++ code, so you might want
to check first:
>>> from sgp4.api import accelerated
>>> print(accelerated)
True
To call the array routine, make NumPy arrays for ``jd`` and ``fr`` that
are the same length:
>>> import numpy as np
>>> np.set_printoptions(precision=2)
>>> jd = np.array((2458826, 2458826, 2458826, 2458826))
>>> fr = np.array((0.0001, 0.0002, 0.0003, 0.0004))
>>> e, r, v = satellite.sgp4_array(jd, fr)
>>> print(e)
[0 0 0 0]
>>> print(r)
[[-3431.31 2620.15 -5252.97]
[-3478.86 2575.14 -5243.87]
[-3526.09 2529.89 -5234.28]
[-3572.98 2484.41 -5224.19]]
>>> print(v)
[[-5.52 -5.19 1.02]
[-5.49 -5.22 1.08]
[-5.45 -5.25 1.14]
[-5.41 -5.28 1.2 ]]
To avoid the expense of Python loops when you have many satellites and
dates, build a ``SatrecArray`` from several individual satellites. Its
``sgp4()`` method will expect both ``jd`` and ``fr`` to be NumPy arrays,
so if you only have one date, be sure to provide NumPy arrays of length
one. Here is a sample computation for 2 satellites and 4 dates:
>>> u = '1 20580U 90037B 19342.88042116 .00000361 00000-0 11007-4 0 9996'
>>> w = '2 20580 28.4682 146.6676 0002639 185.9222 322.7238 15.09309432427086'
>>> satellite2 = Satrec.twoline2rv(u, w)
>>> from sgp4.api import SatrecArray
>>> a = SatrecArray([satellite, satellite2])
>>> e, r, v = a.sgp4(jd, fr)
>>> np.set_printoptions(precision=2)
>>> print(e)
[[0 0 0 0]
[0 0 0 0]]
>>> print(r)
[[[-3431.31 2620.15 -5252.97]
[-3478.86 2575.14 -5243.87]
[-3526.09 2529.89 -5234.28]
[-3572.98 2484.41 -5224.19]]
[[ 5781.85 2564. -2798.22]
[ 5749.36 2618.59 -2814.63]
[ 5716.35 2672.94 -2830.78]
[ 5682.83 2727.05 -2846.68]]]
>>> print(v)
[[[-5.52 -5.19 1.02]
[-5.49 -5.22 1.08]
[-5.45 -5.25 1.14]
[-5.41 -5.28 1.2 ]]
[[-3.73 6.33 -1.91]
[-3.79 6.3 -1.88]
[-3.85 6.28 -1.85]
[-3.91 6.25 -1.83]]]
Export
------
If you have a ``Satrec`` you want to share with friends or persist to a
file, there’s an export routine that will turn it back into a TLE:
>>> from sgp4 import exporter
>>> line1, line2 = exporter.export_tle(satellite)
>>> line1
'1 25544U 98067A 19343.69339541 .00001764 00000-0 38792-4 0 9991'
>>> line2
'2 25544 51.6439 211.2001 0007417 17.6667 85.6398 15.50103472202482'
Happily, these are exactly the two TLE lines that we used to create this
satellite object:
>>> (s == line1) and (t == line2)
True
Another export routine is available that produces the fields defined by
the new OMM format (see the “OMM” section above):
>>> from pprint import pprint
>>> fields = exporter.export_omm(satellite, 'ISS (ZARYA)')
>>> pprint(fields)
{'ARG_OF_PERICENTER': 17.6667,
'BSTAR': 3.8792e-05,
'CENTER_NAME': 'EARTH',
'CLASSIFICATION_TYPE': 'U',
'ECCENTRICITY': 0.0007417,
'ELEMENT_SET_NO': 999,
'EPHEMERIS_TYPE': 0,
'EPOCH': '2019-12-09T16:38:29.363423',
'INCLINATION': 51.6439,
'MEAN_ANOMALY': 85.6398,
'MEAN_ELEMENT_THEORY': 'SGP4',
'MEAN_MOTION': 15.501034720000002,
'MEAN_MOTION_DDOT': 0.0,
'MEAN_MOTION_DOT': 1.764e-05,
'NORAD_CAT_ID': 25544,
'OBJECT_ID': '1998-067A',
'OBJECT_NAME': 'ISS (ZARYA)',
'RA_OF_ASC_NODE': 211.2001,
'REF_FRAME': 'TEME',
'REV_AT_EPOCH': 20248,
'TIME_SYSTEM': 'UTC'}
Gravity
-------
The SGP4 algorithm operates atop a set of constants specifying how
strong the Earth’s gravity is. The most recent official paper on SGP4
(see below) specifies that “We use WGS-72 as the default value”, so this
Python module uses the same default. But in case you want to use either
the old legacy version of the WGS-72 constants, or else the non-standard
but more modern WGS-84 constants, the ``twoline2rv()`` constructor takes
an optional argument:
>>> from sgp4.api import WGS72OLD, WGS72, WGS84
>>> satellite3 = Satrec.twoline2rv(s, t, WGS84)
You will in general get less accurate results if you choose WGS-84.
Even though it reflects more recent and accurate measures of the Earth,
satellite TLEs across the industry are most likely generated with WGS-72
as their basis. The positions you generate will better agree with the
real positions of each satellite if you use the same underlying gravity
constants as were used to generate the TLE.
Providing your own elements
---------------------------
If instead of parsing a TLE you want to specify orbital elements
directly, you can pass them as floating point numbers to a satellite
object’s ``sgp4init()`` method. For example, here’s how to build the
same International Space Station orbit that we loaded from a TLE in the
first code example above:
>>> satellite2 = Satrec()
>>> satellite2.sgp4init(
... WGS72, # gravity model
... 'i', # 'a' = old AFSPC mode, 'i' = improved mode
... 25544, # satnum: Satellite number
... 25545.69339541, # epoch: days since 1949 December 31 00:00 UT
... 3.8792e-05, # bstar: drag coefficient (1/earth radii)
... 0.0, # ndot: ballistic coefficient (radians/minute^2)
... 0.0, # nddot: mean motion 2nd derivative (radians/minute^3)
... 0.0007417, # ecco: eccentricity
... 0.3083420829620822, # argpo: argument of perigee (radians)
... 0.9013560935706996, # inclo: inclination (radians)
... 1.4946964807494398, # mo: mean anomaly (radians)
... 0.06763602333248933, # no_kozai: mean motion (radians/minute)
... 3.686137125541276, # nodeo: R.A. of ascending node (radians)
... )
These numbers don’t look the same as the numbers in the TLE, because the
underlying ``sgp4init()`` routine uses different units: radians rather
than degrees. But this is the same orbit and will produce the same
positions.
Note that ``ndot`` and ``nddot`` are ignored by the SGP4 propagator, so
you can leave them ``0.0`` without any effect on the resulting satellite
positions. But they do at least get saved to the satellite object, and
written out if you write the parameters to a TLE or OMM file (see the
“Export” section, above).
To compute the “epoch” argument, take the epoch’s Julian date and
subtract 2433281.5 days.
While the underlying ``sgp4init()`` routine leaves the attributes
``epochyr``, ``epochdays``, ``jdsatepoch``, and ``jdsatepochF`` unset,
this library goes ahead and sets them anyway for you, using the epoch
you provided.
See the next section for the complete list of attributes that are
available from the satellite record once it has been initialized.
Attributes
----------
There are several dozen ``Satrec`` attributes that expose data from the
underlying C++ SGP4 record. They fall into the following categories.
*Identification*
These are copied directly from the TLE record but aren’t used by the
propagation math.
| ``satnum_str`` — Satellite number, as a 5-character string.
| ``satnum`` — Satellite number, converted to an integer.
| ``classification`` — ``'U'``, ``'C'``, or ``'S'``
indicating the element set is Unclassified, Classified, or Secret.
| ``ephtype`` — Integer “ephemeris type”, used internally by space
agencies to mark element sets that are not ready for publication;
this field should always be ``0`` in published TLEs.
| ``elnum`` — Element set number.
| ``revnum`` — Satellite’s revolution number at the moment of the epoch,
presumably counting from 1 following launch.
*Orbital Elements*
These are the orbital parameters, copied verbatim from the text of the
TLE record. They describe the orbit at the moment of the TLE’s epoch
and so remain constant even as the satellite record is used over and
over again to propagate positions for different times.
| ``epochyr`` — Epoch date: the last two digits of the year.
| ``epochdays`` — Epoch date: the number of days into the year,
including a decimal fraction for the UTC time of day.
| ``ndot`` — First time derivative of the mean motion
(loaded from the TLE, but otherwise ignored).
| ``nddot`` — Second time derivative of the mean motion
(loaded from the TLE, but otherwise ignored).
| ``bstar`` — Ballistic drag coefficient B* (1/earth radii).
| ``inclo`` — Inclination (radians).
| ``nodeo`` — Right ascension of ascending node (radians).
| ``ecco`` — Eccentricity.
| ``argpo`` — Argument of perigee (radians).
| ``mo`` — Mean anomaly (radians).
| ``no_kozai`` — Mean motion (radians/minute).
| ``no`` — Alias for ``no_kozai``, for compatibility with old code.
You can also access the epoch as a Julian date:
| ``jdsatepoch`` — Whole part of the epoch’s Julian date.
| ``jdsatepochF`` — Fractional part of the epoch’s Julian date.
*Computed Orbit Properties*
These are computed when the satellite is first loaded,
as a convenience for callers who might be interested in them.
They aren’t used by the SGP4 propagator itself.
| ``a`` — Semi-major axis (earth radii).
| ``altp`` — Altitude of the satellite at perigee
(earth radii, assuming a spherical Earth).
| ``alta`` — Altitude of the satellite at apogee
(earth radii, assuming a spherical Earth).
| ``argpdot`` — Rate at which the argument of perigee is changing
(radians/minute).
| ``gsto`` — Greenwich Sidereal Time at the satellite’s epoch (radians).
| ``mdot`` — Rate at which the mean anomaly is changing (radians/minute)
| ``nodedot`` — Rate at which the right ascension of the ascending node
is changing (radians/minute).
*Propagator Mode*
| ``operationmode`` — A single character that directs SGP4
to either operate in its modern ``'i'`` improved mode
or in its legacy ``'a'`` AFSPC mode.
| ``method`` — A single character, chosen automatically
when the orbital elements were loaded, that indicates whether SGP4
has chosen to use its built-in ``'n'`` Near Earth
or ``'d'`` Deep Space mode for this satellite.
*Result of Most Recent Propagation*
| ``t`` —
The time you gave when you most recently asked SGP4
to compute this satellite’s position,
measured in minutes before (negative) or after (positive)
the satellite’s epoch.
| ``error`` —
Error code produced by the most recent SGP4 propagation
you performed with this element set.
The possible ``error`` codes are:
0. No error.
1. Mean eccentricity is outside the range 0 ≤ e < 1.
2. Mean motion has fallen below zero.
3. Perturbed eccentricity is outside the range 0 ≤ e ≤ 1.
4. Length of the orbit’s semi-latus rectum has fallen below zero.
5. (No longer used.)
6. Orbit has decayed: the computed position is underground.
(The position is still returned, in case the vector is helpful
to software that might be searching for the moment of re-entry.)
*Mean Elements From Most Recent Propagation*
Partway through each propagation, the SGP4 routine saves a set of
“singly averaged mean elements” that describe the orbit’s shape at the
moment for which a position is being computed. They are averaged with
respect to the mean anomaly and include the effects of secular gravity,
atmospheric drag, and — in Deep Space mode — of those pertubations from
the Sun and Moon that SGP4 averages over an entire revolution of each of
those bodies. They omit both the shorter-term and longer-term periodic
pertubations from the Sun and Moon that SGP4 applies right before
computing each position.
| ``am`` — Average semi-major axis (earth radii).
| ``em`` — Average eccentricity.
| ``im`` — Average inclination (radians).
| ``Om`` — Average right ascension of ascending node (radians).
| ``om`` — Average argument of perigee (radians).
| ``mm`` — Average mean anomaly (radians).
| ``nm`` — Average mean motion (radians/minute).
*Gravity Model Parameters*
When the satellite record is initialized, your choice of gravity model
results in a slate of eight constants being copied in:
| ``tumin`` — Minutes in one “time unit”.
| ``xke`` — The reciprocal of ``tumin``.
| ``mu`` — Earth’s gravitational parameter (km³/s²).
| ``radiusearthkm`` — Radius of the earth (km).
| ``j2``, ``j3``, ``j4`` — Un-normalized zonal harmonic values J₂, J₃, and J₄.
| ``j3oj2`` — The ratio J₃/J₂.
Printing satellite attributes
-----------------------------
If you want to print out a satellite, this library provides a convenient
“attribute dump” routine that takes a satellite and generates lines that
list its attributes::
from sys import stdout
from sgp4.conveniences import dump_satrec
stdout.writelines(dump_satrec(satellite))
If you want to compare two satellites, then simply pass a second
argument; the second satellite’s attributes will be printed in a second
column next to those of the first. ::
stdout.writelines(dump_satrec(satellite, satellite2))
Validation against the official algorithm
-----------------------------------------
This implementation passes all of the automated tests in the August 2010
release of the reference implementation of SGP4 by Vallado et al., who
originally published their revision of SGP4 in 2006:
Vallado, David A., Paul Crawford, Richard Hujsak, and T.S. Kelso,
“Revisiting Spacetrack Report #3,” presented at the AIAA/AAS
Astrodynamics Specialist Conference, Keystone, CO, 2006 August
21–24.
If you would like to review the paper, it is `available online
`_. You can
always download the latest version of their code for comparison against
this Python module (or other implementations) at `AIAA-2006-6753.zip
`_.
For developers
--------------
Developers can check out this full project from GitHub:
https://github.com/brandon-rhodes/python-sgp4
To run its unit tests, install Python 2, Python 3, and the ``tox``
testing tool. The tests runing in Python 2 will exercise the fallback
pure-Python version of the routines, while Python 3 exercises the fast
new C++ accelerated code::
cd python-sgp4
tox
Legacy API
----------
Before this library pivoted to wrapping Vallado's official C++ code and
was operating in pure Python only, it had a slightly quirkier API, which
is still supported for compatibility with older clients. You can learn
about it by reading the documentation from version 1.4 or earlier:
https://pypi.org/project/sgp4/1.4/
Changelog
---------
2023-04-27 — 2.22
* Added a ``satnum_str`` attribute, exposing the fact that the C++ now
stores the satellite number as a string; and check that ``satnum`` is
never greater than 339999.
* Fixed the units of the ``nddot`` attribute when the value is loaded
from an OMM record. (Since the TLE computation itself ignores this
attribute, this did not affect any satellite positions.)
* Enhanced the fallback Python version of ``twoline2rv()`` to verify
that TLE lines are ASCII, and added documentation using it to
double-check TLEs that might suffer from non-ASCII characters.
* If the user doesn’t set a satellite’s ``classification``, it now
defaults to ``'U'`` for ‘unclassified’.
2022-04-06 — 2.21
* Added ``dump_satrec()`` to the ``sgp4.conveniences`` module.
* Fixed the ``Satrec`` attribute ``.error``, which was previously
building a nonsense integer from the wrong data in memory.
* Removed ``.whichconst`` from Python ``Satrec``, to help users avoid
writing code that will break when the C++ extension is available.
2021-07-01 — 2.20
* Taught ``sgp4init()`` to round both ``epochdays`` and ``jdsatepochF``
to the same 8 decimal places used for the date fraction in a TLE, if
the user-supplied ``epoch`` itself has 8 or fewer digits behind the
decimal point. This should make it easier to build satellites that
round-trip to TLE format with perfect accuracy.
* Fixed how ``export_tle()`` formats the BSTAR field when its value, if
written in scientific notation, has a positive exponent.
* Fixed the ``epochyr`` assigned by ``sgp4init()`` so years before 2000
have two digits instead of three (for example, so that 1980 produces
an ``epochyr`` of 80 instead of 980).
2021-04-22 — 2.19
* Extended the documentation on the Python Package Index and in the
module docstring so it lists every ``Satrec`` attribute that this
library exposes; even the more obscure ones might be useful to folks
working to analyze satellite orbits.
2021-03-08 — 2.18
* If a TLE satellite number lacks the required 5 digits,
``twoline2rv()`` now gives the underlying C++ library a little help so
it can still parse the classification and international designator
correctly.
* The ``Satrec`` attributes ``jdsatepoch``, ``jdsatepochF``,
``epochyr``, and ``epochdays`` are now writeable, so users can adjust
their values manually — which should make up for the fact that the
``sgp4init()`` method can’t set them with full floating point
precision.
| 2021-02-17 — 2.17 — Fixed where in the output array the ``sgp4_array()`` method writes NaN values when an SGP4 propagation fails.
| 2021-02-12 — 2.16 — Fixed ``days2mdhms()`` rounding to always match TLE epoch.
| 2021-01-08 — 2.15 — Fixed parsing of the ``satnum`` TLE field in the Python fallback code, when the field has a leading space; added OMM export routine.
| 2020-12-16 — 2.14 — New data formats: added OMM message support for both XML and CSV, and added support for the new Alpha-5 extension to TLE files.
| 2020-10-14 — 2.13 — Enhanced ``sgp4init()`` with custom code that also sets the ``epochdays`` and ``epochyr`` satellite attributes.
| 2020-05-28 — 2.12 — Moved the decision of whether to set the locale during ``twoline2rv()`` from import time to runtime, for users who change locales after their application is up and running.
| 2020-05-24 — 2.11 — Fixed a regression in how dates are split into hours, minutes, and seconds that would sometimes produce a time whose second=60, crashing the pure-Python version of the library.
| 2020-05-22 — 2.10 — Switch the locale temporarily to ``C`` during the C++ accelerated ``twoline2rv()``, since it does not protect its ``sscanf()`` calls from locales that, like German, expect comma decimal points instead of the period decimal points always used in a TLE.
| 2020-05-21 — 2.9 — Added ``sat_epoch_datetime()``, expanded documentation around converting a satellite epoch to a date and time, and started rounding the epoch to exactly the digits provided in the TLE; and removed the ``Satrec.epoch`` attribute from Python fallback code to better match the C++ version.
| 2020-05-07 — 2.8 — New function ``jday_datetime()`` is now available in the ``sgp4.conveniences`` module, thanks to Egemen Imre.
| 2020-04-24 — 2.7 — New method ``sgp4init()`` (thank you, Chris Lewicki!) is available.
| 2020-04-20 — 2.6 — New routine ``export_tle()`` (thank you, Egemen Imre!) is available. Improved how the accelerated C++ backend parses the ``intldesg`` string and the ``revnum`` integer.
| 2020-03-22 — 2.5 — Gave the new accelerated ``twoline2rv()`` an optional argument that lets the user choose a non-standard set of gravity constants.
| 2020-02-25 — 2.4 — Improved the ``jday()`` docstring; made the old legacy Python resilient if the day of the month is out-of-range (past the end of the month) in a TLE; and Mark Rutten fixed the C++ so it compiles on Windows!
| 2020-02-04 — 2.3 — Removed experimental code that caused performance problems for users with Numba installed.
| 2020-02-02 — 2.2 — A second release on Palindrome Day: fix the Satrec ``.epochyr`` attribute so it behaves the same way in Python as it does in the official C library, where it is only the last 2 digits of the year; and make ``.no`` available in the Python fallback case as well.
| 2020-02-02 — 2.1 — Add vectorized array method to Satrec object; add ``.no`` attribute to new Satrec object to support old code that has not migrated to the new name ``.no_kozai``; gave Python wrapper classes ``__slots__`` to avoid the expense of a per-object attribute dictionary.
| 2020-01-30 — 2.0 — Rewrite API to use genuine Vallado C++ code on those systems where it can be compiled; add accelerated vectorized array interface; make ``gstime()`` a public function; clarify format error message.
| 2015-01-15 — 1.4 — Display detailed help when TLE input does not match format.
| 2014-06-26 — 1.3 — Return ``(NaN,NaN,NaN)`` vectors on error and set ``.error_message``
| 2013-11-29 — 1.2 — Made ``epochyr`` 4 digits; add ``datetime`` for ``.epoch``
| 2012-11-22 — 1.1 — Python 3 compatibility; more documentation
| 2012-08-27 — 1.0 — Initial release
"""
__version__ = '2.22'
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/alpha5.py 0000644 0001751 0000173 00000001136 14422467341 014326 0 ustar 00runner docker """Alpha 5 encoding of satellite numbers to fit in 5 characters."""
def to_alpha5(n):
if n < 100000:
return '%05d' % n
if n > 339999:
raise ValueError('satellite number cannot exceed 339999,'
" whose Alpha 5 encoding is 'Z9999'")
i, n = divmod(n, 10000)
i += ord('A') - 10
if i >= ord('I'): i += 1
if i >= ord('O'): i += 1
return '%c%04d' % (i, n)
def from_alpha5(s):
if not s[0].isalpha():
return int(s)
c, s = s[0], s[1:]
n = ord(c) - ord('A') + 10
n -= c > 'I'
n -= c > 'O'
return n * 10000 + int(s)
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/api.py 0000644 0001751 0000173 00000001562 14422467341 013730 0 ustar 00runner docker """Public API that tries to import C++ module, but falls back to Python."""
__all__ = (
'SGP4_ERRORS', 'Satrec', 'SatrecArray', 'WGS72OLD', 'WGS72', 'WGS84',
'accelerated', 'jday', 'days2mdhms',
)
from .functions import jday, days2mdhms
SGP4_ERRORS = {
1: 'mean eccentricity is outside the range 0.0 to 1.0',
2: 'nm is less than zero',
3: 'perturbed eccentricity is outside the range 0.0 to 1.0',
4: 'semilatus rectum is less than zero',
5: '(error 5 no longer in use; it meant the satellite was underground)',
6: 'mrt is less than 1.0 which indicates the satellite has decayed',
}
try:
from .wrapper import Satrec, SatrecArray
accelerated = True
except ImportError:
from .model import Satrec, SatrecArray
from .model import WGS72OLD, WGS72, WGS84
accelerated = False
else:
from .vallado_cpp import WGS72OLD, WGS72, WGS84
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/conveniences.py 0000644 0001751 0000173 00000006707 14422467341 015644 0 ustar 00runner docker """Various conveniences.
Higher-level libraries like Skyfield that use this one usually have
their own date and time handling. But for folks using this library by
itself, native Python datetime handling could be convenient.
"""
import datetime as dt
import sgp4
from .functions import days2mdhms, jday
class _UTC(dt.tzinfo):
'UTC'
zero = dt.timedelta(0)
def __repr__(self):
return 'UTC'
def dst(self, datetime):
return self.zero
def tzname(self, datetime):
return 'UTC'
def utcoffset(self, datetime):
return self.zero
UTC = _UTC()
def jday_datetime(datetime):
"""Return two floats that, when added, produce the specified Julian date.
The first float returned gives the date, while the second float
provides an additional offset for the particular hour, minute, and
second of that date. Because the second float is much smaller in
magnitude it can, unlike the first float, be accurate down to very
small fractions of a second.
>>> jd, fr = jday(2020, 2, 11, 13, 57, 0)
>>> jd
2458890.5
>>> fr
0.58125
Note that the first float, which gives the moment of midnight that
commences the given calendar date, always carries the fraction
``.5`` because Julian dates begin and end at noon. This made Julian
dates more convenient for astronomers in Europe, by making the whole
night belong to a single Julian date.
The input is a native `datetime` object. Timezone of the input is
converted internally to UTC.
"""
u = datetime.astimezone(UTC)
year = u.year
mon = u.month
day = u.day
hr = u.hour
minute = u.minute
sec = u.second + u.microsecond * 1e-6
return jday(year, mon, day, hr, minute, sec)
def sat_epoch_datetime(sat):
"""Return the epoch of the given satellite as a Python datetime."""
year = sat.epochyr
year += 1900 + (year < 57) * 100
days = sat.epochdays
month, day, hour, minute, second = days2mdhms(year, days)
if month == 12 and day > 31: # for that time the ISS epoch was "Dec 32"
year += 1
month = 1
day -= 31
second, fraction = divmod(second, 1.0)
second = int(second)
micro = int(fraction * 1e6)
return dt.datetime(year, month, day, hour, minute, second, micro, UTC)
_ATTRIBUTES = None
def dump_satrec(sat, sat2=None):
"""Yield lines that list the attributes of one or two satellites."""
global _ATTRIBUTES
if _ATTRIBUTES is None:
_ATTRIBUTES = []
for line in sgp4.__doc__.splitlines():
if line.endswith('*'):
title = line.strip('*')
_ATTRIBUTES.append(title)
elif line.startswith('| ``'):
pieces = line.split('``')
_ATTRIBUTES.append(pieces[1])
i = 2
while pieces[i] == ', ':
_ATTRIBUTES.append(pieces[i+1])
i += 2
for item in _ATTRIBUTES:
if item[0].isupper():
title = item
yield '\n'
yield '# -------- {0} --------\n'.format(title)
else:
name = item
value = getattr(sat, item, '(not set)')
line = '{0} = {1!r}\n'.format(item, value)
if sat2 is not None:
value2 = getattr(sat2, name, '(not set)')
verdict = '==' if (value == value2) else '!='
line = '{0:39} {1} {2!r}\n'.format(line[:-1], verdict, value2)
yield line
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/earth_gravity.py 0000644 0001751 0000173 00000000567 14422467341 016033 0 ustar 00runner docker """Three earth-gravity models for use with SGP4."""
from collections import namedtuple
from sgp4.propagation import getgravconst
EarthGravity = namedtuple(
'EarthGravity',
'tumin mu radiusearthkm xke j2 j3 j4 j3oj2',
)
wgs72old = EarthGravity(*getgravconst('wgs72old'))
wgs72 = EarthGravity(*getgravconst('wgs72'))
wgs84 = EarthGravity(*getgravconst('wgs84'))
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/exporter.py 0000644 0001751 0000173 00000011245 14422467341 015026 0 ustar 00runner docker """Export orbit data to a Two-Line-Element representation.
Contributed by Egemen Imre https://github.com/egemenimre
"""
from math import pi
from sgp4.io import compute_checksum
from sgp4.conveniences import sat_epoch_datetime
# Define constants
_deg2rad = pi / 180.0 # 0.0174532925199433
_xpdotp = 1440.0 / (2.0 * pi) # 229.1831180523293
def export_tle(satrec):
"""Generate the TLE for a given `Satrec` object; returns two strings."""
# --------------------- Start generating line 1 ---------------------
# Build the list by appending successive items
pieces = ['1 ', satrec.satnum_str]
append = pieces.append
# Add classification code (use "U" if empty)
classification = getattr(satrec, 'classification', 'U')
append(classification.strip() or 'U')
append(' ')
# Add int'l designator and pad to 8 chars
intldesg = getattr(satrec, 'intldesg', '')
append('{0:8} '.format(intldesg))
# Add epoch year and days in YYDDD.DDDDDDDD format
epochyr = satrec.epochyr
# Undo non-standard 4-digit year for old satrec objects
epochyr %= 100
append(str(epochyr).zfill(2) + "{:012.8f}".format(satrec.epochdays) + " ")
# Add First Time Derivative of the Mean Motion (don't use "+")
append("{0: 8.8f}".format(satrec.ndot * (_xpdotp * 1440.0)).replace("0", "", 1) + " ")
# Add Second Time Derivative of Mean Motion
append(_abbreviate_rate(satrec.nddot * _xpdotp * 20736000.0, '-0'))
# Add BSTAR
append(_abbreviate_rate(satrec.bstar * 10.0, '+0'))
# Add Ephemeris Type and Element Number
ephtype = getattr(satrec, 'ephtype', 0)
elnum = getattr(satrec, 'elnum', 0)
append('{0} {1:4}'.format(ephtype, elnum))
# Join all the parts and add the Checksum
line1 = ''.join(pieces)
line1 += str(compute_checksum(line1))
# --------------------- Start generating line 2 ---------------------
# Reset the str array
pieces = ['2 ', satrec.satnum_str]
append = pieces.append
# Add the inclination (deg)
if not 0 <= satrec.inclo <= pi:
raise ValueError("Inclination must be between 0 and pi, got %r", satrec.inclo)
append(' {0:8.4f} '.format(satrec.inclo / _deg2rad))
# Add the RAAN (deg)
if not 0 <= satrec.nodeo <= 2 * pi:
raise ValueError("RAAN must be between 0 and 2 pi, got %r", satrec.nodeo)
append("{0:8.4f}".format(satrec.nodeo / _deg2rad).rjust(8, " ") + " ")
# Add the eccentricity (delete the leading zero an decimal point)
append("{0:8.7f}".format(satrec.ecco).replace("0.", "") + " ")
# Add the Argument of Perigee (deg)
if not 0 <= satrec.argpo <= 2 * pi:
raise ValueError("Argument of Perigee must be between 0 and 2 pi, got %r", satrec.argpo)
append("{0:8.4f}".format(satrec.argpo / _deg2rad).rjust(8, " ") + " ")
# Add the Mean Anomaly (deg)
if not 0 <= satrec.mo <= 2 * pi:
raise ValueError("Mean Anomaly must be between 0 and 2 pi, got %r", satrec.mo)
append("{0:8.4f}".format(satrec.mo / _deg2rad).rjust(8, " ") + " ")
# Add the Mean Motion (revs/day)
append("{0:11.8f}".format(satrec.no_kozai * _xpdotp).rjust(8, " "))
# Add the rev number at epoch
append(str(satrec.revnum).rjust(5))
# Join all the parts and add the Checksum
line2 = ''.join(pieces)
line2 += str(compute_checksum(line2))
return line1, line2
def _abbreviate_rate(value, zero_exponent_string):
return (
'{0: 4.4e} '.format(value)
.replace('.', '')
.replace('e+00', zero_exponent_string)
.replace('e-0', '-')
.replace('e+0', '+')
)
def export_omm(satrec, object_name):
launch_year = int(satrec.intldesg[:2])
launch_year += 1900 + (launch_year < 57) * 100
object_id = '{0}-{1}'.format(launch_year, satrec.intldesg[2:])
return {
"OBJECT_NAME": object_name,
"OBJECT_ID": object_id,
"CENTER_NAME": "EARTH",
"REF_FRAME": "TEME",
"TIME_SYSTEM": "UTC",
"MEAN_ELEMENT_THEORY": "SGP4",
"EPOCH": sat_epoch_datetime(satrec).strftime('%Y-%m-%dT%H:%M:%S.%f'),
"MEAN_MOTION": satrec.no_kozai * _xpdotp,
"ECCENTRICITY": satrec.ecco,
"INCLINATION": satrec.inclo / _deg2rad,
"RA_OF_ASC_NODE": satrec.nodeo / _deg2rad,
"ARG_OF_PERICENTER": satrec.argpo / _deg2rad,
"MEAN_ANOMALY": satrec.mo / _deg2rad,
"EPHEMERIS_TYPE": satrec.ephtype,
"CLASSIFICATION_TYPE": satrec.classification,
"NORAD_CAT_ID": satrec.satnum,
"ELEMENT_SET_NO": satrec.elnum,
"REV_AT_EPOCH": satrec.revnum,
"BSTAR": satrec.bstar,
"MEAN_MOTION_DOT": satrec.ndot * (_xpdotp * 1440.0),
"MEAN_MOTION_DDOT": satrec.nddot * (_xpdotp * 1440.0 * 1440),
}
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/ext.py 0000644 0001751 0000173 00000041574 14422467341 013766 0 ustar 00runner docker # -*- coding: utf-8 -*-
"""Utility routines from "sgp4ext.cpp"."""
from math import (acos, asinh, atan2, copysign, cos, fabs, fmod,
pi, sin, sinh, sqrt, tan)
from .functions import days2mdhms
undefined = None
"""
/* -----------------------------------------------------------------------------
*
* function mag
*
* this procedure finds the magnitude of a vector. the tolerance is set to
* 0.000001, thus the 1.0e-12 for the squared test of underflows.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec - vector
*
* outputs :
* vec - answer stored in fourth component
*
* locals :
* none.
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
"""
def mag(x):
return sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
"""
/* -----------------------------------------------------------------------------
*
* procedure cross
*
* this procedure crosses two vectors.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* outvec - vector result of a x b
*
* locals :
* none.
*
* coupling :
* mag magnitude of a vector
---------------------------------------------------------------------------- */
"""
def cross(vec1, vec2, outvec):
outvec[0]= vec1[1]*vec2[2] - vec1[2]*vec2[1];
outvec[1]= vec1[2]*vec2[0] - vec1[0]*vec2[2];
outvec[2]= vec1[0]*vec2[1] - vec1[1]*vec2[0];
"""
/* -----------------------------------------------------------------------------
*
* function dot
*
* this function finds the dot product of two vectors.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* dot - result
*
* locals :
* none.
*
* coupling :
* none.
*
* --------------------------------------------------------------------------- */
"""
def dot(x, y):
return (x[0]*y[0] + x[1]*y[1] + x[2]*y[2]);
"""
/* -----------------------------------------------------------------------------
*
* procedure angle
*
* this procedure calculates the angle between two vectors. the output is
* set to 999999.1 to indicate an undefined value. be sure to check for
* this at the output phase.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* theta - angle between the two vectors -pi to pi
*
* locals :
* temp - temporary real variable
*
* coupling :
* dot dot product of two vectors
* --------------------------------------------------------------------------- */
"""
def angle(vec1, vec2):
small = 0.00000001;
undefined = 999999.1;
magv1 = mag(vec1);
magv2 = mag(vec2);
if magv1*magv2 > small*small:
temp= dot(vec1,vec2) / (magv1*magv2);
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
return acos( temp );
else:
return undefined;
"""
/* -----------------------------------------------------------------------------
*
* function newtonnu
*
* this function solves keplers equation when the true anomaly is known.
* the mean and eccentric, parabolic, or hyperbolic anomaly is also found.
* the parabolic limit at 168° is arbitrary. the hyperbolic anomaly is also
* limited. the hyperbolic sine is used because it's not double valued.
*
* author : david vallado 719-573-2600 27 may 2002
*
* revisions
* vallado - fix small 24 sep 2002
*
* inputs description range / units
* ecc - eccentricity 0.0 to
* nu - true anomaly -2pi to 2pi rad
*
* outputs :
* e0 - eccentric anomaly 0.0 to 2pi rad 153.02 °
* m - mean anomaly 0.0 to 2pi rad 151.7425 °
*
* locals :
* e1 - eccentric anomaly, next value rad
* sine - sine of e
* cose - cosine of e
* ktr - index
*
* coupling :
* asinh - arc hyperbolic sine
*
* references :
* vallado 2007, 85, alg 5
* --------------------------------------------------------------------------- */
"""
def newtonnu(ecc, nu):
# --------------------- implementation ---------------------
e0= 999999.9;
m = 999999.9;
small = 0.00000001;
# --------------------------- circular ------------------------
if fabs(ecc) < small:
m = nu;
e0= nu;
else:
# ---------------------- elliptical -----------------------
if ecc < 1.0-small:
sine= ( sqrt( 1.0 -ecc*ecc ) * sin(nu) ) / ( 1.0 +ecc*cos(nu) );
cose= ( ecc + cos(nu) ) / ( 1.0 + ecc*cos(nu) );
e0 = atan2( sine,cose );
m = e0 - ecc*sin(e0);
else:
# -------------------- hyperbolic --------------------
if ecc > 1.0 + small:
if ecc > 1.0 and fabs(nu)+0.00001 < pi-acos(1.0 /ecc):
sine= ( sqrt( ecc*ecc-1.0 ) * sin(nu) ) / ( 1.0 + ecc*cos(nu) );
e0 = asinh( sine );
m = ecc*sinh(e0) - e0;
else:
# ----------------- parabolic ---------------------
if fabs(nu) < 168.0*pi/180.0:
e0= tan( nu*0.5 );
m = e0 + (e0*e0*e0)/3.0;
if ecc < 1.0:
m = fmod( m,2.0 *pi );
if m < 0.0:
m = m + 2.0 *pi;
e0 = fmod( e0,2.0 *pi );
return e0, m
"""
/* -----------------------------------------------------------------------------
*
* function rv2coe
*
* this function finds the classical orbital elements given the geocentric
* equatorial position and velocity vectors.
*
* author : david vallado 719-573-2600 21 jun 2002
*
* revisions
* vallado - fix special cases 5 sep 2002
* vallado - delete extra check in inclination code 16 oct 2002
* vallado - add constant file use 29 jun 2003
* vallado - add mu 2 apr 2007
*
* inputs description range / units
* r - ijk position vector km
* v - ijk velocity vector km / s
* mu - gravitational parameter km3 / s2
*
* outputs :
* p - semilatus rectum km
* a - semimajor axis km
* ecc - eccentricity
* incl - inclination 0.0 to pi rad
* omega - longitude of ascending node 0.0 to 2pi rad
* argp - argument of perigee 0.0 to 2pi rad
* nu - true anomaly 0.0 to 2pi rad
* m - mean anomaly 0.0 to 2pi rad
* arglat - argument of latitude (ci) 0.0 to 2pi rad
* truelon - true longitude (ce) 0.0 to 2pi rad
* lonper - longitude of periapsis (ee) 0.0 to 2pi rad
*
* locals :
* hbar - angular momentum h vector km2 / s
* ebar - eccentricity e vector
* nbar - line of nodes n vector
* c1 - v**2 - u/r
* rdotv - r dot v
* hk - hk unit vector
* sme - specfic mechanical energy km2 / s2
* i - index
* e - eccentric, parabolic,
* hyperbolic anomaly rad
* temp - temporary variable
* typeorbit - type of orbit ee, ei, ce, ci
*
* coupling :
* mag - magnitude of a vector
* cross - cross product of two vectors
* angle - find the angle between two vectors
* newtonnu - find the mean anomaly
*
* references :
* vallado 2007, 126, alg 9, ex 2-5
* --------------------------------------------------------------------------- */
"""
def rv2coe(r, v, mu):
hbar = [None, None, None]
nbar = [None, None, None]
ebar = [None, None, None]
typeorbit = [None, None, None];
twopi = 2.0 * pi;
halfpi = 0.5 * pi;
small = 0.00000001;
undefined = 999999.1;
infinite = 999999.9;
# ------------------------- implementation -----------------
magr = mag( r );
magv = mag( v );
# ------------------ find h n and e vectors ----------------
cross( r,v, hbar );
magh = mag( hbar );
if magh > small:
nbar[0]= -hbar[1];
nbar[1]= hbar[0];
nbar[2]= 0.0;
magn = mag( nbar );
c1 = magv*magv - mu /magr;
rdotv = dot( r,v );
for i in range(0, 3):
ebar[i]= (c1*r[i] - rdotv*v[i])/mu;
ecc = mag( ebar );
# ------------ find a e and semi-latus rectum ----------
sme= ( magv*magv*0.5 ) - ( mu /magr );
if fabs( sme ) > small:
a= -mu / (2.0 *sme);
else:
a= infinite;
p = magh*magh/mu;
# ----------------- find inclination -------------------
hk= hbar[2]/magh;
incl= acos( hk );
# -------- determine type of orbit for later use --------
# ------ elliptical, parabolic, hyperbolic inclined -------
typeorbit = 'ei'
if ecc < small:
# ---------------- circular equatorial ---------------
if incl < small or fabs(incl-pi) < small:
typeorbit = 'ce'
else:
# -------------- circular inclined ---------------
typeorbit = 'ci'
else:
# - elliptical, parabolic, hyperbolic equatorial --
if incl < small or fabs(incl-pi) < small:
typeorbit = 'ee'
# ---------- find longitude of ascending node ------------
if magn > small:
temp= nbar[0] / magn;
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
omega= acos( temp );
if nbar[1] < 0.0:
omega= twopi - omega;
else:
omega= undefined;
# ---------------- find argument of perigee ---------------
if typeorbit == 'ei':
argp = angle( nbar,ebar);
if ebar[2] < 0.0:
argp= twopi - argp;
else:
argp= undefined;
# ------------ find true anomaly at epoch -------------
if typeorbit[0] == 'e':
nu = angle( ebar,r);
if rdotv < 0.0:
nu= twopi - nu;
else:
nu= undefined;
# ---- find argument of latitude - circular inclined -----
if typeorbit == 'ci':
arglat = angle( nbar,r );
if r[2] < 0.0:
arglat= twopi - arglat;
m = arglat;
else:
arglat= undefined;
# -- find longitude of perigee - elliptical equatorial ----
if ecc > small and typeorbit == 'ee':
temp= ebar[0]/ecc;
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
lonper= acos( temp );
if ebar[1] < 0.0:
lonper= twopi - lonper;
if incl > halfpi:
lonper= twopi - lonper;
else:
lonper= undefined;
# -------- find true longitude - circular equatorial ------
if magr > small and typeorbit == 'ce':
temp= r[0]/magr;
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
truelon= acos( temp );
if r[1] < 0.0:
truelon= twopi - truelon;
if incl > halfpi:
truelon= twopi - truelon;
m = truelon;
else:
truelon= undefined;
# ------------ find mean anomaly for all orbits -----------
if typeorbit[0] == 'e':
e, m = newtonnu(ecc, nu);
else:
p = undefined;
a = undefined;
ecc = undefined;
incl = undefined;
omega= undefined;
argp = undefined;
nu = undefined;
m = undefined;
arglat = undefined;
truelon= undefined;
lonper = undefined;
return p, a, ecc, incl, omega, argp, nu, m, arglat, truelon, lonper
"""
/* -----------------------------------------------------------------------------
*
* procedure jday
*
* this procedure finds the julian date given the year, month, day, and time.
* the julian date is defined by each elapsed day since noon, jan 1, 4713 bc.
*
* algorithm : calculate the answer in one step for efficiency
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* year - year 1900 .. 2100
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - universal time hour 0 .. 23
* min - universal time min 0 .. 59
* sec - universal time sec 0.0 .. 59.999
*
* outputs :
* jd - julian date days from 4713 bc
*
* locals :
* none.
*
* coupling :
* none.
*
* references :
* vallado 2007, 189, alg 14, ex 3-14
*
* --------------------------------------------------------------------------- */
"""
def jday(year, mon, day, hr, minute, sec):
return (367.0 * year -
7.0 * (year + ((mon + 9.0) // 12.0)) * 0.25 // 1.0 +
275.0 * mon // 9.0 +
day + 1721013.5 +
((sec / 60.0 + minute) / 60.0 + hr) / 24.0 # ut in days
# - 0.5*sgn(100.0*year + mon - 190002.5) + 0.5;
)
"""
/* -----------------------------------------------------------------------------
*
* procedure invjday
*
* this procedure finds the year, month, day, hour, minute and second
* given the julian date. tu can be ut1, tdt, tdb, etc.
*
* algorithm : set up starting values
* find leap year - use 1900 because 2000 is a leap year
* find the elapsed days through the year in a loop
* call routine to find each individual value
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* jd - julian date days from 4713 bc
*
* outputs :
* year - year 1900 .. 2100
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - hour 0 .. 23
* min - minute 0 .. 59
* sec - second 0.0 .. 59.999
*
* locals :
* days - day of year plus fractional
* portion of a day days
* tu - julian centuries from 0 h
* jan 0, 1900
* temp - temporary double values
* leapyrs - number of leap years from 1900
*
* coupling :
* days2mdhms - finds month, day, hour, minute and second given days and year
*
* references :
* vallado 2007, 208, alg 22, ex 3-13
* --------------------------------------------------------------------------- */
"""
def invjday(jd):
# --------------- find year and days of the year ---------------
temp = jd - 2415019.5;
tu = temp / 365.25;
year = 1900 + int(tu // 1.0);
leapyrs = int(((year - 1901) * 0.25) // 1.0);
# optional nudge by 8.64x10-7 sec to get even outputs
days = temp - ((year - 1900) * 365.0 + leapyrs) + 0.00000000001;
# ------------ check for case of beginning of a year -----------
if (days < 1.0):
year = year - 1;
leapyrs = int(((year - 1901) * 0.25) // 1.0);
days = temp - ((year - 1900) * 365.0 + leapyrs);
# ----------------- find remaing data -------------------------
mon, day, hr, minute, sec = days2mdhms(year, days, None);
sec = sec - 0.00000086400;
return year, mon, day, hr, minute, sec
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/functions.py 0000644 0001751 0000173 00000006104 14422467341 015164 0 ustar 00runner docker """General-purpose routines.
It seemed a shame for the ``api`` module to have to import large legacy
modules to offer simple date handling, so this small module holds the
routines instead.
"""
def jday(year, mon, day, hr, minute, sec):
"""Return two floats that, when added, produce the specified Julian date.
The first float returned gives the date, while the second float
provides an additional offset for the particular hour, minute, and
second of that date. Because the second float is much smaller in
magnitude it can, unlike the first float, be accurate down to very
small fractions of a second.
>>> jd, fr = jday(2020, 2, 11, 13, 57, 0)
>>> jd
2458890.5
>>> fr
0.58125
Note that the first float, which gives the moment of midnight that
commences the given calendar date, always carries the fraction
``.5`` because Julian dates begin and end at noon. This made
Julian dates more convenient for astronomers in Europe, by making
the whole night belong to a single Julian date.
This function is a simple translation to Python of the C++ routine
``jday()`` in Vallado's ``SGP4.cpp``.
"""
jd = (367.0 * year
- 7 * (year + ((mon + 9) // 12.0)) * 0.25 // 1.0
+ 275 * mon / 9.0 // 1.0
+ day
+ 1721013.5)
fr = (sec + minute * 60.0 + hr * 3600.0) / 86400.0;
return jd, fr
def days2mdhms(year, days, round_to_microsecond=6):
"""Convert a float point number of days into the year into date and time.
Given the integer year plus the "day of the year" where 1.0 means
the beginning of January 1, 2.0 means the beginning of January 2,
and so forth, return the Gregorian calendar month, day, hour,
minute, and floating point seconds.
>>> days2mdhms(2000, 1.0) # January 1
(1, 1, 0, 0, 0.0)
>>> days2mdhms(2000, 32.0) # February 1
(2, 1, 0, 0, 0.0)
>>> days2mdhms(2000, 366.0) # December 31, since 2000 was a leap year
(12, 31, 0, 0, 0.0)
The floating point seconds are rounded to an even number of
microseconds if ``round_to_microsecond`` is true.
"""
second = days * 86400.0
if round_to_microsecond:
second = round(second, round_to_microsecond)
minute, second = divmod(second, 60.0)
if round_to_microsecond:
second = round(second, round_to_microsecond)
minute = int(minute)
hour, minute = divmod(minute, 60)
day_of_year, hour = divmod(hour, 24)
is_leap = year % 400 == 0 or (year % 4 == 0 and year % 100 != 0)
month, day = _day_of_year_to_month_day(day_of_year, is_leap)
if month == 13: # behave like the original in case of overflow
month = 12
day += 31
return month, day, int(hour), int(minute), second
def _day_of_year_to_month_day(day_of_year, is_leap):
"""Core logic for turning days into months, for easy testing."""
february_bump = (2 - is_leap) * (day_of_year >= 60 + is_leap)
august = day_of_year >= 215
month, day = divmod(2 * (day_of_year - 1 + 30 * august + february_bump), 61)
month += 1 - august
day //= 2
day += 1
return month, day
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/io.py 0000644 0001751 0000173 00000024542 14422467341 013571 0 ustar 00runner docker """Read the TLE earth satellite file format.
This is a minimally-edited copy of "sgp4io.cpp".
"""
import re
from datetime import datetime
from math import pi, pow
from sgp4.ext import days2mdhms, invjday, jday
from sgp4.propagation import sgp4init
INT_RE = re.compile(r'[+-]?\d*')
FLOAT_RE = re.compile(r'[+-]?\d*(\.\d*)?')
LINE1 = '1 NNNNNC NNNNNAAA NNNNN.NNNNNNNN +.NNNNNNNN +NNNNN-N +NNNNN-N N NNNNN'
LINE2 = '2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN'
error_message = """TLE format error
The Two-Line Element (TLE) format was designed for punch cards, and so
is very strict about the position of every period, space, and digit.
Your line does not quite match. Here is the official format for line {0}
with an N where each digit should go, followed by the line you provided:
{1}
{2}"""
"""
/* ----------------------------------------------------------------
*
* sgp4io.cpp
*
* this file contains a function to read two line element sets. while
* not formerly part of the sgp4 mathematical theory, it is
* required for practical implemenation.
*
* companion code for
* fundamentals of astrodynamics and applications
* 2007
* by david vallado
*
* (w) 719-573-2600, email dvallado@agi.com
*
* current :
* 27 Aug 10 david vallado
* fix input format and delete unused variables in twoline2rv
* changes :
* 3 sep 08 david vallado
* add operationmode for afspc (a) or improved (i)
* 9 may 07 david vallado
* fix year correction to 57
* 27 mar 07 david vallado
* misc fixes to manual inputs
* 14 aug 06 david vallado
* original baseline
* ---------------------------------------------------------------- */
"""
"""
/* -----------------------------------------------------------------------------
*
* function twoline2rv
*
* this function converts the two line element set character string data to
* variables and initializes the sgp4 variables. several intermediate varaibles
* and quantities are determined. note that the result is a structure so multiple
* satellites can be processed simultaneously without having to reinitialize. the
* verification mode is an important option that permits quick checks of any
* changes to the underlying technical theory. this option works using a
* modified tle file in which the start, stop, and delta time values are
* included at the end of the second line of data. this only works with the
* verification mode. the catalog mode simply propagates from -1440 to 1440 min
* from epoch and is useful when performing entire catalog runs.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs :
* longstr1 - first line of the tle
* longstr2 - second line of the tle
* typerun - type of run verification 'v', catalog 'c',
* manual 'm'
* typeinput - type of manual input mfe 'm', epoch 'e', dayofyr 'd'
* opsmode - mode of operation afspc or improved 'a', 'i'
* whichconst - which set of constants to use 72, 84
*
* outputs :
* satrec - structure containing all the sgp4 satellite information
*
* coupling :
* getgravconst-
* days2mdhms - conversion of days to month, day, hour, minute, second
* jday - convert day month year hour minute second into julian date
* sgp4init - initialize the sgp4 variables
*
* references :
* norad spacetrack report #3
* vallado, crawford, hujsak, kelso 2006
--------------------------------------------------------------------------- */
"""
def twoline2rv(longstr1, longstr2, whichconst, opsmode='i', satrec=None):
"""Return a Satellite imported from two lines of TLE data.
Provide the two TLE lines as strings `longstr1` and `longstr2`,
and select which standard set of gravitational constants you want
by providing `gravity_constants`:
`sgp4.earth_gravity.wgs72` - Standard WGS 72 model
`sgp4.earth_gravity.wgs84` - More recent WGS 84 model
`sgp4.earth_gravity.wgs72old` - Legacy support for old SGP4 behavior
Normally, computations are made using various recent improvements
to the algorithm. If you want to turn some of these off and go
back into "opsmode" mode, then set `opsmode` to `a`.
"""
deg2rad = pi / 180.0; # 0.0174532925199433
xpdotp = 1440.0 / (2.0 *pi); # 229.1831180523293
# For compatibility with our 1.x API, build an old Satellite object
# if the caller fails to supply a satrec. In that case we perform
# the necessary import here to avoid an import loop.
if satrec is None:
from sgp4.model import Satellite
satrec = Satellite()
satrec.error = 0;
line = longstr1.rstrip()
try:
longstr1.encode('ascii')
longstr2.encode('ascii')
except UnicodeEncodeError:
r1 = repr(longstr1)[1:-1]
r2 = repr(longstr2)[1:-1]
raise ValueError('your TLE lines are broken because they contain'
' non-ASCII characters:\n\n%s\n%s' % (r1, r2))
if (len(line) >= 64 and
line.startswith('1 ') and
line[8] == ' ' and
line[23] == '.' and
line[32] == ' ' and
line[34] == '.' and
line[43] == ' ' and
line[52] == ' ' and
line[61] == ' ' and
line[63] == ' '):
satrec.satnum_str = line[2:7]
satrec.classification = line[7] or 'U'
satrec.intldesg = line[9:17].rstrip()
two_digit_year = int(line[18:20])
satrec.epochdays = float(line[20:32])
satrec.ndot = float(line[33:43])
satrec.nddot = float(line[44] + '.' + line[45:50])
nexp = int(line[50:52])
satrec.bstar = float(line[53] + '.' + line[54:59])
ibexp = int(line[59:61])
satrec.ephtype = line[62]
satrec.elnum = int(line[64:68])
else:
raise ValueError(error_message.format(1, LINE1, line))
line = longstr2.rstrip()
if (len(line) >= 69 and
line.startswith('2 ') and
line[7] == ' ' and
line[11] == '.' and
line[16] == ' ' and
line[20] == '.' and
line[25] == ' ' and
line[33] == ' ' and
line[37] == '.' and
line[42] == ' ' and
line[46] == '.' and
line[51] == ' '):
if satrec.satnum_str != line[2:7]:
raise ValueError('Object numbers in lines 1 and 2 do not match')
satrec.inclo = float(line[8:16])
satrec.nodeo = float(line[17:25])
satrec.ecco = float('0.' + line[26:33].replace(' ', '0'))
satrec.argpo = float(line[34:42])
satrec.mo = float(line[43:51])
satrec.no_kozai = float(line[52:63])
satrec.revnum = line[63:68]
#except (AssertionError, IndexError, ValueError):
else:
raise ValueError(error_message.format(2, LINE2, line))
# ---- find no, ndot, nddot ----
satrec.no_kozai = satrec.no_kozai / xpdotp; # rad/min
satrec.nddot= satrec.nddot * pow(10.0, nexp);
satrec.bstar= satrec.bstar * pow(10.0, ibexp);
# ---- convert to sgp4 units ----
satrec.ndot = satrec.ndot / (xpdotp*1440.0); # ? * minperday
satrec.nddot= satrec.nddot / (xpdotp*1440.0*1440);
# ---- find standard orbital elements ----
satrec.inclo = satrec.inclo * deg2rad;
satrec.nodeo = satrec.nodeo * deg2rad;
satrec.argpo = satrec.argpo * deg2rad;
satrec.mo = satrec.mo * deg2rad;
"""
// ----------------------------------------------------------------
// find sgp4epoch time of element set
// remember that sgp4 uses units of days from 0 jan 1950 (sgp4epoch)
// and minutes from the epoch (time)
// ----------------------------------------------------------------
// ---------------- temp fix for years from 1957-2056 -------------------
// --------- correct fix will occur when year is 4-digit in tle ---------
"""
if two_digit_year < 57:
year = two_digit_year + 2000;
else:
year = two_digit_year + 1900;
mon,day,hr,minute,sec = days2mdhms(year, satrec.epochdays);
sec_whole, sec_fraction = divmod(sec, 1.0)
satrec.epochyr = year
satrec.jdsatepoch = jday(year,mon,day,hr,minute,sec);
try:
satrec.epoch = datetime(year, mon, day, hr, minute, int(sec_whole),
int(sec_fraction * 1000000.0 // 1.0))
except ValueError:
# Sometimes a TLE says something like "2019 + 366.82137887 days"
# which would be December 32nd which causes a ValueError.
year, mon, day, hr, minute, sec = invjday(satrec.jdsatepoch)
satrec.epoch = datetime(year, mon, day, hr, minute, int(sec_whole),
int(sec_fraction * 1000000.0 // 1.0))
# ---------------- initialize the orbit at sgp4epoch -------------------
sgp4init(whichconst, opsmode, satrec.satnum_str, satrec.jdsatepoch-2433281.5, satrec.bstar,
satrec.ndot, satrec.nddot, satrec.ecco, satrec.argpo, satrec.inclo, satrec.mo,
satrec.no_kozai, satrec.nodeo, satrec)
return satrec
def verify_checksum(*lines):
"""Verify the checksum of one or more TLE lines.
Raises `ValueError` if any of the lines fails its checksum, and
includes the failing line in the error message.
"""
for line in lines:
checksum = line[68:69]
if not checksum.isdigit():
continue
checksum = int(checksum)
computed = compute_checksum(line)
if checksum != computed:
complaint = ('TLE line gives its checksum as {}'
' but in fact tallies to {}:\n{}')
raise ValueError(complaint.format(checksum, computed, line))
def fix_checksum(line):
"""Return a new copy of the TLE `line`, with the correct checksum appended.
This discards any existing checksum at the end of the line, if a
checksum is already present.
"""
return line[:68].ljust(68) + str(compute_checksum(line))
def compute_checksum(line):
"""Compute the TLE checksum for the given line."""
return sum((int(c) if c.isdigit() else c == '-') for c in line[0:68]) % 10
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/model.py 0000644 0001751 0000173 00000016502 14422467341 014257 0 ustar 00runner docker """The Satellite class."""
from sgp4.alpha5 import from_alpha5
from sgp4.earth_gravity import wgs72old, wgs72, wgs84
from sgp4.ext import invjday, jday
from sgp4.io import twoline2rv
from sgp4.propagation import sgp4, sgp4init
WGS72OLD = 0
WGS72 = 1
WGS84 = 2
gravity_constants = wgs72old, wgs72, wgs84 # indexed using enum values above
minutes_per_day = 1440.
class Satrec(object):
"""Slow Python-only version of the satellite object."""
# Approximate the behavior of the C-accelerated class by locking
# down attribute access, to avoid folks accidentally writing code
# against this class and adding extra attributes, then moving to a
# computer where the C-accelerated class is used and having their
# code suddenly produce errors.
__slots__ = (
'Om', 'a', 'alta', 'altp', 'am', 'argpdot', 'argpo', 'atime', 'aycof',
'bstar', 'cc1', 'cc4', 'cc5', 'classification', 'con41', 'd2', 'd2201',
'd2211', 'd3', 'd3210', 'd3222', 'd4', 'd4410', 'd4422', 'd5220',
'd5232', 'd5421', 'd5433', 'dedt', 'del1', 'del2', 'del3', 'delmo',
'didt', 'dmdt', 'dnodt', 'domdt', 'e3', 'ecco', 'ee2', 'elnum', 'em',
'ephtype', 'epoch', 'epochdays', 'epochyr', 'error', 'error_message',
'eta', 'gsto', 'im', 'inclo', 'init', 'intldesg', 'irez', 'isimp',
'j2', 'j3', 'j3oj2', 'j4', 'jdsatepoch', 'mdot', 'method', 'mm', 'mo',
'mu', 'nddot', 'ndot', 'nm', 'no_kozai', 'no_unkozai', 'nodecf',
'nodedot', 'nodeo', 'om', 'omgcof', 'operationmode', 'peo', 'pgho',
'pho', 'pinco', 'plo', 'radiusearthkm', 'revnum', 'satnum_str', 'se2',
'se3', 'sgh2', 'sgh3', 'sgh4', 'sh2', 'sh3', 'si2', 'si3', 'sinmao',
'sl2', 'sl3', 'sl4', 't', 't2cof', 't3cof', 't4cof', 't5cof', 'tumin',
'x1mth2', 'x7thm1', 'xfact', 'xgh2', 'xgh3', 'xgh4',
'xh2', 'xh3', 'xi2', 'xi3', 'xke', 'xl2', 'xl3', 'xl4', 'xlamo',
'xlcof', 'xli', 'xmcof', 'xni', 'zmol', 'zmos',
'jdsatepochF'
)
array = None # replaced, if needed, with NumPy array()
@property
def no(self):
return self.no_kozai
@property
def satnum(self):
return from_alpha5(self.satnum_str)
@classmethod
def twoline2rv(cls, line1, line2, whichconst=WGS72):
whichconst = gravity_constants[whichconst]
self = cls()
twoline2rv(line1, line2, whichconst, 'i', self)
# Expose the same attribute types as the C++ code.
self.ephtype = int(self.ephtype.strip() or '0')
self.revnum = int(self.revnum)
# Install a fancy split JD of the kind the C++ natively supports.
# We rebuild it from the TLE year and day to maintain precision.
year = self.epochyr
days, fraction = divmod(self.epochdays, 1.0)
self.jdsatepoch = year * 365 + (year - 1) // 4 + days + 1721044.5
self.jdsatepochF = round(fraction, 8) # exact number of digits in TLE
# Remove the legacy datetime "epoch", which is not provided by
# the C++ version of the object.
del self.epoch
# Undo my non-standard 4-digit year
self.epochyr %= 100
return self
def sgp4init(self, whichconst, opsmode, satnum, epoch, bstar,
ndot, nddot, ecco, argpo, inclo, mo, no_kozai, nodeo):
whichconst = gravity_constants[whichconst]
whole, fraction = divmod(epoch, 1.0)
whole_jd = whole + 2433281.5
# Go out on a limb: if `epoch` has no decimal digits past the 8
# decimal places stored in a TLE, then assume the user is trying
# to specify an exact decimal fraction.
if round(epoch, 8) == epoch:
fraction = round(fraction, 8)
self.jdsatepoch = whole_jd
self.jdsatepochF = fraction
y, m, d, H, M, S = invjday(whole_jd)
jan0 = jday(y, 1, 0, 0, 0, 0.0)
self.epochyr = y % 100
self.epochdays = whole_jd - jan0 + fraction
self.classification = 'U'
sgp4init(whichconst, opsmode, satnum, epoch, bstar, ndot, nddot,
ecco, argpo, inclo, mo, no_kozai, nodeo, self)
def sgp4(self, jd, fr):
tsince = ((jd - self.jdsatepoch) * minutes_per_day +
(fr - self.jdsatepochF) * minutes_per_day)
r, v = sgp4(self, tsince)
return self.error, r, v
def sgp4_tsince(self, tsince):
r, v = sgp4(self, tsince)
return self.error, r, v
def sgp4_array(self, jd, fr):
"""Compute positions and velocities for the times in a NumPy array.
Given NumPy arrays ``jd`` and ``fr`` of the same length that
supply the whole part and the fractional part of one or more
Julian dates, return a tuple ``(e, r, v)`` of three vectors:
* ``e``: nonzero for any dates that produced errors, 0 otherwise.
* ``r``: position vectors in kilometers.
* ``v``: velocity vectors in kilometers per second.
"""
# Import NumPy the first time sgp4_array() is called.
array = self.array
if array is None:
from numpy import array
Satrec.array = array
results = []
z = list(zip(jd, fr))
for jd_i, fr_i in z:
results.append(self.sgp4(jd_i, fr_i))
elist, rlist, vlist = zip(*results)
e = array(elist)
r = array(rlist)
v = array(vlist)
r.shape = v.shape = len(jd), 3
return e, r, v
class SatrecArray(object):
"""Slow Python-only version of the satellite array."""
__slots__ = ('_satrecs',)
array = None # replaced with NumPy array(), if the user tries calling
def __init__(self, satrecs):
self._satrecs = satrecs
# Import NumPy the first time a SatrecArray is instantiated.
if self.array is None:
from numpy import array
SatrecArray.array = array
def sgp4(self, jd, fr):
"""Compute positions and velocities for the satellites in this array.
Given NumPy scalars or arrays ``jd`` and ``fr`` supplying the
whole part and the fractional part of one or more Julian dates,
return a tuple ``(e, r, v)`` of three vectors that are each as
long as ``jd`` and ``fr``:
* ``e``: nonzero for any dates that produced errors, 0 otherwise.
* ``r``: (x,y,z) position vector in kilometers.
* ``v``: (dx,dy,dz) velocity vector in kilometers per second.
"""
results = []
z = list(zip(jd, fr))
for satrec in self._satrecs:
for jd_i, fr_i in z:
results.append(satrec.sgp4(jd_i, fr_i))
elist, rlist, vlist = zip(*results)
e = self.array(elist)
r = self.array(rlist)
v = self.array(vlist)
jdlen = len(jd)
mylen = len(self._satrecs)
e.shape = (mylen, jdlen)
r.shape = v.shape = (mylen, jdlen, 3)
return e, r, v
class Satellite(object):
"""The old Satellite object, for compatibility with sgp4 1.x."""
jdsatepochF = 0.0 # for compatibility with new Satrec; makes tests simpler
def propagate(self, year, month=1, day=1, hour=0, minute=0, second=0.0):
"""Return a position and velocity vector for a given date and time."""
j = jday(year, month, day, hour, minute, second)
m = (j - self.jdsatepoch) * minutes_per_day
r, v = sgp4(self, m)
return r, v
no = Satrec.no
satnum = Satrec.satnum
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/omm.py 0000644 0001751 0000173 00000003664 14422467341 013754 0 ustar 00runner docker """Support for the new Orbit Mean-Elements Message format for TLE data."""
import csv
import xml.etree.ElementTree as ET
from datetime import datetime
from math import pi
from sgp4.api import WGS72
def parse_csv(file):
return csv.DictReader(file)
def parse_xml(file):
root = ET.parse(file).getroot()
for segment in root.findall('.//segment'):
metadata = segment.find('metadata')
data = segment.find('data')
meanElements = data.find('meanElements')
tleParameters = data.find('tleParameters')
fields = {}
for element in metadata, meanElements, tleParameters:
fields.update((field.tag, field.text) for field in element)
yield fields
_epoch0 = datetime(1949, 12, 31)
_to_radians = pi / 180.0
_ndot_units = 1036800.0 / pi # See SGP4.cpp for details.
_nddot_units = 2985984000.0 / 2.0 / pi # See SGP4.cpp for details.
def initialize(sat, fields):
sat.classification = fields['CLASSIFICATION_TYPE']
sat.intldesg = fields['OBJECT_ID'][2:].replace('-', '')
sat.ephtype = int(fields['EPHEMERIS_TYPE'])
sat.elnum = int(fields['ELEMENT_SET_NO'])
sat.revnum = int(fields['REV_AT_EPOCH'])
epoch_datetime = datetime.strptime(fields['EPOCH'], '%Y-%m-%dT%H:%M:%S.%f')
epoch = (epoch_datetime - _epoch0).total_seconds() / 86400.0
argpo = float(fields['ARG_OF_PERICENTER']) * _to_radians
bstar = float(fields['BSTAR'])
ecco = float(fields['ECCENTRICITY'])
inclo = float(fields['INCLINATION']) * _to_radians
mo = float(fields['MEAN_ANOMALY']) * _to_radians
nddot = float(fields['MEAN_MOTION_DDOT']) / _nddot_units
ndot = float(fields['MEAN_MOTION_DOT']) / _ndot_units
no_kozai = float(fields['MEAN_MOTION']) / 720.0 * pi
nodeo = float(fields['RA_OF_ASC_NODE']) * _to_radians
satnum = int(fields['NORAD_CAT_ID'])
sat.sgp4init(WGS72, 'i', satnum, epoch, bstar, ndot, nddot, ecco,
argpo, inclo, mo, no_kozai, nodeo)
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/propagation.py 0000644 0001751 0000173 00000221401 14422467341 015476 0 ustar 00runner docker """The sgp4 procedures for analytical propagation of a satellite.
I have made the rather unorthodox decision to leave as much of this C++
code alone as possible: if a line of code would run without change in
Python, then I refused to re-indent it or remove its terminal semicolon,
so that in the future it will be easier to keep updating this file as
the original author's C++ continues to improve. Thus, 5-space
indentation (!) prevails in this file.
I have even kept all of the C++ block comments (by turning them into
Python string constants) to make this easier to navigate and maintain,
as well as to make it more informative for people who encounter this
code for the first time here in its Python form.
| - Brandon Rhodes
| Common Grounds Coffee House, Bluffton, Ohio
| On a very hot August day in 2012
"""
from math import atan2, cos, fabs, pi, sin, sqrt
from sgp4.alpha5 import to_alpha5
deg2rad = pi / 180.0;
_nan = float('NaN')
false = (_nan, _nan, _nan)
true = True
twopi = 2.0 * pi
"""
/* ----------------------------------------------------------------
*
* sgp4unit.cpp
*
* this file contains the sgp4 procedures for analytical propagation
* of a satellite. the code was originally released in the 1980 and 1986
* spacetrack papers. a detailed discussion of the theory and history
* may be found in the 2006 aiaa paper by vallado, crawford, hujsak,
* and kelso.
*
* companion code for
* fundamentals of astrodynamics and applications
* 2013
* by david vallado
*
* (w) 719-573-2600, email dvallado@agi.com, davallado@gmail.com
*
* current :
* 7 dec 15 david vallado
* fix jd, jdfrac
* changes :
* 3 nov 14 david vallado
* update to msvs2013 c++
* 30 aug 10 david vallado
* delete unused variables in initl
* replace pow integer 2, 3 with multiplies for speed
* 3 nov 08 david vallado
* put returns in for error codes
* 29 sep 08 david vallado
* fix atime for faster operation in dspace
* add operationmode for afspc (a) or improved (i)
* performance mode
* 16 jun 08 david vallado
* update small eccentricity check
* 16 nov 07 david vallado
* misc fixes for better compliance
* 20 apr 07 david vallado
* misc fixes for constants
* 11 aug 06 david vallado
* chg lyddane choice back to strn3, constants, misc doc
* 15 dec 05 david vallado
* misc fixes
* 26 jul 05 david vallado
* fixes for paper
* note that each fix is preceded by a
* comment with "sgp4fix" and an explanation of
* what was changed
* 10 aug 04 david vallado
* 2nd printing baseline working
* 14 may 01 david vallado
* 2nd edition baseline
* 80 norad
* original baseline
* ---------------------------------------------------------------- */
"""
"""
/* -----------------------------------------------------------------------------
*
* procedure dpper
*
* this procedure provides deep space long period periodic contributions
* to the mean elements. by design, these periodics are zero at epoch.
* this used to be dscom which included initialization, but it's really a
* recurring function.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* e3 -
* ee2 -
* peo -
* pgho -
* pho -
* pinco -
* plo -
* se2 , se3 , sgh2, sgh3, sgh4, sh2, sh3, si2, si3, sl2, sl3, sl4 -
* t -
* xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
* zmol -
* zmos -
* ep - eccentricity 0.0 - 1.0
* inclo - inclination - needed for lyddane modification
* nodep - right ascension of ascending node
* argpp - argument of perigee
* mp - mean anomaly
*
* outputs :
* ep - eccentricity 0.0 - 1.0
* inclp - inclination
* nodep - right ascension of ascending node
* argpp - argument of perigee
* mp - mean anomaly
*
* locals :
* alfdp -
* betdp -
* cosip , sinip , cosop , sinop ,
* dalf -
* dbet -
* dls -
* f2, f3 -
* pe -
* pgh -
* ph -
* pinc -
* pl -
* sel , ses , sghl , sghs , shl , shs , sil , sinzf , sis ,
* sll , sls
* xls -
* xnoh -
* zf -
* zm -
*
* coupling :
* none.
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def _dpper(satrec, inclo, init, ep, inclp, nodep, argpp, mp, opsmode):
# Copy satellite attributes into local variables for convenience
# and symmetry in writing formulae.
e3 = satrec.e3
ee2 = satrec.ee2
peo = satrec.peo
pgho = satrec.pgho
pho = satrec.pho
pinco = satrec.pinco
plo = satrec.plo
se2 = satrec.se2
se3 = satrec.se3
sgh2 = satrec.sgh2
sgh3 = satrec.sgh3
sgh4 = satrec.sgh4
sh2 = satrec.sh2
sh3 = satrec.sh3
si2 = satrec.si2
si3 = satrec.si3
sl2 = satrec.sl2
sl3 = satrec.sl3
sl4 = satrec.sl4
t = satrec.t
xgh2 = satrec.xgh2
xgh3 = satrec.xgh3
xgh4 = satrec.xgh4
xh2 = satrec.xh2
xh3 = satrec.xh3
xi2 = satrec.xi2
xi3 = satrec.xi3
xl2 = satrec.xl2
xl3 = satrec.xl3
xl4 = satrec.xl4
zmol = satrec.zmol
zmos = satrec.zmos
# ---------------------- constants -----------------------------
zns = 1.19459e-5;
zes = 0.01675;
znl = 1.5835218e-4;
zel = 0.05490;
# --------------- calculate time varying periodics -----------
zm = zmos + zns * t;
# be sure that the initial call has time set to zero
if init == 'y':
zm = zmos;
zf = zm + 2.0 * zes * sin(zm);
sinzf = sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * cos(zf);
ses = se2* f2 + se3 * f3;
sis = si2 * f2 + si3 * f3;
sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf;
sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf;
shs = sh2 * f2 + sh3 * f3;
zm = zmol + znl * t;
if init == 'y':
zm = zmol;
zf = zm + 2.0 * zel * sin(zm);
sinzf = sin(zf);
f2 = 0.5 * sinzf * sinzf - 0.25;
f3 = -0.5 * sinzf * cos(zf);
sel = ee2 * f2 + e3 * f3;
sil = xi2 * f2 + xi3 * f3;
sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf;
sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf;
shll = xh2 * f2 + xh3 * f3;
pe = ses + sel;
pinc = sis + sil;
pl = sls + sll;
pgh = sghs + sghl;
ph = shs + shll;
if init == 'n':
pe = pe - peo;
pinc = pinc - pinco;
pl = pl - plo;
pgh = pgh - pgho;
ph = ph - pho;
inclp = inclp + pinc;
ep = ep + pe;
sinip = sin(inclp);
cosip = cos(inclp);
"""
/* ----------------- apply periodics directly ------------ */
// sgp4fix for lyddane choice
// strn3 used original inclination - this is technically feasible
// gsfc used perturbed inclination - also technically feasible
// probably best to readjust the 0.2 limit value and limit discontinuity
// 0.2 rad = 11.45916 deg
// use next line for original strn3 approach and original inclination
// if (inclo >= 0.2)
// use next line for gsfc version and perturbed inclination
"""
if inclp >= 0.2:
ph /= sinip
pgh -= cosip * ph
argpp += pgh
nodep += ph
mp += pl
else:
# ---- apply periodics with lyddane modification ----
sinop = sin(nodep);
cosop = cos(nodep);
alfdp = sinip * sinop;
betdp = sinip * cosop;
dalf = ph * cosop + pinc * cosip * sinop;
dbet = -ph * sinop + pinc * cosip * cosop;
alfdp = alfdp + dalf;
betdp = betdp + dbet;
nodep = nodep % twopi if nodep >= 0.0 else -(-nodep % twopi)
# sgp4fix for afspc written intrinsic functions
# nodep used without a trigonometric function ahead
if nodep < 0.0 and opsmode == 'a':
nodep = nodep + twopi;
xls = mp + argpp + pl + pgh + (cosip - pinc * sinip) * nodep
xnoh = nodep;
nodep = atan2(alfdp, betdp);
# sgp4fix for afspc written intrinsic functions
# nodep used without a trigonometric function ahead
if nodep < 0.0 and opsmode == 'a':
nodep = nodep + twopi;
if fabs(xnoh - nodep) > pi:
if nodep < xnoh:
nodep = nodep + twopi;
else:
nodep = nodep - twopi;
mp += pl
argpp = xls - mp - cosip * nodep;
return ep, inclp, nodep, argpp, mp
"""
/*-----------------------------------------------------------------------------
*
* procedure dscom
*
* this procedure provides deep space common items used by both the secular
* and periodics subroutines. input is provided as shown. this routine
* used to be called dpper, but the functions inside weren't well organized.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* epoch -
* ep - eccentricity
* argpp - argument of perigee
* tc -
* inclp - inclination
* nodep - right ascension of ascending node
* np - mean motion
*
* outputs :
* sinim , cosim , sinomm , cosomm , snodm , cnodm
* day -
* e3 -
* ee2 -
* em - eccentricity
* emsq - eccentricity squared
* gam -
* peo -
* pgho -
* pho -
* pinco -
* plo -
* rtemsq -
* se2, se3 -
* sgh2, sgh3, sgh4 -
* sh2, sh3, si2, si3, sl2, sl3, sl4 -
* s1, s2, s3, s4, s5, s6, s7 -
* ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3 -
* sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33 -
* xgh2, xgh3, xgh4, xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
* nm - mean motion
* z1, z2, z3, z11, z12, z13, z21, z22, z23, z31, z32, z33 -
* zmol -
* zmos -
*
* locals :
* a1, a2, a3, a4, a5, a6, a7, a8, a9, a10 -
* betasq -
* cc -
* ctem, stem -
* x1, x2, x3, x4, x5, x6, x7, x8 -
* xnodce -
* xnoi -
* zcosg , zsing , zcosgl , zsingl , zcosh , zsinh , zcoshl , zsinhl ,
* zcosi , zsini , zcosil , zsinil ,
* zx -
* zy -
*
* coupling :
* none.
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def _dscom(
epoch, ep, argpp, tc, inclp,
nodep, np,
e3, ee2,
peo, pgho, pho,
pinco, plo, se2, se3,
sgh2, sgh3, sgh4, sh2, sh3,
si2, si3, sl2, sl3, sl4,
xgh2, xgh3, xgh4, xh2,
xh3, xi2, xi3, xl2, xl3,
xl4, zmol, zmos,
):
# -------------------------- constants -------------------------
zes = 0.01675;
zel = 0.05490;
c1ss = 2.9864797e-6;
c1l = 4.7968065e-7;
zsinis = 0.39785416;
zcosis = 0.91744867;
zcosgs = 0.1945905;
zsings = -0.98088458;
# --------------------- local variables ------------------------
nm = np;
em = ep;
snodm = sin(nodep);
cnodm = cos(nodep);
sinomm = sin(argpp);
cosomm = cos(argpp);
sinim = sin(inclp);
cosim = cos(inclp);
emsq = em * em;
betasq = 1.0 - emsq;
rtemsq = sqrt(betasq);
# ----------------- initialize lunar solar terms ---------------
peo = 0.0;
pinco = 0.0;
plo = 0.0;
pgho = 0.0;
pho = 0.0;
day = epoch + 18261.5 + tc / 1440.0;
xnodce = (4.5236020 - 9.2422029e-4 * day) % twopi
stem = sin(xnodce);
ctem = cos(xnodce);
zcosil = 0.91375164 - 0.03568096 * ctem;
zsinil = sqrt(1.0 - zcosil * zcosil);
zsinhl = 0.089683511 * stem / zsinil;
zcoshl = sqrt(1.0 - zsinhl * zsinhl);
gam = 5.8351514 + 0.0019443680 * day;
zx = 0.39785416 * stem / zsinil;
zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
zx = atan2(zx, zy);
zx = gam + zx - xnodce;
zcosgl = cos(zx);
zsingl = sin(zx);
# ------------------------- do solar terms ---------------------
zcosg = zcosgs;
zsing = zsings;
zcosi = zcosis;
zsini = zsinis;
zcosh = cnodm;
zsinh = snodm;
cc = c1ss;
xnoi = 1.0 / nm;
for lsflg in 1, 2:
a1 = zcosg * zcosh + zsing * zcosi * zsinh;
a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
a8 = zsing * zsini;
a9 = zsing * zsinh + zcosg * zcosi * zcosh;
a10 = zcosg * zsini;
a2 = cosim * a7 + sinim * a8;
a4 = cosim * a9 + sinim * a10;
a5 = -sinim * a7 + cosim * a8;
a6 = -sinim * a9 + cosim * a10;
x1 = a1 * cosomm + a2 * sinomm;
x2 = a3 * cosomm + a4 * sinomm;
x3 = -a1 * sinomm + a2 * cosomm;
x4 = -a3 * sinomm + a4 * cosomm;
x5 = a5 * sinomm;
x6 = a6 * sinomm;
x7 = a5 * cosomm;
x8 = a6 * cosomm;
z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * emsq;
z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * emsq;
z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * emsq;
z11 = -6.0 * a1 * a5 + emsq * (-24.0 * x1 * x7-6.0 * x3 * x5);
z12 = -6.0 * (a1 * a6 + a3 * a5) + emsq * \
(-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
z13 = -6.0 * a3 * a6 + emsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
z21 = 6.0 * a2 * a5 + emsq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
z22 = 6.0 * (a4 * a5 + a2 * a6) + emsq * \
(24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
z23 = 6.0 * a4 * a6 + emsq * (24.0 * x2 * x6 - 6.0 * x4 * x8);
z1 = z1 + z1 + betasq * z31;
z2 = z2 + z2 + betasq * z32;
z3 = z3 + z3 + betasq * z33;
s3 = cc * xnoi;
s2 = -0.5 * s3 / rtemsq;
s4 = s3 * rtemsq;
s1 = -15.0 * em * s4;
s5 = x1 * x3 + x2 * x4;
s6 = x2 * x3 + x1 * x4;
s7 = x2 * x4 - x1 * x3;
# ----------------------- do lunar terms -------------------
if lsflg == 1:
ss1 = s1;
ss2 = s2;
ss3 = s3;
ss4 = s4;
ss5 = s5;
ss6 = s6;
ss7 = s7;
sz1 = z1;
sz2 = z2;
sz3 = z3;
sz11 = z11;
sz12 = z12;
sz13 = z13;
sz21 = z21;
sz22 = z22;
sz23 = z23;
sz31 = z31;
sz32 = z32;
sz33 = z33;
zcosg = zcosgl;
zsing = zsingl;
zcosi = zcosil;
zsini = zsinil;
zcosh = zcoshl * cnodm + zsinhl * snodm;
zsinh = snodm * zcoshl - cnodm * zsinhl;
cc = c1l;
zmol = (4.7199672 + 0.22997150 * day - gam) % twopi
zmos = (6.2565837 + 0.017201977 * day) % twopi
# ------------------------ do solar terms ----------------------
se2 = 2.0 * ss1 * ss6;
se3 = 2.0 * ss1 * ss7;
si2 = 2.0 * ss2 * sz12;
si3 = 2.0 * ss2 * (sz13 - sz11);
sl2 = -2.0 * ss3 * sz2;
sl3 = -2.0 * ss3 * (sz3 - sz1);
sl4 = -2.0 * ss3 * (-21.0 - 9.0 * emsq) * zes;
sgh2 = 2.0 * ss4 * sz32;
sgh3 = 2.0 * ss4 * (sz33 - sz31);
sgh4 = -18.0 * ss4 * zes;
sh2 = -2.0 * ss2 * sz22;
sh3 = -2.0 * ss2 * (sz23 - sz21);
# ------------------------ do lunar terms ----------------------
ee2 = 2.0 * s1 * s6;
e3 = 2.0 * s1 * s7;
xi2 = 2.0 * s2 * z12;
xi3 = 2.0 * s2 * (z13 - z11);
xl2 = -2.0 * s3 * z2;
xl3 = -2.0 * s3 * (z3 - z1);
xl4 = -2.0 * s3 * (-21.0 - 9.0 * emsq) * zel;
xgh2 = 2.0 * s4 * z32;
xgh3 = 2.0 * s4 * (z33 - z31);
xgh4 = -18.0 * s4 * zel;
xh2 = -2.0 * s2 * z22;
xh3 = -2.0 * s2 * (z23 - z21);
return (
snodm, cnodm, sinim, cosim, sinomm,
cosomm,day, e3, ee2, em,
emsq, gam, peo, pgho, pho,
pinco, plo, rtemsq, se2, se3,
sgh2, sgh3, sgh4, sh2, sh3,
si2, si3, sl2, sl3, sl4,
s1, s2, s3, s4, s5,
s6, s7, ss1, ss2, ss3,
ss4, ss5, ss6, ss7, sz1,
sz2, sz3, sz11, sz12, sz13,
sz21, sz22, sz23, sz31, sz32,
sz33, xgh2, xgh3, xgh4, xh2,
xh3, xi2, xi3, xl2, xl3,
xl4, nm, z1, z2, z3,
z11, z12, z13, z21, z22,
z23, z31, z32, z33, zmol,
zmos
)
"""
/*-----------------------------------------------------------------------------
*
* procedure dsinit
*
* this procedure provides deep space contributions to mean motion dot due
* to geopotential resonance with half day and one day orbits.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* cosim, sinim-
* emsq - eccentricity squared
* argpo - argument of perigee
* s1, s2, s3, s4, s5 -
* ss1, ss2, ss3, ss4, ss5 -
* sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33 -
* t - time
* tc -
* gsto - greenwich sidereal time rad
* mo - mean anomaly
* mdot - mean anomaly dot (rate)
* no - mean motion
* nodeo - right ascension of ascending node
* nodedot - right ascension of ascending node dot (rate)
* xpidot -
* z1, z3, z11, z13, z21, z23, z31, z33 -
* eccm - eccentricity
* argpm - argument of perigee
* inclm - inclination
* mm - mean anomaly
* xn - mean motion
* nodem - right ascension of ascending node
*
* outputs :
* em - eccentricity
* argpm - argument of perigee
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* nodem - right ascension of ascending node
* irez - flag for resonance 0-none, 1-one day, 2-half day
* atime -
* d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -
* dedt -
* didt -
* dmdt -
* dndt -
* dnodt -
* domdt -
* del1, del2, del3 -
* ses , sghl , sghs , sgs , shl , shs , sis , sls
* theta -
* xfact -
* xlamo -
* xli -
* xni
*
* locals :
* ainv2 -
* aonv -
* cosisq -
* eoc -
* f220, f221, f311, f321, f322, f330, f441, f442, f522, f523, f542, f543 -
* g200, g201, g211, g300, g310, g322, g410, g422, g520, g521, g532, g533 -
* sini2 -
* temp -
* temp1 -
* theta -
* xno2 -
*
* coupling :
* getgravconst
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def _dsinit(
# sgp4fix no longer needed pass in xke
# whichconst,
xke,
cosim, emsq, argpo, s1, s2,
s3, s4, s5, sinim, ss1,
ss2, ss3, ss4, ss5, sz1,
sz3, sz11, sz13, sz21, sz23,
sz31, sz33, t, tc, gsto,
mo, mdot, no, nodeo, nodedot,
xpidot, z1, z3, z11, z13,
z21, z23, z31, z33, ecco,
eccsq, em, argpm, inclm, mm,
nm, nodem,
irez,
atime, d2201, d2211, d3210, d3222,
d4410, d4422, d5220, d5232, d5421,
d5433, dedt, didt, dmdt,
dnodt, domdt, del1, del2, del3,
xfact, xlamo, xli, xni,
):
q22 = 1.7891679e-6;
q31 = 2.1460748e-6;
q33 = 2.2123015e-7;
root22 = 1.7891679e-6;
root44 = 7.3636953e-9;
root54 = 2.1765803e-9;
rptim = 4.37526908801129966e-3; # equates to 7.29211514668855e-5 rad/sec
root32 = 3.7393792e-7;
root52 = 1.1428639e-7;
x2o3 = 2.0 / 3.0;
znl = 1.5835218e-4;
zns = 1.19459e-5;
# sgp4fix identify constants and allow alternate values
# just xke is used here so pass it in rather than have multiple calls
# xke = whichconst.xke
# -------------------- deep space initialization ------------
irez = 0;
if 0.0034906585 < nm < 0.0052359877:
irez = 1;
if 8.26e-3 <= nm <= 9.24e-3 and em >= 0.5:
irez = 2;
# ------------------------ do solar terms -------------------
ses = ss1 * zns * ss5;
sis = ss2 * zns * (sz11 + sz13);
sls = -zns * ss3 * (sz1 + sz3 - 14.0 - 6.0 * emsq);
sghs = ss4 * zns * (sz31 + sz33 - 6.0);
shs = -zns * ss2 * (sz21 + sz23);
# sgp4fix for 180 deg incl
if inclm < 5.2359877e-2 or inclm > pi - 5.2359877e-2:
shs = 0.0;
if sinim != 0.0:
shs = shs / sinim;
sgs = sghs - cosim * shs;
# ------------------------- do lunar terms ------------------
dedt = ses + s1 * znl * s5;
didt = sis + s2 * znl * (z11 + z13);
dmdt = sls - znl * s3 * (z1 + z3 - 14.0 - 6.0 * emsq);
sghl = s4 * znl * (z31 + z33 - 6.0);
shll = -znl * s2 * (z21 + z23);
# sgp4fix for 180 deg incl
if inclm < 5.2359877e-2 or inclm > pi - 5.2359877e-2:
shll = 0.0;
domdt = sgs + sghl;
dnodt = shs;
if sinim != 0.0:
domdt = domdt - cosim / sinim * shll;
dnodt = dnodt + shll / sinim;
# ----------- calculate deep space resonance effects --------
dndt = 0.0;
theta = (gsto + tc * rptim) % twopi
em = em + dedt * t;
inclm = inclm + didt * t;
argpm = argpm + domdt * t;
nodem = nodem + dnodt * t;
mm = mm + dmdt * t;
"""
// sgp4fix for negative inclinations
// the following if statement should be commented out
//if (inclm < 0.0)
// {
// inclm = -inclm;
// argpm = argpm - pi;
// nodem = nodem + pi;
// }
"""
# -------------- initialize the resonance terms -------------
if irez != 0:
aonv = pow(nm / xke, x2o3);
# ---------- geopotential resonance for 12 hour orbits ------
if irez == 2:
cosisq = cosim * cosim;
emo = em;
em = ecco;
emsqo = emsq;
emsq = eccsq;
eoc = em * emsq;
g201 = -0.306 - (em - 0.64) * 0.440;
if em <= 0.65:
g211 = 3.616 - 13.2470 * em + 16.2900 * emsq;
g310 = -19.302 + 117.3900 * em - 228.4190 * emsq + 156.5910 * eoc;
g322 = -18.9068 + 109.7927 * em - 214.6334 * emsq + 146.5816 * eoc;
g410 = -41.122 + 242.6940 * em - 471.0940 * emsq + 313.9530 * eoc;
g422 = -146.407 + 841.8800 * em - 1629.014 * emsq + 1083.4350 * eoc;
g520 = -532.114 + 3017.977 * em - 5740.032 * emsq + 3708.2760 * eoc;
else:
g211 = -72.099 + 331.819 * em - 508.738 * emsq + 266.724 * eoc;
g310 = -346.844 + 1582.851 * em - 2415.925 * emsq + 1246.113 * eoc;
g322 = -342.585 + 1554.908 * em - 2366.899 * emsq + 1215.972 * eoc;
g410 = -1052.797 + 4758.686 * em - 7193.992 * emsq + 3651.957 * eoc;
g422 = -3581.690 + 16178.110 * em - 24462.770 * emsq + 12422.520 * eoc;
if em > 0.715:
g520 =-5149.66 + 29936.92 * em - 54087.36 * emsq + 31324.56 * eoc;
else:
g520 = 1464.74 - 4664.75 * em + 3763.64 * emsq;
if em < 0.7:
g533 = -919.22770 + 4988.6100 * em - 9064.7700 * emsq + 5542.21 * eoc;
g521 = -822.71072 + 4568.6173 * em - 8491.4146 * emsq + 5337.524 * eoc;
g532 = -853.66600 + 4690.2500 * em - 8624.7700 * emsq + 5341.4 * eoc;
else:
g533 =-37995.780 + 161616.52 * em - 229838.20 * emsq + 109377.94 * eoc;
g521 =-51752.104 + 218913.95 * em - 309468.16 * emsq + 146349.42 * eoc;
g532 =-40023.880 + 170470.89 * em - 242699.48 * emsq + 115605.82 * eoc;
sini2= sinim * sinim;
f220 = 0.75 * (1.0 + 2.0 * cosim+cosisq);
f221 = 1.5 * sini2;
f321 = 1.875 * sinim * (1.0 - 2.0 * cosim - 3.0 * cosisq);
f322 = -1.875 * sinim * (1.0 + 2.0 * cosim - 3.0 * cosisq);
f441 = 35.0 * sini2 * f220;
f442 = 39.3750 * sini2 * sini2;
f522 = 9.84375 * sinim * (sini2 * (1.0 - 2.0 * cosim- 5.0 * cosisq) +
0.33333333 * (-2.0 + 4.0 * cosim + 6.0 * cosisq) );
f523 = sinim * (4.92187512 * sini2 * (-2.0 - 4.0 * cosim +
10.0 * cosisq) + 6.56250012 * (1.0+2.0 * cosim - 3.0 * cosisq));
f542 = 29.53125 * sinim * (2.0 - 8.0 * cosim+cosisq *
(-12.0 + 8.0 * cosim + 10.0 * cosisq));
f543 = 29.53125 * sinim * (-2.0 - 8.0 * cosim+cosisq *
(12.0 + 8.0 * cosim - 10.0 * cosisq));
xno2 = nm * nm;
ainv2 = aonv * aonv;
temp1 = 3.0 * xno2 * ainv2;
temp = temp1 * root22;
d2201 = temp * f220 * g201;
d2211 = temp * f221 * g211;
temp1 = temp1 * aonv;
temp = temp1 * root32;
d3210 = temp * f321 * g310;
d3222 = temp * f322 * g322;
temp1 = temp1 * aonv;
temp = 2.0 * temp1 * root44;
d4410 = temp * f441 * g410;
d4422 = temp * f442 * g422;
temp1 = temp1 * aonv;
temp = temp1 * root52;
d5220 = temp * f522 * g520;
d5232 = temp * f523 * g532;
temp = 2.0 * temp1 * root54;
d5421 = temp * f542 * g521;
d5433 = temp * f543 * g533;
xlamo = (mo + nodeo + nodeo-theta - theta) % twopi
xfact = mdot + dmdt + 2.0 * (nodedot + dnodt - rptim) - no;
em = emo;
emsq = emsqo;
# ---------------- synchronous resonance terms --------------
if irez == 1:
g200 = 1.0 + emsq * (-2.5 + 0.8125 * emsq);
g310 = 1.0 + 2.0 * emsq;
g300 = 1.0 + emsq * (-6.0 + 6.60937 * emsq);
f220 = 0.75 * (1.0 + cosim) * (1.0 + cosim);
f311 = 0.9375 * sinim * sinim * (1.0 + 3.0 * cosim) - 0.75 * (1.0 + cosim);
f330 = 1.0 + cosim;
f330 = 1.875 * f330 * f330 * f330;
del1 = 3.0 * nm * nm * aonv * aonv;
del2 = 2.0 * del1 * f220 * g200 * q22;
del3 = 3.0 * del1 * f330 * g300 * q33 * aonv;
del1 = del1 * f311 * g310 * q31 * aonv;
xlamo = (mo + nodeo + argpo - theta) % twopi
xfact = mdot + xpidot - rptim + dmdt + domdt + dnodt - no;
# ------------ for sgp4, initialize the integrator ----------
xli = xlamo;
xni = no;
atime = 0.0;
nm = no + dndt;
return (
em, argpm, inclm, mm,
nm, nodem,
irez, atime,
d2201, d2211, d3210, d3222,
d4410, d4422, d5220, d5232,
d5421, d5433, dedt, didt,
dmdt, dndt, dnodt, domdt,
del1, del2, del3, xfact,
xlamo, xli, xni,
)
"""
/*-----------------------------------------------------------------------------
*
* procedure dspace
*
* this procedure provides deep space contributions to mean elements for
* perturbing third body. these effects have been averaged over one
* revolution of the sun and moon. for earth resonance effects, the
* effects have been averaged over no revolutions of the satellite.
* (mean motion)
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -
* dedt -
* del1, del2, del3 -
* didt -
* dmdt -
* dnodt -
* domdt -
* irez - flag for resonance 0-none, 1-one day, 2-half day
* argpo - argument of perigee
* argpdot - argument of perigee dot (rate)
* t - time
* tc -
* gsto - gst
* xfact -
* xlamo -
* no - mean motion
* atime -
* em - eccentricity
* ft -
* argpm - argument of perigee
* inclm - inclination
* xli -
* mm - mean anomaly
* xni - mean motion
* nodem - right ascension of ascending node
*
* outputs :
* atime -
* em - eccentricity
* argpm - argument of perigee
* inclm - inclination
* xli -
* mm - mean anomaly
* xni -
* nodem - right ascension of ascending node
* dndt -
* nm - mean motion
*
* locals :
* delt -
* ft -
* theta -
* x2li -
* x2omi -
* xl -
* xldot -
* xnddt -
* xndt -
* xomi -
*
* coupling :
* none -
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def _dspace(
irez,
d2201, d2211, d3210, d3222, d4410,
d4422, d5220, d5232, d5421, d5433,
dedt, del1, del2, del3, didt,
dmdt, dnodt, domdt, argpo, argpdot,
t, tc, gsto, xfact, xlamo,
no,
atime, em, argpm, inclm, xli,
mm, xni, nodem, nm,
):
fasx2 = 0.13130908;
fasx4 = 2.8843198;
fasx6 = 0.37448087;
g22 = 5.7686396;
g32 = 0.95240898;
g44 = 1.8014998;
g52 = 1.0508330;
g54 = 4.4108898;
rptim = 4.37526908801129966e-3; # equates to 7.29211514668855e-5 rad/sec
stepp = 720.0;
stepn = -720.0;
step2 = 259200.0;
# ----------- calculate deep space resonance effects -----------
dndt = 0.0;
theta = (gsto + tc * rptim) % twopi
em = em + dedt * t;
inclm = inclm + didt * t;
argpm = argpm + domdt * t;
nodem = nodem + dnodt * t;
mm = mm + dmdt * t;
"""
// sgp4fix for negative inclinations
// the following if statement should be commented out
// if (inclm < 0.0)
// {
// inclm = -inclm;
// argpm = argpm - pi;
// nodem = nodem + pi;
// }
/* - update resonances : numerical (euler-maclaurin) integration - */
/* ------------------------- epoch restart ---------------------- */
// sgp4fix for propagator problems
// the following integration works for negative time steps and periods
// the specific changes are unknown because the original code was so convoluted
// sgp4fix take out atime = 0.0 and fix for faster operation
"""
ft = 0.0;
if irez != 0:
# sgp4fix streamline check
if atime == 0.0 or t * atime <= 0.0 or fabs(t) < fabs(atime):
atime = 0.0;
xni = no;
xli = xlamo;
# sgp4fix move check outside loop
if t > 0.0:
delt = stepp;
else:
delt = stepn;
iretn = 381; # added for do loop
# iret = 0; # added for loop
while iretn == 381:
# ------------------- dot terms calculated -------------
# ----------- near - synchronous resonance terms -------
if irez != 2:
xndt = del1 * sin(xli - fasx2) + del2 * sin(2.0 * (xli - fasx4)) + \
del3 * sin(3.0 * (xli - fasx6));
xldot = xni + xfact;
xnddt = del1 * cos(xli - fasx2) + \
2.0 * del2 * cos(2.0 * (xli - fasx4)) + \
3.0 * del3 * cos(3.0 * (xli - fasx6));
xnddt = xnddt * xldot;
else:
# --------- near - half-day resonance terms --------
xomi = argpo + argpdot * atime;
x2omi = xomi + xomi;
x2li = xli + xli;
xndt = (d2201 * sin(x2omi + xli - g22) + d2211 * sin(xli - g22) +
d3210 * sin(xomi + xli - g32) + d3222 * sin(-xomi + xli - g32)+
d4410 * sin(x2omi + x2li - g44)+ d4422 * sin(x2li - g44) +
d5220 * sin(xomi + xli - g52) + d5232 * sin(-xomi + xli - g52)+
d5421 * sin(xomi + x2li - g54) + d5433 * sin(-xomi + x2li - g54));
xldot = xni + xfact;
xnddt = (d2201 * cos(x2omi + xli - g22) + d2211 * cos(xli - g22) +
d3210 * cos(xomi + xli - g32) + d3222 * cos(-xomi + xli - g32) +
d5220 * cos(xomi + xli - g52) + d5232 * cos(-xomi + xli - g52) +
2.0 * (d4410 * cos(x2omi + x2li - g44) +
d4422 * cos(x2li - g44) + d5421 * cos(xomi + x2li - g54) +
d5433 * cos(-xomi + x2li - g54)));
xnddt = xnddt * xldot;
# ----------------------- integrator -------------------
# sgp4fix move end checks to end of routine
if fabs(t - atime) >= stepp:
# iret = 0;
iretn = 381;
else:
ft = t - atime;
iretn = 0;
if iretn == 381:
xli = xli + xldot * delt + xndt * step2;
xni = xni + xndt * delt + xnddt * step2;
atime = atime + delt;
nm = xni + xndt * ft + xnddt * ft * ft * 0.5;
xl = xli + xldot * ft + xndt * ft * ft * 0.5;
if irez != 1:
mm = xl - 2.0 * nodem + 2.0 * theta;
dndt = nm - no;
else:
mm = xl - nodem - argpm + theta;
dndt = nm - no;
nm = no + dndt;
return (
atime, em, argpm, inclm, xli,
mm, xni, nodem, dndt, nm,
)
"""
/*-----------------------------------------------------------------------------
*
* procedure initl
*
* this procedure initializes the spg4 propagator. all the initialization is
* consolidated here instead of having multiple loops inside other routines.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* satn - satellite number - not needed, placed in satrec
* xke - reciprocal of tumin
* j2 - j2 zonal harmonic
* ecco - eccentricity 0.0 - 1.0
* epoch - epoch time in days from jan 0, 1950. 0 hr
* inclo - inclination of satellite
* no - mean motion of satellite
*
* outputs :
* ainv - 1.0 / a
* ao - semi major axis
* con41 -
* con42 - 1.0 - 5.0 cos(i)
* cosio - cosine of inclination
* cosio2 - cosio squared
* eccsq - eccentricity squared
* method - flag for deep space 'd', 'n'
* omeosq - 1.0 - ecco * ecco
* posq - semi-parameter squared
* rp - radius of perigee
* rteosq - square root of (1.0 - ecco*ecco)
* sinio - sine of inclination
* gsto - gst at time of observation rad
* no - mean motion of satellite
*
* locals :
* ak -
* d1 -
* del -
* adel -
* po -
*
* coupling :
* getgravconst- no longer used
* gstime - find greenwich sidereal time from the julian date
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def _initl(
# not needeed. included in satrec if needed later
# satn,
# sgp4fix assin xke and j2
# whichconst,
xke, j2,
ecco, epoch, inclo, no,
method,
opsmode,
):
# sgp4fix use old way of finding gst
# ----------------------- earth constants ----------------------
# sgp4fix identify constants and allow alternate values
# only xke and j2 are used here so pass them in directly
# tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 = whichconst
x2o3 = 2.0 / 3.0;
# ------------- calculate auxillary epoch quantities ----------
eccsq = ecco * ecco;
omeosq = 1.0 - eccsq;
rteosq = sqrt(omeosq);
cosio = cos(inclo);
cosio2 = cosio * cosio;
# ------------------ un-kozai the mean motion -----------------
ak = pow(xke / no, x2o3);
d1 = 0.75 * j2 * (3.0 * cosio2 - 1.0) / (rteosq * omeosq);
del_ = d1 / (ak * ak);
adel = ak * (1.0 - del_ * del_ - del_ *
(1.0 / 3.0 + 134.0 * del_ * del_ / 81.0));
del_ = d1/(adel * adel);
no = no / (1.0 + del_);
ao = pow(xke / no, x2o3);
sinio = sin(inclo);
po = ao * omeosq;
con42 = 1.0 - 5.0 * cosio2;
con41 = -con42-cosio2-cosio2;
ainv = 1.0 / ao;
posq = po * po;
rp = ao * (1.0 - ecco);
method = 'n';
# sgp4fix modern approach to finding sidereal time
if opsmode == 'a':
# sgp4fix use old way of finding gst
# count integer number of days from 0 jan 1970
ts70 = epoch - 7305.0;
ds70 = (ts70 + 1.0e-8) // 1.0;
tfrac = ts70 - ds70;
# find greenwich location at epoch
c1 = 1.72027916940703639e-2;
thgr70= 1.7321343856509374;
fk5r = 5.07551419432269442e-15;
c1p2p = c1 + twopi;
gsto = (thgr70 + c1*ds70 + c1p2p*tfrac + ts70*ts70*fk5r) % twopi
if gsto < 0.0:
gsto = gsto + twopi;
else:
gsto = _gstime(epoch + 2433281.5);
return (
no,
method,
ainv, ao, con41, con42, cosio,
cosio2,eccsq, omeosq, posq,
rp, rteosq,sinio , gsto,
)
"""
/*-----------------------------------------------------------------------------
*
* procedure sgp4init
*
* this procedure initializes variables for sgp4.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* opsmode - mode of operation afspc or improved 'a', 'i'
* whichconst - which set of constants to use 72, 84
* satn - satellite number
* bstar - sgp4 type drag coefficient kg/m2er
* ecco - eccentricity
* epoch - epoch time in days from jan 0, 1950. 0 hr
* argpo - argument of perigee (output if ds)
* inclo - inclination
* mo - mean anomaly (output if ds)
* no - mean motion
* nodeo - right ascension of ascending node
*
* outputs :
* satrec - common values for subsequent calls
* return code - non-zero on error.
* 1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
* 2 - mean motion less than 0.0
* 3 - pert elements, ecc < 0.0 or ecc > 1.0
* 4 - semi-latus rectum < 0.0
* 5 - epoch elements are sub-orbital
* 6 - satellite has decayed
*
* locals :
* cnodm , snodm , cosim , sinim , cosomm , sinomm
* cc1sq , cc2 , cc3
* coef , coef1
* cosio4 -
* day -
* dndt -
* em - eccentricity
* emsq - eccentricity squared
* eeta -
* etasq -
* gam -
* argpm - argument of perigee
* nodem -
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* perige - perigee
* pinvsq -
* psisq -
* qzms24 -
* rtemsq -
* s1, s2, s3, s4, s5, s6, s7 -
* sfour -
* ss1, ss2, ss3, ss4, ss5, ss6, ss7 -
* sz1, sz2, sz3
* sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33 -
* tc -
* temp -
* temp1, temp2, temp3 -
* tsi -
* xpidot -
* xhdot1 -
* z1, z2, z3 -
* z11, z12, z13, z21, z22, z23, z31, z32, z33 -
*
* coupling :
* getgravconst-
* initl -
* dscom -
* dpper -
* dsinit -
* sgp4 -
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def sgp4init(
whichconst, opsmode, satn, epoch,
xbstar, xndot, xnddot, xecco, xargpo,
xinclo, xmo, xno_kozai,
xnodeo, satrec,
):
"""
/* ------------------------ initialization --------------------- */
// sgp4fix divisor for divide by zero check on inclination
// the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
// 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency
"""
temp4 = 1.5e-12;
# ----------- set all near earth variables to zero ------------
satrec.isimp = 0; satrec.method = 'n'; satrec.aycof = 0.0;
satrec.con41 = 0.0; satrec.cc1 = 0.0; satrec.cc4 = 0.0;
satrec.cc5 = 0.0; satrec.d2 = 0.0; satrec.d3 = 0.0;
satrec.d4 = 0.0; satrec.delmo = 0.0; satrec.eta = 0.0;
satrec.argpdot = 0.0; satrec.omgcof = 0.0; satrec.sinmao = 0.0;
satrec.t = 0.0; satrec.t2cof = 0.0; satrec.t3cof = 0.0;
satrec.t4cof = 0.0; satrec.t5cof = 0.0; satrec.x1mth2 = 0.0;
satrec.x7thm1 = 0.0; satrec.mdot = 0.0; satrec.nodedot = 0.0;
satrec.xlcof = 0.0; satrec.xmcof = 0.0; satrec.nodecf = 0.0;
# ----------- set all deep space variables to zero ------------
satrec.irez = 0; satrec.d2201 = 0.0; satrec.d2211 = 0.0;
satrec.d3210 = 0.0; satrec.d3222 = 0.0; satrec.d4410 = 0.0;
satrec.d4422 = 0.0; satrec.d5220 = 0.0; satrec.d5232 = 0.0;
satrec.d5421 = 0.0; satrec.d5433 = 0.0; satrec.dedt = 0.0;
satrec.del1 = 0.0; satrec.del2 = 0.0; satrec.del3 = 0.0;
satrec.didt = 0.0; satrec.dmdt = 0.0; satrec.dnodt = 0.0;
satrec.domdt = 0.0; satrec.e3 = 0.0; satrec.ee2 = 0.0;
satrec.peo = 0.0; satrec.pgho = 0.0; satrec.pho = 0.0;
satrec.pinco = 0.0; satrec.plo = 0.0; satrec.se2 = 0.0;
satrec.se3 = 0.0; satrec.sgh2 = 0.0; satrec.sgh3 = 0.0;
satrec.sgh4 = 0.0; satrec.sh2 = 0.0; satrec.sh3 = 0.0;
satrec.si2 = 0.0; satrec.si3 = 0.0; satrec.sl2 = 0.0;
satrec.sl3 = 0.0; satrec.sl4 = 0.0; satrec.gsto = 0.0;
satrec.xfact = 0.0; satrec.xgh2 = 0.0; satrec.xgh3 = 0.0;
satrec.xgh4 = 0.0; satrec.xh2 = 0.0; satrec.xh3 = 0.0;
satrec.xi2 = 0.0; satrec.xi3 = 0.0; satrec.xl2 = 0.0;
satrec.xl3 = 0.0; satrec.xl4 = 0.0; satrec.xlamo = 0.0;
satrec.zmol = 0.0; satrec.zmos = 0.0; satrec.atime = 0.0;
satrec.xli = 0.0; satrec.xni = 0.0;
# ------------------------ earth constants -----------------------
# sgp4fix identify constants and allow alternate values
# this is now the only call for the constants
(satrec.tumin, satrec.mu, satrec.radiusearthkm, satrec.xke,
satrec.j2, satrec.j3, satrec.j4, satrec.j3oj2) = whichconst;
# -------------------------------------------------------------------------
# The SGP4 library has changed `satn` from an integer to a string.
# But to avoid breaking our API contract with existing Python code,
# we are still willing to accept an integer.
if isinstance(satn, int):
satn = to_alpha5(satn)
satrec.error = 0;
satrec.operationmode = opsmode;
satrec.satnum_str = satn;
satrec.classification = 'U' # so attribute is not missing in Python
"""
// sgp4fix - note the following variables are also passed directly via satrec.
// it is possible to streamline the sgp4init call by deleting the "x"
// variables, but the user would need to set the satrec.* values first. we
// include the additional assignments in case twoline2rv is not used.
"""
satrec.bstar = xbstar;
# sgp4fix allow additional parameters in the struct
satrec.ndot = xndot;
satrec.nddot = xnddot;
satrec.ecco = xecco;
satrec.argpo = xargpo;
satrec.inclo = xinclo;
satrec.mo = xmo;
# sgp4fix rename variables to clarify which mean motion is intended
satrec.no_kozai= xno_kozai;
satrec.nodeo = xnodeo;
# single averaged mean elements
satrec.am = 0.0
satrec.em = 0.0
satrec.im = 0.0
satrec.Om = 0.0
satrec.mm = 0.0
satrec.nm = 0.0
# ------------------------ earth constants ----------------------- */
# sgp4fix identify constants and allow alternate values no longer needed
# getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
ss = 78.0 / satrec.radiusearthkm + 1.0;
# sgp4fix use multiply for speed instead of pow
qzms2ttemp = (120.0 - 78.0) / satrec.radiusearthkm;
qzms2t = qzms2ttemp * qzms2ttemp * qzms2ttemp * qzms2ttemp;
x2o3 = 2.0 / 3.0;
satrec.init = 'y';
satrec.t = 0.0;
# sgp4fix remove satn as it is not needed in initl
(
satrec.no_unkozai,
method,
ainv, ao, satrec.con41, con42, cosio,
cosio2,eccsq, omeosq, posq,
rp, rteosq,sinio , satrec.gsto,
) = _initl(
satrec.xke, satrec.j2, satrec.ecco, epoch, satrec.inclo, satrec.no_kozai, satrec.method,
satrec.operationmode
);
satrec.a = pow( satrec.no_unkozai*satrec.tumin , (-2.0/3.0) );
satrec.alta = satrec.a*(1.0 + satrec.ecco) - 1.0;
satrec.altp = satrec.a*(1.0 - satrec.ecco) - 1.0;
"""
// sgp4fix remove this check as it is unnecessary
// the mrt check in sgp4 handles decaying satellite cases even if the starting
// condition is below the surface of te earth
// if (rp < 1.0)
// {
// printf("# *** satn%d epoch elts sub-orbital ***\n", satn);
// satrec.error = 5;
// }
"""
if omeosq >= 0.0 or satrec.no_unkozai >= 0.0:
satrec.isimp = 0;
if rp < 220.0 / satrec.radiusearthkm + 1.0:
satrec.isimp = 1;
sfour = ss;
qzms24 = qzms2t;
perige = (rp - 1.0) * satrec.radiusearthkm;
# - for perigees below 156 km, s and qoms2t are altered -
if perige < 156.0:
sfour = perige - 78.0;
if perige < 98.0:
sfour = 20.0;
# sgp4fix use multiply for speed instead of pow
qzms24temp = (120.0 - sfour) / satrec.radiusearthkm;
qzms24 = qzms24temp * qzms24temp * qzms24temp * qzms24temp;
sfour = sfour / satrec.radiusearthkm + 1.0;
pinvsq = 1.0 / posq;
tsi = 1.0 / (ao - sfour);
satrec.eta = ao * satrec.ecco * tsi;
etasq = satrec.eta * satrec.eta;
eeta = satrec.ecco * satrec.eta;
psisq = fabs(1.0 - etasq);
coef = qzms24 * pow(tsi, 4.0);
coef1 = coef / pow(psisq, 3.5);
cc2 = coef1 * satrec.no_unkozai * (ao * (1.0 + 1.5 * etasq + eeta *
(4.0 + etasq)) + 0.375 * satrec.j2 * tsi / psisq * satrec.con41 *
(8.0 + 3.0 * etasq * (8.0 + etasq)));
satrec.cc1 = satrec.bstar * cc2;
cc3 = 0.0;
if satrec.ecco > 1.0e-4:
cc3 = -2.0 * coef * tsi * satrec.j3oj2 * satrec.no_unkozai * sinio / satrec.ecco;
satrec.x1mth2 = 1.0 - cosio2;
satrec.cc4 = 2.0* satrec.no_unkozai * coef1 * ao * omeosq * \
(satrec.eta * (2.0 + 0.5 * etasq) + satrec.ecco *
(0.5 + 2.0 * etasq) - satrec.j2 * tsi / (ao * psisq) *
(-3.0 * satrec.con41 * (1.0 - 2.0 * eeta + etasq *
(1.5 - 0.5 * eeta)) + 0.75 * satrec.x1mth2 *
(2.0 * etasq - eeta * (1.0 + etasq)) * cos(2.0 * satrec.argpo)));
satrec.cc5 = 2.0 * coef1 * ao * omeosq * (1.0 + 2.75 *
(etasq + eeta) + eeta * etasq);
cosio4 = cosio2 * cosio2;
temp1 = 1.5 * satrec.j2 * pinvsq * satrec.no_unkozai;
temp2 = 0.5 * temp1 * satrec.j2 * pinvsq;
temp3 = -0.46875 * satrec.j4 * pinvsq * pinvsq * satrec.no_unkozai;
satrec.mdot = satrec.no_unkozai + 0.5 * temp1 * rteosq * satrec.con41 + 0.0625 * \
temp2 * rteosq * (13.0 - 78.0 * cosio2 + 137.0 * cosio4);
satrec.argpdot = (-0.5 * temp1 * con42 + 0.0625 * temp2 *
(7.0 - 114.0 * cosio2 + 395.0 * cosio4) +
temp3 * (3.0 - 36.0 * cosio2 + 49.0 * cosio4));
xhdot1 = -temp1 * cosio;
satrec.nodedot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * cosio2) +
2.0 * temp3 * (3.0 - 7.0 * cosio2)) * cosio;
xpidot = satrec.argpdot+ satrec.nodedot;
satrec.omgcof = satrec.bstar * cc3 * cos(satrec.argpo);
satrec.xmcof = 0.0;
if satrec.ecco > 1.0e-4:
satrec.xmcof = -x2o3 * coef * satrec.bstar / eeta;
satrec.nodecf = 3.5 * omeosq * xhdot1 * satrec.cc1;
satrec.t2cof = 1.5 * satrec.cc1;
# sgp4fix for divide by zero with xinco = 180 deg
if fabs(cosio+1.0) > 1.5e-12:
satrec.xlcof = -0.25 * satrec.j3oj2 * sinio * (3.0 + 5.0 * cosio) / (1.0 + cosio);
else:
satrec.xlcof = -0.25 * satrec.j3oj2 * sinio * (3.0 + 5.0 * cosio) / temp4;
satrec.aycof = -0.5 * satrec.j3oj2 * sinio;
# sgp4fix use multiply for speed instead of pow
delmotemp = 1.0 + satrec.eta * cos(satrec.mo);
satrec.delmo = delmotemp * delmotemp * delmotemp;
satrec.sinmao = sin(satrec.mo);
satrec.x7thm1 = 7.0 * cosio2 - 1.0;
# --------------- deep space initialization -------------
if 2*pi / satrec.no_unkozai >= 225.0:
satrec.method = 'd';
satrec.isimp = 1;
tc = 0.0;
inclm = satrec.inclo;
(
snodm, cnodm, sinim, cosim, sinomm,
cosomm,day, satrec.e3, satrec.ee2, em,
emsq, gam, satrec.peo, satrec.pgho, satrec.pho,
satrec.pinco, satrec.plo, rtemsq, satrec.se2, satrec.se3,
satrec.sgh2, satrec.sgh3, satrec.sgh4, satrec.sh2, satrec.sh3,
satrec.si2, satrec.si3, satrec.sl2, satrec.sl3, satrec.sl4,
s1, s2, s3, s4, s5,
s6, s7, ss1, ss2, ss3,
ss4, ss5, ss6, ss7, sz1,
sz2, sz3, sz11, sz12, sz13,
sz21, sz22, sz23, sz31, sz32,
sz33, satrec.xgh2, satrec.xgh3, satrec.xgh4, satrec.xh2,
satrec.xh3, satrec.xi2, satrec.xi3, satrec.xl2, satrec.xl3,
satrec.xl4, nm, z1, z2, z3,
z11, z12, z13, z21, z22,
z23, z31, z32, z33, satrec.zmol,
satrec.zmos
) = _dscom(
epoch, satrec.ecco, satrec.argpo, tc, satrec.inclo, satrec.nodeo,
satrec.no_unkozai,
satrec.e3, satrec.ee2,
satrec.peo, satrec.pgho, satrec.pho, satrec.pinco,
satrec.plo, satrec.se2, satrec.se3,
satrec.sgh2, satrec.sgh3, satrec.sgh4,
satrec.sh2, satrec.sh3, satrec.si2, satrec.si3,
satrec.sl2, satrec.sl3, satrec.sl4,
satrec.xgh2, satrec.xgh3, satrec.xgh4, satrec.xh2,
satrec.xh3, satrec.xi2, satrec.xi3, satrec.xl2,
satrec.xl3, satrec.xl4,
satrec.zmol, satrec.zmos
);
(satrec.ecco, satrec.inclo, satrec.nodeo, satrec.argpo, satrec.mo
) = _dpper(
satrec, inclm, satrec.init,
satrec.ecco, satrec.inclo, satrec.nodeo, satrec.argpo, satrec.mo,
satrec.operationmode
);
argpm = 0.0;
nodem = 0.0;
mm = 0.0;
(
em, argpm, inclm, mm,
nm, nodem,
satrec.irez, satrec.atime,
satrec.d2201, satrec.d2211, satrec.d3210, satrec.d3222,
satrec.d4410, satrec.d4422, satrec.d5220, satrec.d5232,
satrec.d5421, satrec.d5433, satrec.dedt, satrec.didt,
satrec.dmdt, dndt, satrec.dnodt, satrec.domdt,
satrec.del1, satrec.del2, satrec.del3, satrec.xfact,
satrec.xlamo, satrec.xli, satrec.xni
) = _dsinit(
satrec.xke,
cosim, emsq, satrec.argpo, s1, s2, s3, s4, s5, sinim, ss1, ss2, ss3, ss4,
ss5, sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33, satrec.t, tc,
satrec.gsto, satrec.mo, satrec.mdot, satrec.no_unkozai, satrec.nodeo,
satrec.nodedot, xpidot, z1, z3, z11, z13, z21, z23, z31, z33,
satrec.ecco, eccsq, em, argpm, inclm, mm, nm, nodem,
satrec.irez, satrec.atime,
satrec.d2201, satrec.d2211, satrec.d3210, satrec.d3222 ,
satrec.d4410, satrec.d4422, satrec.d5220, satrec.d5232,
satrec.d5421, satrec.d5433, satrec.dedt, satrec.didt,
satrec.dmdt, satrec.dnodt, satrec.domdt,
satrec.del1, satrec.del2, satrec.del3, satrec.xfact,
satrec.xlamo, satrec.xli, satrec.xni
);
#----------- set variables if not deep space -----------
if satrec.isimp != 1:
cc1sq = satrec.cc1 * satrec.cc1;
satrec.d2 = 4.0 * ao * tsi * cc1sq;
temp = satrec.d2 * tsi * satrec.cc1 / 3.0;
satrec.d3 = (17.0 * ao + sfour) * temp;
satrec.d4 = 0.5 * temp * ao * tsi * (221.0 * ao + 31.0 * sfour) * \
satrec.cc1;
satrec.t3cof = satrec.d2 + 2.0 * cc1sq;
satrec.t4cof = 0.25 * (3.0 * satrec.d3 + satrec.cc1 *
(12.0 * satrec.d2 + 10.0 * cc1sq));
satrec.t5cof = 0.2 * (3.0 * satrec.d4 +
12.0 * satrec.cc1 * satrec.d3 +
6.0 * satrec.d2 * satrec.d2 +
15.0 * cc1sq * (2.0 * satrec.d2 + cc1sq));
"""
/* finally propogate to zero epoch to initialize all others. */
// sgp4fix take out check to let satellites process until they are actually below earth surface
// if(satrec.error == 0)
"""
sgp4(satrec, 0.0, whichconst);
satrec.init = 'n';
# sgp4fix return boolean. satrec.error contains any error codes
return true;
"""
/*-----------------------------------------------------------------------------
*
* procedure sgp4
*
* this procedure is the sgp4 prediction model from space command. this is an
* updated and combined version of sgp4 and sdp4, which were originally
* published separately in spacetrack report #3. this version follows the
* methodology from the aiaa paper (2006) describing the history and
* development of the code.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* satrec - initialised structure from sgp4init() call.
* tsince - time eince epoch (minutes)
*
* outputs :
* r - position vector km
* v - velocity km/sec
* return code - non-zero on error.
* 1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
* 2 - mean motion less than 0.0
* 3 - pert elements, ecc < 0.0 or ecc > 1.0
* 4 - semi-latus rectum < 0.0
* 5 - epoch elements are sub-orbital
* 6 - satellite has decayed
*
* locals :
* am -
* axnl, aynl -
* betal -
* cosim , sinim , cosomm , sinomm , cnod , snod , cos2u ,
* sin2u , coseo1 , sineo1 , cosi , sini , cosip , sinip ,
* cosisq , cossu , sinsu , cosu , sinu
* delm -
* delomg -
* dndt -
* eccm -
* emsq -
* ecose -
* el2 -
* eo1 -
* eccp -
* esine -
* argpm -
* argpp -
* omgadf -
* pl -
* r -
* rtemsq -
* rdotl -
* rl -
* rvdot -
* rvdotl -
* su -
* t2 , t3 , t4 , tc
* tem5, temp , temp1 , temp2 , tempa , tempe , templ
* u , ux , uy , uz , vx , vy , vz
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* nodem - right asc of ascending node
* xinc -
* xincp -
* xl -
* xlm -
* mp -
* xmdf -
* xmx -
* xmy -
* nodedf -
* xnode -
* nodep -
* np -
*
* coupling :
* getgravconst-
* dpper
* dpspace
*
* references :
* hoots, roehrich, norad spacetrack report #3 1980
* hoots, norad spacetrack report #6 1986
* hoots, schumacher and glover 2004
* vallado, crawford, hujsak, kelso 2006
----------------------------------------------------------------------------*/
"""
def sgp4(satrec, tsince, whichconst=None):
mrt = 0.0
"""
/* ------------------ set mathematical constants --------------- */
// sgp4fix divisor for divide by zero check on inclination
// the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
// 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency
"""
temp4 = 1.5e-12;
twopi = 2.0 * pi;
x2o3 = 2.0 / 3.0;
# sgp4fix identify constants and allow alternate values
# tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 = whichconst
vkmpersec = satrec.radiusearthkm * satrec.xke/60.0;
# --------------------- clear sgp4 error flag -----------------
satrec.t = tsince;
satrec.error = 0;
satrec.error_message = None
# ------- update for secular gravity and atmospheric drag -----
xmdf = satrec.mo + satrec.mdot * satrec.t;
argpdf = satrec.argpo + satrec.argpdot * satrec.t;
nodedf = satrec.nodeo + satrec.nodedot * satrec.t;
argpm = argpdf;
mm = xmdf;
t2 = satrec.t * satrec.t;
nodem = nodedf + satrec.nodecf * t2;
tempa = 1.0 - satrec.cc1 * satrec.t;
tempe = satrec.bstar * satrec.cc4 * satrec.t;
templ = satrec.t2cof * t2;
if satrec.isimp != 1:
delomg = satrec.omgcof * satrec.t;
# sgp4fix use mutliply for speed instead of pow
delmtemp = 1.0 + satrec.eta * cos(xmdf);
delm = satrec.xmcof * \
(delmtemp * delmtemp * delmtemp -
satrec.delmo);
temp = delomg + delm;
mm = xmdf + temp;
argpm = argpdf - temp;
t3 = t2 * satrec.t;
t4 = t3 * satrec.t;
tempa = tempa - satrec.d2 * t2 - satrec.d3 * t3 - \
satrec.d4 * t4;
tempe = tempe + satrec.bstar * satrec.cc5 * (sin(mm) -
satrec.sinmao);
templ = templ + satrec.t3cof * t3 + t4 * (satrec.t4cof +
satrec.t * satrec.t5cof);
nm = satrec.no_unkozai;
em = satrec.ecco;
inclm = satrec.inclo;
if satrec.method == 'd':
tc = satrec.t;
(
atime, em, argpm, inclm, xli,
mm, xni, nodem, dndt, nm,
) = _dspace(
satrec.irez,
satrec.d2201, satrec.d2211, satrec.d3210,
satrec.d3222, satrec.d4410, satrec.d4422,
satrec.d5220, satrec.d5232, satrec.d5421,
satrec.d5433, satrec.dedt, satrec.del1,
satrec.del2, satrec.del3, satrec.didt,
satrec.dmdt, satrec.dnodt, satrec.domdt,
satrec.argpo, satrec.argpdot, satrec.t, tc,
satrec.gsto, satrec.xfact, satrec.xlamo,
satrec.no_unkozai, satrec.atime,
em, argpm, inclm, satrec.xli, mm, satrec.xni,
nodem, nm
);
if nm <= 0.0:
satrec.error_message = ('mean motion {0:f} is less than zero'
.format(nm))
satrec.error = 2;
# sgp4fix add return
return false, false;
am = pow((satrec.xke / nm),x2o3) * tempa * tempa;
nm = satrec.xke / pow(am, 1.5);
em = em - tempe;
# fix tolerance for error recognition
# sgp4fix am is fixed from the previous nm check
if em >= 1.0 or em < -0.001: # || (am < 0.95)
satrec.error_message = ('mean eccentricity {0:f} not within'
' range 0.0 <= e < 1.0'.format(em))
satrec.error = 1;
# sgp4fix to return if there is an error in eccentricity
return false, false;
# sgp4fix fix tolerance to avoid a divide by zero
if em < 1.0e-6:
em = 1.0e-6;
mm = mm + satrec.no_unkozai * templ;
xlm = mm + argpm + nodem;
emsq = em * em;
temp = 1.0 - emsq;
nodem = nodem % twopi if nodem >= 0.0 else -(-nodem % twopi)
argpm = argpm % twopi
xlm = xlm % twopi
mm = (xlm - argpm - nodem) % twopi
# sgp4fix recover singly averaged mean elements
satrec.am = am;
satrec.em = em;
satrec.im = inclm;
satrec.Om = nodem;
satrec.om = argpm;
satrec.mm = mm;
satrec.nm = nm;
# ----------------- compute extra mean quantities -------------
sinim = sin(inclm);
cosim = cos(inclm);
# -------------------- add lunar-solar periodics --------------
ep = em;
xincp = inclm;
argpp = argpm;
nodep = nodem;
mp = mm;
sinip = sinim;
cosip = cosim;
if satrec.method == 'd':
ep, xincp, nodep, argpp, mp = _dpper(
satrec, satrec.inclo,
'n', ep, xincp, nodep, argpp, mp, satrec.operationmode
);
if xincp < 0.0:
xincp = -xincp;
nodep = nodep + pi;
argpp = argpp - pi;
if ep < 0.0 or ep > 1.0:
satrec.error_message = ('perturbed eccentricity {0:f} not within'
' range 0.0 <= e <= 1.0'.format(ep))
satrec.error = 3;
# sgp4fix add return
return false, false;
# -------------------- long period periodics ------------------
if satrec.method == 'd':
sinip = sin(xincp);
cosip = cos(xincp);
satrec.aycof = -0.5*satrec.j3oj2*sinip;
# sgp4fix for divide by zero for xincp = 180 deg
if fabs(cosip+1.0) > 1.5e-12:
satrec.xlcof = -0.25 * satrec.j3oj2 * sinip * (3.0 + 5.0 * cosip) / (1.0 + cosip);
else:
satrec.xlcof = -0.25 * satrec.j3oj2 * sinip * (3.0 + 5.0 * cosip) / temp4;
axnl = ep * cos(argpp);
temp = 1.0 / (am * (1.0 - ep * ep));
aynl = ep* sin(argpp) + temp * satrec.aycof;
xl = mp + argpp + nodep + temp * satrec.xlcof * axnl;
# --------------------- solve kepler's equation ---------------
u = (xl - nodep) % twopi
eo1 = u;
tem5 = 9999.9;
ktr = 1;
# sgp4fix for kepler iteration
# the following iteration needs better limits on corrections
while fabs(tem5) >= 1.0e-12 and ktr <= 10:
sineo1 = sin(eo1);
coseo1 = cos(eo1);
tem5 = 1.0 - coseo1 * axnl - sineo1 * aynl;
tem5 = (u - aynl * coseo1 + axnl * sineo1 - eo1) / tem5;
if fabs(tem5) >= 0.95:
tem5 = 0.95 if tem5 > 0.0 else -0.95;
eo1 = eo1 + tem5;
ktr = ktr + 1;
# ------------- short period preliminary quantities -----------
ecose = axnl*coseo1 + aynl*sineo1;
esine = axnl*sineo1 - aynl*coseo1;
el2 = axnl*axnl + aynl*aynl;
pl = am*(1.0-el2);
if pl < 0.0:
satrec.error_message = ('semilatus rectum {0:f} is less than zero'
.format(pl))
satrec.error = 4;
# sgp4fix add return
return false, false;
else:
rl = am * (1.0 - ecose);
rdotl = sqrt(am) * esine/rl;
rvdotl = sqrt(pl) / rl;
betal = sqrt(1.0 - el2);
temp = esine / (1.0 + betal);
sinu = am / rl * (sineo1 - aynl - axnl * temp);
cosu = am / rl * (coseo1 - axnl + aynl * temp);
su = atan2(sinu, cosu);
sin2u = (cosu + cosu) * sinu;
cos2u = 1.0 - 2.0 * sinu * sinu;
temp = 1.0 / pl;
temp1 = 0.5 * satrec.j2 * temp;
temp2 = temp1 * temp;
# -------------- update for short period periodics ------------
if satrec.method == 'd':
cosisq = cosip * cosip;
satrec.con41 = 3.0*cosisq - 1.0;
satrec.x1mth2 = 1.0 - cosisq;
satrec.x7thm1 = 7.0*cosisq - 1.0;
mrt = rl * (1.0 - 1.5 * temp2 * betal * satrec.con41) + \
0.5 * temp1 * satrec.x1mth2 * cos2u;
su = su - 0.25 * temp2 * satrec.x7thm1 * sin2u;
xnode = nodep + 1.5 * temp2 * cosip * sin2u;
xinc = xincp + 1.5 * temp2 * cosip * sinip * cos2u;
mvt = rdotl - nm * temp1 * satrec.x1mth2 * sin2u / satrec.xke;
rvdot = rvdotl + nm * temp1 * (satrec.x1mth2 * cos2u +
1.5 * satrec.con41) / satrec.xke;
# --------------------- orientation vectors -------------------
sinsu = sin(su);
cossu = cos(su);
snod = sin(xnode);
cnod = cos(xnode);
sini = sin(xinc);
cosi = cos(xinc);
xmx = -snod * cosi;
xmy = cnod * cosi;
ux = xmx * sinsu + cnod * cossu;
uy = xmy * sinsu + snod * cossu;
uz = sini * sinsu;
vx = xmx * cossu - cnod * sinsu;
vy = xmy * cossu - snod * sinsu;
vz = sini * cossu;
# --------- position and velocity (in km and km/sec) ----------
_mr = mrt * satrec.radiusearthkm
r = (_mr * ux, _mr * uy, _mr * uz)
v = ((mvt * ux + rvdot * vx) * vkmpersec,
(mvt * uy + rvdot * vy) * vkmpersec,
(mvt * uz + rvdot * vz) * vkmpersec)
# sgp4fix for decaying satellites
if mrt < 1.0:
satrec.error_message = ('mrt {0:f} is less than 1.0 indicating'
' the satellite has decayed'.format(mrt))
satrec.error = 6;
return r, v;
"""
/* -----------------------------------------------------------------------------
*
* function gstime
*
* this function finds the greenwich sidereal time.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* jdut1 - julian date in ut1 days from 4713 bc
*
* outputs :
* gstime - greenwich sidereal time 0 to 2pi rad
*
* locals :
* temp - temporary variable for doubles rad
* tut1 - julian centuries from the
* jan 1, 2000 12 h epoch (ut1)
*
* coupling :
* none
*
* references :
* vallado 2004, 191, eq 3-45
* --------------------------------------------------------------------------- */
"""
def gstime(jdut1):
tut1 = (jdut1 - 2451545.0) / 36525.0;
temp = -6.2e-6* tut1 * tut1 * tut1 + 0.093104 * tut1 * tut1 + \
(876600.0*3600 + 8640184.812866) * tut1 + 67310.54841; # sec
temp = (temp * deg2rad / 240.0) % twopi # 360/86400 = 1/240, to deg, to rad
# ------------------------ check quadrants ---------------------
if temp < 0.0:
temp += twopi;
return temp;
# The routine was originally marked private, so make it available under
# the old name for compatibility:
_gstime = gstime
"""
/* -----------------------------------------------------------------------------
*
* function getgravconst
*
* this function gets constants for the propagator. note that mu is identified to
* facilitiate comparisons with newer models. the common useage is wgs72.
*
* author : david vallado 719-573-2600 21 jul 2006
*
* inputs :
* whichconst - which set of constants to use wgs72old, wgs72, wgs84
*
* outputs :
* tumin - minutes in one time unit
* mu - earth gravitational parameter
* radiusearthkm - radius of the earth in km
* xke - reciprocal of tumin
* j2, j3, j4 - un-normalized zonal harmonic values
* j3oj2 - j3 divided by j2
*
* locals :
*
* coupling :
* none
*
* references :
* norad spacetrack report #3
* vallado, crawford, hujsak, kelso 2006
--------------------------------------------------------------------------- */
"""
def getgravconst(whichconst):
if whichconst == 'wgs72old':
mu = 398600.79964; # in km3 / s2
radiusearthkm = 6378.135; # km
xke = 0.0743669161;
tumin = 1.0 / xke;
j2 = 0.001082616;
j3 = -0.00000253881;
j4 = -0.00000165597;
j3oj2 = j3 / j2;
# ------------ wgs-72 constants ------------
elif whichconst == 'wgs72':
mu = 398600.8; # in km3 / s2
radiusearthkm = 6378.135; # km
xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm/mu);
tumin = 1.0 / xke;
j2 = 0.001082616;
j3 = -0.00000253881;
j4 = -0.00000165597;
j3oj2 = j3 / j2;
elif whichconst == 'wgs84':
# ------------ wgs-84 constants ------------
mu = 398600.5; # in km3 / s2
radiusearthkm = 6378.137; # km
xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm/mu);
tumin = 1.0 / xke;
j2 = 0.00108262998905;
j3 = -0.00000253215306;
j4 = -0.00000161098761;
j3oj2 = j3 / j2;
return tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/sample_omm.csv 0000644 0001751 0000173 00000000557 14422467341 015456 0 ustar 00runner docker OBJECT_NAME,OBJECT_ID,EPOCH,MEAN_MOTION,ECCENTRICITY,INCLINATION,RA_OF_ASC_NODE,ARG_OF_PERICENTER,MEAN_ANOMALY,EPHEMERIS_TYPE,CLASSIFICATION_TYPE,NORAD_CAT_ID,ELEMENT_SET_NO,REV_AT_EPOCH,BSTAR,MEAN_MOTION_DOT,MEAN_MOTION_DDOT
VANGUARD 1,1958-002B,2020-10-13T04:52:48.472320,10.84869164,.1845686,34.2443,225.5254,162.2516,205.2356,0,U,5,999,21814,-.22483E-4,-1.6E-7,0
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/sample_omm.xml 0000644 0001751 0000173 00000002231 14422467341 015452 0 ustar 00runner docker
VANGUARD 11958-002BEARTHTEMEUTCSGP42020-10-13T04:52:48.47232010.84869164.184568634.2443225.5254162.2516205.23560U599921814-.22483E-4-1.6E-70
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/tcppver.out 0000644 0001751 0000173 00000421602 14422467341 015022 0 ustar 00runner docker 5 xx
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4632 xx
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720.00000000 13725.09398980 -2180.70877090 863.29684523 3.878478111 1.656846496 4.944867241 26548.333034 0.707487 64.58751 349.28080 270.07012 93.86588 17.75424 2006 6 26 1:28:40.058410
840.00000000 19089.63879226 9456.29670247 27026.79562883 -0.656614299 1.309112636 2.449371941 26536.083726 0.707453 64.58130 349.27341 270.05293 150.35125 78.01690 2006 6 26 3:28:40.058423
960.00000000 11106.41248373 16627.60874079 38727.35140296 -1.409722680 0.698582526 0.891383535 26536.406111 0.707515 64.57959 349.26035 270.05600 169.61686 138.25614 2006 6 26 5:28:40.058396
1080.00000000 72.40958621 19575.08054144 40492.12544001 -1.593394604 0.113655142 -0.390556063 26536.485208 0.707520 64.57944 349.24727 270.06258 184.50420 198.49115 2006 6 26 7:28:40.058410
1200.00000000 -10905.89252576 17965.41205111 32850.07298244 -1.371396120 -0.601706604 -1.782817058 26536.148885 0.707469 64.58054 349.23420 270.06776 201.08065 258.72792 2006 6 26 9:28:40.058423
1320.00000000 -17044.61207568 9635.48491849 13212.59462953 0.129244030 -1.903551430 -3.884569098 26537.753741 0.707381 64.58467 349.22213 270.06223 231.67254 318.97731 2006 6 26 11:28:40.058396
1440.00000000 14369.90303735 -1903.85601062 1722.15319852 3.543393116 1.701687176 4.913881358 26547.006033 0.707440 64.58780 349.21714 270.06935 97.43575 19.21528 2006 6 26 13:28:40.058410
1560.00000000 18983.96210441 9661.12233804 27448.99557732 -0.687189304 1.293808870 2.403630759 26536.025321 0.707422 64.58162 349.20920 270.05262 150.95671 79.47751 2006 6 26 15:28:40.058423
1680.00000000 10878.79336704 16735.31433954 38879.23434264 -1.418239666 0.686235750 0.858951848 26536.356328 0.707481 64.57998 349.19620 270.05577 169.99758 139.71684 2006 6 26 17:28:40.058396
1800.00000000 -184.03743100 19593.09371709 40420.40606889 -1.593348925 0.100448697 -0.421571993 26536.424509 0.707483 64.57986 349.18320 270.06227 184.86453 199.95214 2006 6 26 19:28:40.058410
1920.00000000 -11125.12138631 17870.19488928 32534.21521208 -1.359116236 -0.621413776 -1.821629856 26536.082381 0.707430 64.58101 349.17020 270.06725 201.56409 260.18933 2006 6 26 21:28:40.058423
2040.00000000 -17004.43272827 9316.53926351 12526.11883812 0.220330736 -1.955594322 -3.955058575 26537.937268 0.707343 64.58528 349.15832 270.06103 233.01303 320.43971 2006 6 26 23:28:40.058396
2160.00000000 14960.06492693 -1620.68430805 2574.96359381 3.238634028 1.734723385 4.868880331 26545.757985 0.707389 64.58808 349.15385 270.06784 100.69458 20.67827 2006 6 27 1:28:40.058410
2280.00000000 18873.46347257 9863.57004586 27863.46574735 -0.716736981 1.278632817 2.358448535 26535.969116 0.707385 64.58199 349.14544 270.05170 151.55126 80.93998 2006 6 27 3:28:40.058423
2400.00000000 10649.86857581 16841.14172669 39025.48035006 -1.426527152 0.673901057 0.826632332 26536.307016 0.707442 64.58041 349.13251 270.05492 170.37668 141.17943 2006 6 27 5:28:40.058396
2520.00000000 -440.53459323 19608.95524423 40343.10675451 -1.593138597 0.087147884 -0.452680559 26536.364231 0.707443 64.58032 349.11959 270.06132 185.22637 201.41503 2006 6 27 7:28:40.058410
2640.00000000 -11342.45028909 17771.44223942 32211.12535721 -1.346344015 -0.641464291 -1.860864234 26536.016805 0.707388 64.58151 349.10667 270.06608 202.05475 261.65268 2006 6 27 9:28:40.058423
2760.00000000 -16948.06005711 8987.64254880 11826.28284367 0.318007297 -2.009693492 -4.026726648 26538.152748 0.707301 64.58594 349.09499 270.05912 234.42042 321.90410 2006 6 27 11:28:40.058396
2880.00000000 15500.53445068 -1332.90981042 3419.72315308 2.960917974 1.758331634 4.813698638 26544.607622 0.707336 64.58836 349.09097 270.06558 103.68403 22.14330 2006 6 27 13:28:40.058410
9998 xx
0.00000000 25532.98947267 -27244.26327953 -1.11572421 2.410283885 2.194175683 0.545888526
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-1380.00000000 309.25349929 -36960.43090143 -4198.48007670 3.292429375 -0.002166046 0.402111628 38221.526676 0.027166 9.51133 313.16407 327.33196 349.58789 350.13941 2005 5 27 20: 3:37.089763
-1320.00000000 11949.04009077 -35127.37816804 -2565.89806468 3.119942784 1.012096444 0.497284100 38221.561326 0.027167 9.51133 313.16394 327.36254 7.96041 7.53783 2005 5 27 21: 3:37.089790
-1260.00000000 22400.45329336 -29798.63236321 -677.91515122 2.638533344 1.922477736 0.542792913 38221.583032 0.027163 9.51127 313.16418 327.39232 26.29054 24.93669 2005 5 27 22: 3:37.089777
-1200.00000000 30640.84752458 -21525.02340201 1277.34808722 1.903464941 2.634294312 0.534540934 38221.585627 0.027155 9.51113 313.16452 327.41777 44.48899 42.33979 2005 5 27 23: 3:37.089763
-1140.00000000 35899.56788035 -11152.71158138 3108.72535238 0.997393045 3.079858548 0.474873291 38221.571380 0.027144 9.51092 313.16464 327.43611 62.48274 59.75018 2005 5 28 0: 3:37.089790
-1080.00000000 37732.45438600 288.18821054 4643.87587495 0.016652226 3.225184410 0.371669746 38221.549210 0.027131 9.51067 313.16433 327.44619 80.22210 77.16923 2005 5 28 1: 3:37.089777
-1020.00000000 36045.92961699 11706.61816230 5746.32646574 -0.942409065 3.069888941 0.236662980 38221.530203 0.027118 9.51043 313.16355 327.44829 97.68426 94.59668 2005 5 28 2: 3:37.089763
-960.00000000 31076.77273609 22063.44379776 6325.93403705 -1.794027976 2.642072476 0.083556127 38221.523131 0.027106 9.51023 313.16243 327.44333 114.87345 112.03151 2005 5 28 3: 3:37.089790
-900.00000000 23341.26015320 30460.88002531 6342.91707895 -2.469409743 1.990861658 -0.073612096 38221.531831 0.027095 9.51011 313.16118 327.43216 131.81817 129.47266 2005 5 28 4: 3:37.089777
-840.00000000 13568.39733054 36204.45930900 5806.79548733 -2.919354203 1.178920217 -0.221646814 38221.554837 0.027086 9.51006 313.16007 327.41535 148.56644 146.91929 2005 5 28 5: 3:37.089763
-780.00000000 2628.58762420 38840.10855897 4771.91979854 -3.114400514 0.276239109 -0.348926401 38221.586600 0.027081 9.51004 313.15929 327.39366 165.18009 164.37049 2005 5 28 6: 3:37.089790
-720.00000000 -8535.81598158 38171.79073851 3331.00311285 -3.043839958 -0.644462527 -0.445808894 38221.619464 0.027078 9.51004 313.15891 327.36854 181.72917 181.82473 2005 5 28 7: 3:37.089777
11801 xx
0.00000000 7473.37102491 428.94748312 5828.74846783 5.107155391 6.444680305 -0.186133297
360.00000000 -3305.22148694 32410.84323331 -24697.16974954 -1.301137319 -1.151315600 -0.283335823 24302.998464 0.731602 46.74812 230.32944 47.61951 188.41997 216.32619 1980 8 17 13: 6:40.136822
720.00000000 14271.29083858 24110.44309009 -4725.76320143 -0.320504528 2.679841539 -2.084054355 24260.879269 0.730999 46.75721 230.25074 47.70178 145.49648 62.82214 1980 8 17 19: 6:40.136822
1080.00000000 -9990.05800009 22717.34212448 -23616.88515553 -1.016674392 -2.290267981 0.728923337 24216.350393 0.730514 46.74432 230.17836 47.76610 203.41634 269.87129 1980 8 18 1: 6:40.136822
1440.00000000 9787.87836256 33753.32249667 -15030.79874625 -1.094251553 0.923589906 -1.522311008 24174.266874 0.729877 46.75279 230.10704 47.83650 164.83770 117.47202 1980 8 18 7: 6:40.136822
14128 xx
0.00000000 34747.57932696 24502.37114079 -1.32832986 -1.731642662 2.452772615 0.608510081
120.00000000 18263.33439094 38159.96004751 4186.18304085 -2.744396611 1.255583260 0.528558932 42563.335575 0.001210 11.45711 35.19962 28.32899 1.38958 1.38622 2006 6 25 2:40:57.987566
240.00000000 -3023.38840703 41783.13186459 7273.03412906 -3.035574793 -0.271656544 0.309645251 42563.286498 0.001204 11.45707 35.19984 29.11706 30.32902 30.25940 2006 6 25 4:40:57.987539
360.00000000 -23516.34391907 34424.42065671 8448.49867693 -2.529120477 -1.726186020 0.009582303 42563.266606 0.001192 11.45713 35.19919 29.66338 59.49273 59.37511 2006 6 25 6:40:57.987553
480.00000000 -37837.46699511 18028.39727170 7406.25540271 -1.360069525 -2.725794686 -0.292555349 42563.306835 0.001176 11.45738 35.19852 29.91711 88.91814 88.78342 2006 6 25 8:40:57.987566
600.00000000 -42243.58460661 -3093.72887774 4422.91711801 0.163110919 -3.009980598 -0.517584362 42563.378963 0.001159 11.45773 35.19869 29.78001 118.69825 118.58175 2006 6 25 10:40:57.987539
720.00000000 -35597.57919549 -23407.91145393 282.09554383 1.641405246 -2.506773678 -0.606963478 42563.423811 0.001145 11.45799 35.19977 29.17604 148.91388 148.84611 2006 6 25 12:40:57.987553
840.00000000 -19649.19834455 -37606.11623860 -3932.71525948 2.689647056 -1.349150016 -0.537710698 42563.409025 0.001140 11.45805 35.20091 28.27993 179.40389 179.40253 2006 6 25 14:40:57.987566
960.00000000 1431.30912160 -41982.04949668 -7120.45467057 3.035263353 0.160882945 -0.327993994 42563.360304 0.001146 11.45799 35.20123 27.44408 209.83405 209.89943 2006 6 25 16:40:57.987539
1080.00000000 22136.97605384 -35388.19823762 -8447.62393401 2.587624889 1.630097136 -0.032349004 42563.336241 0.001158 11.45801 35.20064 26.88569 240.00468 240.11968 2006 6 25 18:40:57.987553
1200.00000000 37050.15790219 -19537.23321425 -7564.83463543 1.461844494 2.674654256 0.272202191 42563.371549 0.001174 11.45822 35.19994 26.65134 269.88144 270.01600 2006 6 25 20:40:57.987566
1320.00000000 42253.81760945 1431.81867593 -4699.87621174 -0.049247334 3.019518960 0.505890058 42563.442989 0.001191 11.45854 35.20004 26.80451 299.40514 299.52402 2006 6 25 22:40:57.987539
1440.00000000 36366.59147396 22023.54245720 -601.47121821 -1.549681546 2.571788981 0.607057418 42563.491561 0.001205 11.45879 35.20107 27.38673 328.53010 328.60214 2006 6 26 0:40:57.987553
1560.00000000 20922.12287985 36826.33975981 3654.91125886 -2.644070068 1.447521216 0.548722983 42563.480302 0.001210 11.45883 35.20224 28.23415 357.40864 357.41490 2006 6 26 2:40:57.987566
1680.00000000 -23.77224182 41945.51688402 6950.29891751 -3.043358385 -0.057417440 0.346112094 42563.431184 0.001205 11.45875 35.20263 29.04625 26.32488 26.26370 2006 6 26 4:40:57.987539
1800.00000000 -20964.17821076 36039.06206172 8418.91984963 -2.642795221 -1.546099886 0.052725852 42563.403442 0.001193 11.45873 35.20206 29.62920 55.45507 55.34250 2006 6 26 6:40:57.987553
1920.00000000 -36401.63863057 20669.75286162 7677.19769359 -1.549488154 -2.627052310 -0.254079652 42563.434989 0.001178 11.45890 35.20132 29.92669 84.84130 84.70690 2006 6 26 8:40:57.987566
2040.00000000 -42298.30327543 -119.03351118 4922.96388841 -0.052232768 -3.018152669 -0.493827331 42563.505293 0.001160 11.45920 35.20134 29.85054 114.56521 114.44424 2006 6 26 10:40:57.987539
2160.00000000 -37125.62383511 -20879.63058368 879.86971348 1.456499841 -2.619358421 -0.604081694 42563.556063 0.001146 11.45943 35.20230 29.30881 144.72439 144.64852 2006 6 26 12:40:57.987553
2280.00000000 -22250.12320553 -36182.74736487 -3393.15365183 2.583161226 -1.536647628 -0.556404555 42563.548278 0.001140 11.45946 35.20346 28.43156 175.19681 175.18586 2006 6 26 14:40:57.987566
2400.00000000 -1563.06258654 -42035.43179159 -6780.02161760 3.034917506 -0.052702046 -0.363395654 42563.499945 0.001144 11.45935 35.20388 27.56804 205.65334 205.71014 2006 6 26 16:40:57.987539
2520.00000000 19531.64069587 -36905.65470956 -8395.46892032 2.693682199 1.446079999 -0.075256054 42563.468338 0.001156 11.45930 35.20333 26.96596 235.86418 235.97386 2006 6 26 18:40:57.987553
2640.00000000 35516.53506142 -22123.71916638 -7815.04516935 1.646882125 2.568416058 0.232985912 42563.494530 0.001171 11.45943 35.20253 26.68392 265.78389 265.91776 2006 6 26 20:40:57.987566
2760.00000000 42196.03535976 -1547.32646751 -5187.39401981 0.166491841 3.019211549 0.480665780 42563.563210 0.001188 11.45970 35.20242 26.77785 295.36201 295.48503 2006 6 26 22:40:57.987539
2880.00000000 37802.25393045 19433.57330019 -1198.66634226 -1.359930580 2.677830903 0.602507466 42563.617115 0.001203 11.45992 35.20328 27.30484 324.53841 324.61834 2006 6 27 0:40:57.987553
16925 xx
0.00000000 5559.11686836 -11941.04090781 -19.41235206 3.392116762 -1.946985124 4.250755852
120.00000000 12339.83273749 -2771.14447871 18904.57603433 -0.871247614 2.600917693 0.581560002 14661.168567 0.558851 62.08305 294.96981 245.15626 184.99906 194.60193 2006 5 31 18:10:47.226141
240.00000000 -3385.00215658 7538.13955729 200.59008616 -2.023512865 -4.261808344 -6.856385787 14665.680807 0.558522 62.09661 294.91901 245.14027 293.28617 341.35494 2006 5 31 20:10:47.226115
360.00000000 12805.22442200 -10258.94667177 13780.16486738 0.619279224 1.821510542 2.507365975 14645.112935 0.558062 62.08843 294.88336 245.15354 161.54763 128.23331 2006 5 31 22:10:47.226128
480.00000000 5682.46556318 7199.30270473 15437.67134070 -2.474365406 2.087897336 -2.583767460 14633.894717 0.557848 62.08196 294.82586 245.20054 218.15594 275.17654 2006 6 1 0:10:47.226141
600.00000000 7628.94243982 -12852.72097492 2902.87208981 2.748131081 -0.740084579 4.125307943 14632.350201 0.557354 62.09577 294.78850 245.19066 127.26833 62.32236 2006 6 1 2:10:47.226115
720.00000000 11531.64866625 -858.27542736 19086.85993771 -1.170071901 2.660311986 0.096005705 14618.400478 0.557382 62.08201 294.74405 245.18361 190.26697 209.59661 2006 6 1 4:10:47.226128
840.00000000 -3866.98069515 2603.73442786 -4577.36484577 1.157257298 -8.453281164 -4.683959407 14609.950084 0.556751 62.08671 294.70316 245.19559 347.25738 356.96829 2006 6 1 6:10:47.226141
960.00000000 13054.77732721 -8707.92757730 15537.63259903 0.229846748 2.119467054 2.063396852 14602.295885 0.556633 62.08658 294.65799 245.17457 167.59678 144.51266 2006 6 1 8:10:47.226115
1080.00000000 3496.91064652 8712.83919778 12845.81838327 -2.782184997 1.552950644 -3.554436131 14591.212894 0.556266 62.08343 294.59790 245.22189 228.75852 292.09018 2006 6 1 10:10:47.226128
1200.00000000 9593.07424729 -13023.75963608 6250.46484931 2.072666376 0.278735334 3.778111073 14587.914744 0.555849 62.09368 294.56560 245.20049 138.87074 79.89273 2006 6 1 12:10:47.226141
1320.00000000 10284.79205084 1487.89914169 18824.37381327 -1.530335053 2.663107730 -0.542205966 14575.580204 0.555897 62.08105 294.51611 245.21323 196.99829 227.77813 2006 6 1 14:10:47.226115
1440.00000000 -984.62035146 -5187.03480813 -5745.59594144 4.340271916 -7.266811354 1.777668888 14567.926630 0.555320 62.08542 294.46033 245.19248 58.36949 15.80816 2006 6 1 16:10:47.226128
20413 xx
0.00000000 25123.29290741 -13225.49966286 3249.40351869 0.488683419 4.797897593 -0.961119693
1440.00000000 -151669.05280515 -5645.20454550 -2198.51592118 -0.869182889 -0.870759872 0.156508219 107329.432072 0.778767 11.46945 186.22560 197.88489 157.93798 84.35150 2005 12 30 19: 0: 0.000268
1560.00000000 -157497.71657495 -11884.99595074 -1061.44439402 -0.749657961 -0.864016715 0.157766101 107329.508122 0.778732 11.46619 186.21408 197.89244 160.17028 91.77011 2005 12 30 21: 0: 0.000282
1680.00000000 -162498.32255577 -18062.99733167 81.00915253 -0.638980378 -0.853687105 0.158098992 107329.571762 0.778698 11.46314 186.20285 197.89960 162.24325 99.18901 2005 12 30 23: 0: 0.000255
1800.00000000 -166728.76010920 -24155.99648299 1222.84128677 -0.535600687 -0.840455444 0.157680857 107329.625277 0.778667 11.46032 186.19193 197.90635 164.18719 106.60817 2005 12 31 1: 0: 0.000268
1920.00000000 -169935.81924592 -31767.29787964 2749.01540345 -0.430050431 -0.828904183 0.157812340 107329.670010 0.778636 11.45772 186.08880 198.56496 166.02584 114.02759 2005 12 31 3: 0: 0.000282
2040.00000000 -172703.07831815 -37662.95639336 3883.60052579 -0.338004891 -0.810277487 0.156020035 107329.707949 0.778608 11.45535 186.07803 198.57159 167.77827 121.44722 2005 12 31 5: 0: 0.000255
2160.00000000 -174823.19337404 -43417.55605219 5003.26312809 -0.250258622 -0.789828672 0.153764903 107329.739705 0.778582 11.45321 186.06765 198.57763 169.46004 128.86707 2005 12 31 7: 0: 0.000268
2280.00000000 -176324.63925775 -49018.51958648 6104.85025002 -0.166136613 -0.767706262 0.151092242 107329.766024 0.778557 11.45129 186.05765 198.58307 171.08420 136.28711 2005 12 31 9: 0: 0.000282
2400.00000000 -177231.42142458 -54454.12699497 7185.48661607 -0.085067854 -0.744001567 0.148033403 107329.787476 0.778535 11.44961 186.04805 198.58792 172.66187 143.70731 2005 12 31 11: 0: 0.000255
2520.00000000 -177563.73583232 -59713.14859144 8242.48472591 -0.006561730 -0.718760309 0.144608676 107329.804495 0.778515 11.44815 186.03884 198.59218 174.20274 151.12767 2005 12 31 13: 0: 0.000267
2640.00000000 -177338.48026483 -64784.54644698 9273.27220003 0.069809946 -0.691990238 0.140829236 107329.817407 0.778496 11.44692 186.03004 198.59585 175.71546 158.54815 2005 12 31 15: 0: 0.000281
2760.00000000 -176569.65151461 -69657.21976255 10275.33063459 0.144426878 -0.663665876 0.136698419 107329.826446 0.778480 11.44593 186.02165 198.59894 177.20787 165.96873 2005 12 31 17: 0: 0.000254
2880.00000000 -175268.65299073 -74319.77625463 11246.14177160 0.217631370 -0.633731091 0.132212491 107329.831764 0.778466 11.44516 186.01367 198.60144 178.68732 173.38940 2005 12 31 19: 0: 0.000267
3000.00000000 -173444.53039609 -78760.31560396 12183.13775212 0.289737325 -0.602099929 0.127361017 107329.833446 0.778454 11.44462 186.00610 198.60338 180.16078 180.81013 2005 12 31 21: 0: 0.000281
3120.00000000 -171104.14813653 -82966.21323591 13083.65278381 0.361037779 -0.568655903 0.122126889 107329.831507 0.778444 11.44430 185.99895 198.60474 181.63509 188.23090 2005 12 31 23: 0: 0.000254
3240.00000000 -168252.31543803 -86923.89363433 13944.87382716 0.431811396 -0.533249797 0.116486022 107329.825896 0.778437 11.44421 185.99222 198.60555 183.11712 195.65169 2006 1 1 1: 0: 0.000268
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3480.00000000 -161023.71139825 -94034.02398835 15537.12375729 0.572855321 -0.455766412 0.103848688 107329.803111 0.778429 11.44468 185.98002 198.60552 186.13287 210.49323 2006 1 1 5: 0: 0.000255
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22312 xx
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23177 xx
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240.00000000 -67053.08885388 -14994.69685946 -5897.99072793 -2.860576613 -1.183771565 -0.568473909 241188.455558 0.990674 30.28101 4.15169 29.05234 160.71292 4.53570 1994 11 1 15:59:59.999142
360.00000000 -85227.84253168 -22897.08484471 -9722.59184564 -2.426469823 -1.078592475 -0.525341431 241281.310582 0.990736 30.28476 4.16382 29.05288 163.48883 6.64765 1994 11 1 17:59:59.999155
480.00000000 -100986.00419136 -30171.19698695 -13283.77044765 -2.147108978 -1.000530827 -0.491587582 241334.995602 0.990793 30.28821 4.17269 29.05598 165.29944 8.75802 1994 11 1 19:59:59.999169
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840.00000000 -139863.28332207 -49436.45704153 -22836.80438139 -1.663762568 -0.845315913 -0.421548627 241415.704319 0.990937 30.29572 4.18925 29.07371 168.48089 15.08132 1994 11 2 1:59:59.999169
960.00000000 -150960.22978259 -55227.45413896 -25734.01408879 -1.558730986 -0.808061065 -0.404293846 241431.134912 0.990977 30.29708 4.19238 29.08170 169.17940 17.18685 1994 11 2 3:59:59.999142
1080.00000000 -161381.71414630 -60770.64040903 -28516.26290017 -1.468977174 -0.775190459 -0.388951810 241443.732852 0.991012 30.29782 4.19450 29.09061 169.77752 19.29141 1994 11 2 5:59:59.999155
1200.00000000 -171221.18736947 -66092.76474442 -31195.19847387 -1.390837596 -0.745785633 -0.375140398 241454.272978 0.991043 30.29790 4.19565 29.10039 170.29863 21.39510 1994 11 2 7:59:59.999169
1320.00000000 -180550.82888746 -71215.23290630 -33780.24938270 -1.321788672 -0.719184752 -0.362579495 241463.270793 0.991070 30.29731 4.19584 29.11101 170.75893 23.49801 1994 11 2 9:59:59.999142
1440.00000000 -189427.87533074 -76155.54943344 -36279.19882816 -1.260024473 -0.694896053 -0.351058133 241471.083479 0.991092 30.29602 4.19510 29.12247 171.17009 25.60022 1994 11 2 11:59:59.999155
1560.00000000 -197898.69401409 -80928.29015181 -38698.57972447 -1.204211888 -0.672544709 -0.340413731 241477.966779 0.991110 30.29403 4.19343 29.13474 171.54075 27.70182 1994 11 2 13:59:59.999169
1600.00000000 -200638.82986236 -82484.14969882 -39488.34331447 -1.186748462 -0.665472422 -0.337037582 241480.088691 0.991115 30.29321 4.19267 29.13901 171.65650 28.40224 1994 11 2 14:39:59.999146
23599 xx
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120.00000000 816.64091546 24118.98675475 2932.69459428 -2.626838010 0.504502763 0.062344306 15549.694828 0.578119 6.93348 0.17828 274.61863 173.27933 159.61486 2006 6 20 20:22: 6.640052
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320.00000000 9542.79201056 -533.71253081 -65.73165428 3.926947087 6.459583539 0.785686755 15544.294010 0.578456 6.93773 0.03892 274.89936 81.83675 23.52881 2006 6 20 23:42: 6.640020
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660.00000000 11794.48942915 6382.21138354 780.88439015 0.604412453 5.731729369 0.697574333 15545.613335 0.578381 6.93681 359.82453 275.35227 113.41906 44.20101 2006 6 21 5:22: 6.640052
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24208 xx
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25954 xx
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240.00000000 40159.05128805 -12845.39151157 12.96086316 0.937265422 2.928448287 0.000245505 42165.930350 0.000184 0.01820 266.81362 4.30035 71.14849 71.12848 2004 2 8 20:20: 1.494241
360.00000000 41192.55903455 9013.79606759 12.90495666 -0.656727442 3.003543458 -0.000257479 42165.931472 0.000165 0.01818 267.03031 4.52874 100.78392 100.76533 2004 2 8 22:20: 1.494254
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840.00000000 -28562.51093192 31022.45987587 -9.39562161 -2.261449202 -2.082713897 -0.000689669 42165.935960 0.000156 0.01812 267.83437 340.81305 243.98848 244.00460 2004 2 9 6:20: 1.494268
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26900 xx
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26975 xx
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240.00000000 -3882.62933791 11960.00543452 -25088.14383845 -2.146773699 -1.372461491 -2.579382089 26117.073879 0.560030 68.48255 236.11443 123.77229 130.16671 65.84328 2006 6 24 0:35:47.504546
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28057 xx
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720.00000000 -2090.79884266 -2723.22832193 6266.13356576 1.992640665 6.337529519 3.411803080 7143.567719 0.000886 98.43137 248.18007 166.10977 256.33563 256.43428 2006 6 27 6:52: 4.079695
840.00000000 1091.80560222 4809.88229503 5172.42897894 2.717483546 4.805518977 -5.030019896 7148.104201 0.001198 98.42868 248.27134 49.64708 83.33119 83.19482 2006 6 27 8:52: 4.079709
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1080.00000000 805.72698304 -812.16627907 -7067.58483968 -2.798936020 -6.889265977 0.472770873 7139.798473 0.002771 98.43363 248.42943 93.17484 180.50142 180.50420 2006 6 27 12:52: 4.079695
1200.00000000 -2249.59837532 -6505.84890714 -1956.72365062 -1.731234729 -1.528750230 7.096660885 7156.391905 0.000858 98.42375 248.51302 75.03747 268.91702 269.01529 2006 6 27 14:52: 4.079709
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1800.00000000 -1951.43708472 -6251.71945820 -2886.95472355 -2.024131483 -2.475214272 6.741537478 7154.763448 0.000797 98.42472 248.92120 92.12978 243.80606 243.88802 2006 6 28 0:52: 4.079695
1920.00000000 -2475.70722288 -4331.90569958 5117.31234924 1.235823539 5.322743371 5.091281211 7148.309000 0.001201 98.42856 248.99314 128.52047 277.84975 277.98604 2006 6 28 2:52: 4.079709
2040.00000000 281.46097847 3353.51057102 6302.87900650 2.840647273 6.047222485 -3.337085992 7143.399871 0.000887 98.43147 249.08435 11.88507 105.01812 104.91998 2006 6 28 4:52: 4.079682
2160.00000000 2650.33118860 6584.33434851 -908.29027134 0.675457235 -1.274044972 -7.323921567 7157.479518 0.001039 98.42311 249.15999 111.90557 75.46685 75.35165 2006 6 28 6:52: 4.079695
2280.00000000 1501.17226597 1066.31132756 -6918.71472952 -2.361891904 -6.889669974 -1.574718619 7140.544654 0.002662 98.43318 249.24051 78.83005 178.83747 178.83127 2006 6 28 8:52: 4.079709
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28129 xx
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240.00000000 -3006.50596328 18522.20742011 18941.84078154 -3.375452789 1.032680773 -1.559324534 26559.578962 0.004639 54.72725 324.78155 266.56887 212.95207 213.24205 2006 6 24 17:41:49.461477
360.00000000 -21607.02086957 15432.59962630 206.62470309 -1.306049851 -1.817011568 -3.163725018 26562.088029 0.004629 54.72925 324.77940 265.56225 273.89165 274.42076 2006 6 24 19:41:49.461491
480.00000000 -18453.06134549 -3150.83256134 -18685.83030936 2.106017925 -2.860236337 -1.586151870 26559.602324 0.004611 54.72744 324.77734 266.55088 333.36818 333.60429 2006 6 24 21:41:49.461504
600.00000000 3425.11742384 -18514.73232706 -18588.67200557 3.394666340 -1.003072030 1.610061295 26559.630774 0.004616 54.72755 324.77120 265.84923 34.77421 34.47340 2006 6 24 23:41:49.461477
720.00000000 21858.23838148 -15101.51661554 387.34517048 1.247973967 1.856017403 3.161439948 26562.085763 0.004621 54.72951 324.76918 266.85519 94.16792 93.63964 2006 6 25 1:41:49.461491
840.00000000 18360.69935796 3506.55256762 19024.81678979 -2.122684184 2.830618605 1.537510677 26559.559560 0.004643 54.72767 324.76702 265.87367 155.01858 154.79317 2006 6 25 3:41:49.461504
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1080.00000000 -21758.08331586 15215.44829478 -180.82181406 -1.250144680 -1.856490448 -3.163774870 26562.088483 0.004630 54.72977 324.75889 265.57964 274.89830 275.42679 2006 6 25 7:41:49.461491
1200.00000000 -18193.41290284 -3493.85876912 -18877.14757717 2.153326942 -2.852221264 -1.536617760 26559.550630 0.004608 54.72793 324.75676 266.56769 334.38316 334.61076 2006 6 25 9:41:49.461504
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1440.00000000 22002.20074562 -14879.72595593 774.32827099 1.191573619 1.894561165 3.159953047 26562.082259 0.004619 54.73003 324.74874 266.86759 95.17782 94.65052 2006 6 25 13:41:49.461491
28350 xx
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360.00000000 4788.22345627 782.56169214 4335.14284621 -4.954509026 3.683346464 4.804645839 6499.559344 0.001075 64.99631 344.65400 214.64598 192.67757 192.70463 2006 6 16 11:13:45.407405
480.00000000 -6291.84601644 1547.82790772 -453.67116498 -0.308625588 -3.341538574 -7.082659115 6501.402918 0.000997 65.01469 344.30961 204.13051 340.28893 340.32744 2006 6 16 13:13:45.407419
600.00000000 4480.74573428 -3028.55200374 -3586.94343641 5.320920857 1.199736275 5.626350481 6488.183334 0.000573 65.00211 343.95864 209.39798 113.02357 112.96312 2006 6 16 15:13:45.407392
720.00000000 -446.42460916 2932.28872588 5759.19389757 -7.561000245 1.550975493 -1.374970885 6471.211254 0.001070 64.98172 343.63887 286.01526 175.14933 175.13896 2006 6 16 17:13:45.407405
840.00000000 -3713.79581831 -1382.66125130 -5122.45131136 6.090931626 -3.512629733 -3.467571746 6467.477224 0.001377 64.98864 343.33023 59.77643 181.00806 181.01084 2006 6 16 19:13:45.407419
960.00000000 6058.32017522 -827.47406722 2104.04678651 -1.798403024 3.787067272 6.641439744 6471.014530 0.001294 65.01057 342.99339 78.06727 302.97061 303.09495 2006 6 16 21:13:45.407392
1080.00000000 -5631.73659006 2623.70953644 1766.49125084 -3.216401578 -2.309140959 -6.788609120 6464.578757 0.001504 65.01192 342.63489 106.21713 56.22138 56.07825 2006 6 16 23:13:45.407405
1200.00000000 2776.84991560 -3255.36941953 -4837.19667790 6.748135564 -0.193044825 4.005718698 6447.542625 0.001645 64.99132 342.29217 117.75742 186.50124 186.52261 2006 6 17 1:13:45.407419
1320.00000000 1148.04430837 2486.07343386 5826.34075913 -7.420162295 2.589456382 0.356350006 6435.171751 0.000414 64.98033 341.97488 253.68628 193.44297 193.45401 2006 6 17 3:13:45.407392
1440.00000000 -4527.90871828 -723.29199041 -4527.44608319 5.121674217 -3.909895427 -4.500218556 6434.774399 0.001426 64.99416 341.65351 60.39417 170.43559 170.40841 2006 6 17 5:13:45.407405
28623 xx
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360.00000000 -9708.68629714 26306.14553149 -1204.29478856 -1.824164290 -0.931909596 1.113419052 17354.308840 0.624979 28.54525 114.78570 170.51013 184.33805 194.62715 2006 6 27 1:27:32.414963
480.00000000 -14394.03162892 6659.30765074 5593.38345858 1.556522911 -4.681657614 0.296912248 17349.390394 0.625102 28.53879 114.74400 170.58065 233.53987 308.58496 2006 6 27 3:27:32.414976
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720.00000000 -7558.36739603 27035.11367962 -2385.12054184 -1.999583791 -0.393409283 1.078093515 17344.562691 0.624731 28.54585 114.60541 170.80625 178.98913 176.58319 2006 6 27 7:27:32.414963
840.00000000 -15495.61862220 11550.15897828 5053.83178121 0.469277336 -4.029761073 0.679054742 17340.566145 0.624804 28.54261 114.56467 170.86870 221.10114 290.64195 2006 6 27 9:27:32.414976
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1080.00000000 -5275.80272094 27151.78486008 -3494.50687216 -2.129609388 0.150196480 1.021038089 17334.798205 0.624491 28.54619 114.42511 171.10197 173.69159 158.82687 2006 6 27 13:27:32.414963
1200.00000000 -15601.37656145 15641.29379850 4217.03266850 -0.249183123 -3.405238557 0.888214503 17331.224518 0.624507 28.54526 114.38403 171.16062 211.94210 272.98408 2006 6 27 15:27:32.414976
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1440.00000000 -2914.31065828 26665.20392758 -4511.09814335 -2.216261909 0.710067769 0.940691824 17325.009247 0.624258 28.54628 114.24480 171.39711 168.29579 141.35834 2006 6 27 19:27:32.414963
28626 xx
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240.00000000 23232.82515008 35187.33981802 4.98927428 -2.565776620 1.694193132 0.000163365 42166.250914 0.000038 0.00743 350.74515 12.41165 53.40798 53.40452 2006 6 25 15:12:14.454998
360.00000000 2467.44290178 42093.60909959 5.15062987 -3.069341800 0.179976276 -0.000031739 42166.256312 0.000021 0.00702 351.81369 31.17666 63.65492 63.65278 2006 6 25 17:12:14.455012
480.00000000 -18962.59052991 37661.66243819 4.04433258 -2.746151982 -1.382675777 -0.000197633 42166.261709 0.000004 0.00662 352.89609 92.59585 31.23325 31.23300 2006 6 25 19:12:14.455025
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720.00000000 -42103.20138132 2291.06228893 -0.13274964 -0.166974816 -3.070104560 -0.000311007 42166.272504 0.000034 0.00580 355.10258 238.21722 303.56550 303.56870 2006 6 25 23:12:14.455012
840.00000000 -37580.31858370 -19120.40485693 -2.02755702 1.394367848 -2.740341612 -0.000248591 42166.277902 0.000049 0.00539 356.22456 254.44135 316.30053 316.30437 2006 6 26 1:12:14.455025
960.00000000 -22934.20761876 -35381.23870806 -3.16495932 2.580167539 -1.672360951 -0.000134907 42166.283299 0.000060 0.00498 357.35709 269.63485 330.05665 330.06010 2006 6 26 3:12:14.454998
1080.00000000 -2109.90332389 -42110.71508198 -3.36507889 3.070935369 -0.153808390 -0.000005855 42166.288696 0.000068 0.00457 358.49948 284.45334 344.17885 344.18097 2006 6 26 5:12:14.455012
1200.00000000 19282.77774728 -37495.59250598 -2.71861462 2.734400524 1.406220933 0.000103486 42166.294093 0.000071 0.00417 359.65183 299.12472 358.43875 358.43898 2006 6 26 7:12:14.455025
1320.00000000 35480.60990600 -22779.03375285 -1.52841859 1.661210676 2.587414593 0.000168300 42166.299490 0.000069 0.00376 0.81421 313.77342 12.71135 12.70961 2006 6 26 9:12:14.454998
1440.00000000 42119.96263499 -1925.77567263 -0.19827433 0.140521206 3.071541613 0.000179561 42166.304886 0.000062 0.00336 1.98591 328.51675 26.87953 26.87630 2006 6 26 11:12:14.455012
28872 xx
0.00000000 -6131.82730456 2446.52815528 -253.64211033 -0.144920228 0.995100963 7.658645067
5.00000000 -5799.24256134 2589.14811119 2011.54515100 2.325207364 -0.047125672 7.296234071 6532.131812 0.028892 96.46953 157.99929 243.05004 134.64086 132.24900 2005 11 29 0:33:58.939092
10.00000000 -4769.05061967 2420.46580562 4035.30855837 4.464585796 -1.060923209 6.070907874 6526.273486 0.029375 96.47228 158.00095 241.81874 155.49460 154.06995 2005 11 29 0:38:58.939114
15.00000000 -3175.45157340 1965.98738086 5582.12569607 6.049639376 -1.935777558 4.148607019 6519.457505 0.030322 96.47559 158.00479 241.88251 174.88643 174.56958 2005 11 29 0:43:58.939096
20.00000000 -1210.19024802 1281.54541294 6474.68172772 6.920746273 -2.580517337 1.748783868 6514.336564 0.030902 96.47802 158.01066 243.38375 192.80420 193.60708 2005 11 29 0:48:58.939118
25.00000000 896.73799533 447.12357305 6607.22400507 6.983396282 -2.925846168 -0.872655207 6512.862228 0.030569 96.47849 158.01759 245.19289 210.51094 212.32507 2005 11 29 0:53:58.939101
30.00000000 2896.99663534 -440.04738594 5954.92675486 6.211488246 -2.926949815 -3.433959806 6515.608034 0.029493 96.47675 158.02409 245.84813 229.59404 232.20474 2005 11 29 0:58:58.939123
35.00000000 4545.78970167 -1273.55952872 4580.16512984 4.656984233 -2.568711513 -5.638510954 6521.403980 0.028482 96.47351 158.02882 244.64993 250.85868 253.96339 2005 11 29 1: 3:58.939105
40.00000000 5627.43299371 -1947.94282469 2634.16714930 2.464141047 -1.873985161 -7.195743032 6527.502251 0.028288 96.47026 158.03113 242.66126 273.31432 276.54607 2005 11 29 1: 8:58.939127
45.00000000 5984.72318534 -2371.37691609 349.87996209 -0.121276950 -0.911981546 -7.859613894 6530.555444 0.028747 96.46863 158.03155 241.89724 294.97178 297.93068 2005 11 29 1:13:58.939109
50.00000000 5548.43325922 -2480.16469245 -1979.24314527 -2.763269534 0.199691915 -7.482796996 6528.353658 0.028906 96.46957 158.03163 242.90998 315.24831 317.54473 2005 11 29 1:18:58.939092
29141 xx
0.00000000 423.99295524 -6658.12256149 136.13040356 1.006373613 0.217309983 7.662587892
20.00000000 931.80883587 -1017.17852239 6529.19244527 -0.298847918 7.613891977 1.226399480 6654.859371 0.002792 82.42352 273.47441 254.48318 186.27472 186.30976 2006 6 19 6:45:41.242102
40.00000000 -83.44906141 6286.20208453 2223.49837161 -1.113515974 2.530970283 -7.219445568 6667.409852 0.000967 82.43311 273.45347 259.01762 261.32660 261.43621 2006 6 19 7: 5:41.242111
60.00000000 -958.57681221 3259.26005348 -5722.63732467 -0.101225813 -6.735338321 -3.804851872 6650.404442 0.001731 82.42598 273.44626 354.27502 245.88943 246.07057 2006 6 19 7:25:41.242079
80.00000000 -255.25619985 -5132.59762974 -4221.27233118 1.077709303 -4.905938824 5.892521264 6652.084920 0.000656 82.42981 273.42019 252.81771 67.36659 67.29720 2006 6 19 7:45:41.242088
100.00000000 867.44295097 -5038.40402933 4256.73810533 0.479447535 5.032326446 5.857126248 6646.445447 0.000943 82.42973 273.41562 212.21882 187.98298 187.99800 2006 6 19 8: 5:41.242097
120.00000000 559.16882013 3376.30587937 5699.22017391 -0.906749328 6.646149867 -3.852331832 6633.873397 0.002146 82.42602 273.38941 288.19218 191.94169 191.99264 2006 6 19 8:25:41.242106
140.00000000 -669.85184205 6196.00229484 -2281.95741770 -0.795804092 -2.752114827 -7.202478520 6639.351533 0.001666 82.43307 273.38226 276.79256 283.50264 283.68819 2006 6 19 8:45:41.242075
160.00000000 -784.20708019 -1278.53125553 -6449.19892596 0.636702380 -7.595425203 1.431090802 6615.185547 0.000988 82.42356 273.36071 80.31004 200.39880 200.43831 2006 6 19 9: 5:41.242084
180.00000000 406.15811659 -6607.03115799 148.33021477 1.009818575 0.231843765 7.692047844 6625.576066 0.000764 82.43444 273.34723 331.83273 29.46222 29.41915 2006 6 19 9:25:41.242093
200.00000000 916.34911813 -884.08649248 6491.09810362 -0.302163049 7.669887109 1.084336909 6596.784223 0.002757 82.42336 273.33273 254.08653 187.77997 187.82284 2006 6 19 9:45:41.242102
220.00000000 -104.02490970 6304.31821405 1960.08739882 -1.108873823 2.259522809 -7.351147710 6603.486694 0.000956 82.43346 273.31198 246.54178 276.03282 276.14180 2006 6 19 10: 5:41.242111
240.00000000 -944.61642849 2872.17248379 -5846.94103362 -0.051117686 -6.989747076 -3.413102600 6577.346070 0.001592 82.42534 273.30392 2.77756 240.87045 241.02990 2006 6 19 10:25:41.242079
260.00000000 -187.16569888 -5404.86163467 -3731.97057618 1.094696706 -4.412110995 6.326060952 6573.111994 0.000741 82.43077 273.27798 263.60955 61.43377 61.35924 2006 6 19 10:45:41.242088
280.00000000 884.59720467 -4465.74516163 4725.83632696 0.380656028 5.691554046 5.303910983 6553.914239 0.001257 82.42848 273.27324 213.21629 193.37953 193.41290 2006 6 19 11: 5:41.242097
300.00000000 446.40767236 4086.66839620 5093.05596650 -0.982424447 6.072965199 -4.791630682 6535.077554 0.001618 82.42746 273.24577 291.11394 197.16680 197.22159 2006 6 19 11:25:41.242106
320.00000000 -752.24467495 5588.35473301 -3275.04092573 -0.661161370 -4.016290740 -6.676898026 6523.150138 0.001608 82.43163 273.24054 287.85797 282.58332 282.76309 2006 6 19 11:45:41.242075
340.00000000 -643.72872525 -2585.02528560 -5923.01306608 0.807922142 -7.171597814 3.041115058 6490.083264 0.000695 82.42474 273.21509 123.03058 170.03884 170.02506 2006 6 19 12: 5:41.242084
360.00000000 584.40295819 -6202.35605817 1781.00536019 0.869250450 2.226927514 7.471676765 6481.796204 0.000373 82.43379 273.20643 7.31819 8.78009 8.77357 2006 6 19 12:25:41.242093
380.00000000 779.59211765 1100.73728301 6311.59529480 -0.599552305 7.721032522 -1.275153027 6437.508232 0.002601 82.42317 273.18521 272.09622 187.31813 187.35618 2006 6 19 12:45:41.242102
400.00000000 -403.03155588 6399.18000837 -364.12735875 -1.008861924 -0.516636615 -7.799812287 6427.949611 0.001475 82.43476 273.17168 235.94761 307.33127 307.46560 2006 6 19 13: 5:41.242111
420.00000000 -852.93910071 192.65232023 -6322.47054784 0.396006194 -7.882964919 -0.289331517 6375.610362 0.001229 82.42276 273.15527 61.88829 205.96299 206.02469 2006 6 19 13:25:41.242079
29238 xx
0.00000000 -5566.59512819 -3789.75991159 67.60382245 2.873759367 -3.825340523 6.023253926
120.00000000 4474.27915495 -1447.72286142 4619.83927235 4.712595822 5.668306153 -2.701606741 6722.575685 0.020855 51.54723 213.34037 94.40931 22.09810 21.21193 2006 6 26 8:53:44.456634
240.00000000 1922.17712474 5113.01138342 -4087.08470203 -6.490769651 -0.522350158 -3.896001154 6724.840619 0.020836 51.55602 212.95757 95.05339 134.84550 133.13386 2006 6 26 10:53:44.456607
360.00000000 -6157.93546882 -2094.70798790 -1941.63730960 0.149900661 -5.175192523 5.604262034 6729.860276 0.020524 51.57445 212.48491 94.57294 244.01244 246.14078 2006 6 26 12:53:44.456620
480.00000000 2482.64052411 -3268.45944555 5146.38006190 6.501814698 4.402848754 -0.350943511 6719.018114 0.020320 51.53923 212.07031 96.26478 356.94314 357.06545 2006 6 26 14:53:44.456634
600.00000000 4036.26455287 4827.43347201 -2507.99063955 -5.184409515 1.772280695 -5.331390168 6728.048056 0.020495 51.57078 211.66544 97.68432 110.52055 108.30924 2006 6 26 16:53:44.456607
720.00000000 -5776.81371622 -118.64155319 -3641.22052418 -2.539917207 -5.622701582 4.403125405 6724.820558 0.020547 51.56099 211.18821 97.21262 219.89135 221.41939 2006 6 26 18:53:44.456620
840.00000000 67.98699487 -4456.49213473 4863.71794283 7.183809420 2.418917791 2.015642495 6719.324890 0.020499 51.54373 210.80108 98.23244 332.06973 333.15521 2006 6 26 20:53:44.456634
960.00000000 5520.62207038 3782.38203554 -596.73193161 -3.027966069 3.754152525 -6.013506363 6729.578486 0.020759 51.57938 210.36070 99.82418 86.68512 84.31260 2006 6 26 22:53:44.456607
1080.00000000 -4528.05104455 1808.46273329 -4816.99727762 -4.808419763 -5.185789345 2.642104494 6719.734999 0.020988 51.54703 209.90441 98.71342 197.46314 198.19584 2006 6 27 0:53:44.456620
1200.00000000 -2356.61468078 -4852.51202272 3856.53816184 6.688446735 0.118520958 4.021854210 6722.408929 0.020953 51.55740 209.52106 98.53493 309.41224 311.24882 2006 6 27 2:53:44.456634
1320.00000000 6149.65800134 2173.59423261 1369.29488732 -0.345832777 5.109857861 -5.842951828 6727.916386 0.021118 51.57710 209.05199 100.14201 64.65457 62.48241 2006 6 27 4:53:44.456607
1440.00000000 -2629.55011449 3400.98040158 -5344.38217129 -6.368548448 -3.998963509 0.577253064 6716.496128 0.021225 51.53949 208.63001 98.79198 176.88483 176.75052 2006 6 27 6:53:44.456620
88888 xx
0.00000000 2328.96975262 -5995.22051338 1719.97297192 2.912073281 -0.983417956 -7.090816210
120.00000000 1020.69234558 2286.56260634 -6191.55565927 -3.746543902 6.467532721 1.827985678 6626.008292 0.010522 72.83280 115.75005 63.53918 220.46377 221.25094 1980 10 2 1:41:24.113771
240.00000000 -3226.54349155 3503.70977525 4532.80979343 1.000992116 -5.788042888 5.162585826 6633.568600 0.009051 72.84300 115.55580 59.76008 346.41743 346.65942 1980 10 2 3:41:24.113744
360.00000000 2456.10706533 -6071.93855503 1222.89768554 2.679390040 -0.448290811 -7.228792155 6642.303503 0.009521 72.85473 115.32544 59.25198 109.67444 108.64459 1980 10 2 5:41:24.113757
480.00000000 787.16457349 2719.91800946 -6043.86662024 -3.759883839 6.277439314 2.397897864 6626.659125 0.010283 72.83384 115.10965 63.34327 225.25694 226.09847 1980 10 2 7:41:24.113771
600.00000000 -3110.97648029 3121.73026235 4878.15217035 1.244916056 -6.124880425 4.700576353 6631.933076 0.008795 72.84100 114.91683 59.02796 351.92087 352.06159 1980 10 2 9:41:24.113744
720.00000000 2567.56229695 -6112.50383922 713.96374435 2.440245751 0.098109002 -7.319959258 6642.615358 0.009371 72.85532 114.68868 58.81484 114.75171 113.77366 1980 10 2 11:41:24.113757
840.00000000 556.05661780 3144.52288201 -5855.34636178 -3.754660143 6.044752775 2.957941672 6627.505506 0.010032 72.83515 114.46939 62.86103 230.37982 231.26958 1980 10 2 13:41:24.113771
960.00000000 -2982.47940539 2712.61663711 5192.32330472 1.475566773 -6.427737014 4.202420227 6630.339520 0.008547 72.83905 114.27748 57.92953 357.82813 357.86501 1980 10 2 15:41:24.113744
1080.00000000 2663.08964352 -6115.48290885 196.40072866 2.196121564 0.652415093 -7.362824152 6642.696880 0.009229 72.85560 114.05197 58.08826 120.14672 119.22898 1980 10 2 17:41:24.113757
1200.00000000 328.54999674 3557.09490552 -5626.21427211 -3.731193288 5.769341172 3.504058731 6628.528407 0.009780 72.83669 113.82932 62.06118 235.86432 236.79576 1980 10 2 19:41:24.113771
1320.00000000 -2842.06876757 2278.42343492 5472.33437150 1.691852635 -6.693216335 3.671022712 6628.832330 0.008322 72.83722 113.63775 56.45020 4.15293 4.08430 1980 10 2 21:41:24.113744
1440.00000000 2742.55398832 -6079.67009123 -326.39012649 1.948497651 1.211072678 -7.356193131 6642.539418 0.009109 72.85556 113.41525 57.08019 125.85183 125.00240 1980 10 2 23:41:24.113757
33333 xx
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5.00000000 836.36198558 3131.21861830 27739.12500595 0.806969092 -0.303613357 1.495581060 15591.703950 0.948291 96.38049 148.19713 273.67820 174.39430 116.59606 2005 11 29 0:33:58.939092
10.00000000 12529.16240012 -7305.76672566 24606.25882463 1.077046921 -0.832176467 0.734844393 15620.294215 0.956163 96.35544 138.86115 304.49417 175.41552 122.71671 2005 11 29 0:38:58.939114
15.00000000 17680.27781737 -19040.50274272 13889.53302171 0.838850492 -1.010897050 0.019845764 15735.072365 0.974320 96.11899 129.59336 334.76647 176.93090 128.70759 2005 11 29 0:43:58.939096
20.00000000 23876.96955477 -37275.65263893 -8113.95104473 0.589108130 -0.767768418 -0.260379679 23854.828071 0.998563 46.03989 112.46059 15.25388 179.25121 126.28606 2005 11 29 0:48:58.939118
33334 xx
0.00000000 23876.96955477 -37275.65263893 -8113.95104473 0.589108130 -0.767768418 -0.260379679
33335 xx
0.00000000 42081.34386081 -2649.18487875 0.81820315 0.193184518 3.068627007 0.000438443
20.00000000 42151.86113568 1038.56497521 1.31183638 -0.075730915 3.073768897 0.000428300 42166.241018 0.000038 0.00818 348.82102 11.29619 1.29419 1.29409 2006 6 25 11:32:14.455021
40.00000000 41899.82539501 4718.36752490 1.78786028 -0.344066764 3.055389800 0.000415234 42166.241918 0.000038 0.00811 348.99404 16.07338 1.35763 1.35753 2006 6 25 11:52:14.455030
60.00000000 41327.16536793 8362.06432379 2.24306194 -0.609769675 3.013630372 0.000399389 42166.242817 0.000038 0.00804 349.16745 20.86023 1.41100 1.41090 2006 6 25 12:12:14.454998
80.00000000 40438.26325401 11941.77323201 2.67443598 -0.870806448 2.948810178 0.000380927 42166.243717 0.000037 0.00797 349.34125 25.65723 1.45385 1.45374 2006 6 25 12:32:14.455007
100.00000000 39239.92118669 15430.10177531 3.07920420 -1.125179589 2.861425248 0.000360030 42166.244617 0.000037 0.00791 349.51544 30.46476 1.48578 1.48567 2006 6 25 12:52:14.455016
120.00000000 37741.30917901 18800.35675644 3.45483317 -1.370942600 2.752144282 0.000336890 42166.245516 0.000037 0.00784 349.69000 35.28315 1.50647 1.50636 2006 6 25 13:12:14.455025
140.00000000 35953.89494997 22026.74851504 3.79904972 -1.606214870 2.621803528 0.000311718 42166.246416 0.000037 0.00777 349.86493 40.11263 1.51569 1.51558 2006 6 25 13:32:14.454994
160.00000000 33891.35616861 25084.58827300 4.10985412 -1.829196068 2.471400388 0.000284732 42166.247316 0.000037 0.00770 350.04024 44.95337 1.51328 1.51317 2006 6 25 13:52:14.455003
180.00000000 31569.47578743 27950.47705519 4.38553102 -2.038179917 2.302085784 0.000256165 42166.248215 0.000037 0.00764 350.21591 49.80543 1.49918 1.49907 2006 6 25 14:12:14.455012
200.00000000 29006.02126614 30602.48473998 4.62465800 -2.231567255 2.115155347 0.000226253 42166.249115 0.000037 0.00757 350.39196 54.66878 1.47342 1.47331 2006 6 25 14:32:14.455021
220.00000000 26220.60860999 33020.31786944 4.82611168 -2.407878265 1.912039506 0.000195241 42166.250014 0.000037 0.00750 350.56837 59.54331 1.43611 1.43600 2006 6 25 14:52:14.455030
240.00000000 23234.55226321 35185.47493519 4.98907152 -2.565763805 1.694292541 0.000163378 42166.250914 0.000037 0.00743 350.74515 64.42880 1.38747 1.38737 2006 6 25 15:12:14.454998
260.00000000 20070.70200615 37081.38795177 5.11302111 -2.704015726 1.463580689 0.000130915 42166.251814 0.000037 0.00736 350.92231 69.32494 1.32781 1.32771 2006 6 25 15:32:14.455007
280.00000000 16753.26810433 38693.54923410 5.19774715 -2.821576121 1.221669394 0.000098102 42166.252713 0.000037 0.00730 351.09983 74.23133 1.25753 1.25743 2006 6 25 15:52:14.455016
300.00000000 13307.63604740 40009.62240917 5.24333607 -2.917545416 0.970409795 0.000065188 42166.253613 0.000037 0.00723 351.27773 79.14746 1.17712 1.17704 2006 6 25 16:12:14.455025
320.00000000 9760.17229554 41019.53681249 5.25016837 -2.991189257 0.711724566 0.000032419 42166.254513 0.000036 0.00716 351.45600 84.07275 1.08719 1.08711 2006 6 25 16:32:14.454994
340.00000000 6138.02252001 41715.56454704 5.21891075 -3.041944126 0.447593198 0.000000034 42166.255412 0.000036 0.00709 351.63466 89.00650 0.98841 0.98834 2006 6 25 16:52:14.455003
360.00000000 2468.90388143 42092.37961516 5.15050615 -3.069421652 0.180036856 -0.000031733 42166.256312 0.000036 0.00702 351.81369 93.94797 0.88153 0.88147 2006 6 25 17:12:14.455012
380.00000000 -1219.10706450 42147.09867100 5.04616179 -3.073411586 -0.088897090 -0.000062658 42166.257211 0.000036 0.00696 351.99312 98.89630 0.76740 0.76735 2006 6 25 17:32:14.455021
400.00000000 -4897.78921104 41879.30308168 4.90733536 -3.053883409 -0.357150730 -0.000092529 42166.258111 0.000036 0.00689 352.17293 103.85059 0.64693 0.64688 2006 6 25 17:52:14.455030
420.00000000 -8538.99285015 41291.04212849 4.73571938 -3.010986561 -0.622671362 -0.000121143 42166.259011 0.000036 0.00682 352.35313 108.80986 0.52108 0.52104 2006 6 25 18:12:14.454998
440.00000000 -12114.85507563 40386.81732367 4.53322412 -2.945049303 -0.883427197 -0.000148313 42166.259910 0.000036 0.00675 352.53372 113.77308 0.39089 0.39086 2006 6 25 18:32:14.455007
460.00000000 -15598.01299133 39173.54796277 4.30195895 -2.856576200 -1.137422908 -0.000173864 42166.260810 0.000036 0.00668 352.71471 118.73919 0.25742 0.25740 2006 6 25 18:52:14.455016
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1120.00000000 5256.15079690 -41835.79310235 -3.23223988 3.050717780 0.383286250 0.000034295 42166.290495 0.000038 0.00444 358.88248 278.87839 359.40012 359.40017 2006 6 26 5:52:14.455030
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1340.00000000 37336.09308113 -19592.80269080 -1.30538495 1.428732211 2.722592184 0.000173883 42166.300389 0.000038 0.00369 1.00888 330.52129 0.78076 0.78070 2006 6 26 9:32:14.455007
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1380.00000000 40177.22424735 -12792.69066866 -0.85533591 0.932860106 2.929770230 0.000180519 42166.302188 0.000038 0.00356 1.39898 339.94517 0.99403 0.99396 2006 6 26 10:12:14.455025
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1420.00000000 41790.94551564 -5601.76358958 -0.41263443 0.408489486 3.047444033 0.000181274 42166.303987 0.000038 0.00342 1.79004 349.39665 1.17875 1.17866 2006 6 26 10:52:14.455003
1440.00000000 42120.60775638 -1928.11061608 -0.19841236 0.140602589 3.071483058 0.000179558 42166.304886 0.000038 0.00336 1.98591 354.13456 1.25859 1.25850 2006 6 26 11:12:14.455012
20413 xx
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1844085.00000000 -26889.88686232 -60924.22895005 11096.42526856 1.806614763 2.101954513 -0.639970719 107250.265413 0.962811 16.55875 100.26924 301.44306 203.33764 343.54956 2009 7 2 9:45: 0.000282
1844090.00000000 -26345.68309880 -60289.69885481 10903.76218217 1.817157098 2.125947384 -0.644337692 107249.285617 0.962809 16.55901 100.26926 301.44278 203.55150 343.85845 2009 7 2 9:50: 0.000264
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1844120.00000000 -23011.50493242 -56321.96569019 9718.99437947 1.884253014 2.284614147 -0.672448379 107242.647894 0.962797 16.56059 100.26945 301.44111 204.95645 345.71182 2009 7 2 10:20: 0.000277
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1844135.00000000 -21297.47121883 -54224.49901162 9106.78494287 1.920540902 2.375161082 -0.687903637 107238.739687 0.962791 16.56140 100.26961 301.44025 205.75132 346.63854 2009 7 2 10:35: 0.000264
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1844210.00000000 -12181.24636732 -42238.90613844 5805.79753835 2.137104464 3.012730262 -0.785318582 107208.922519 0.962758 16.56573 100.27153 301.43526 211.22760 351.27244 2009 7 2 11:50: 0.000277
1844215.00000000 -11536.84261368 -41325.68999865 5568.90561221 2.153979041 3.072207323 -0.793431617 107205.947864 0.962756 16.56605 100.27177 301.43485 211.72921 351.58139 2009 7 2 11:55: 0.000259
1844220.00000000 -10887.32310987 -40394.14027737 5329.53827536 2.171177951 3.134913901 -0.801811902 107202.777924 0.962753 16.56637 100.27204 301.43443 212.25660 351.89035 2009 7 2 12: 0: 0.000282
1844225.00000000 -10232.59142737 -39443.24111540 5087.61330523 2.188694483 3.201165036 -0.810474295 107199.391616 0.962750 16.56669 100.27233 301.43399 212.81223 352.19931 2009 7 2 12: 5: 0.000264
1844230.00000000 -9572.55394393 -38471.87551671 4843.04392506 2.206516401 3.271320733 -0.819434438 107195.764621 0.962748 16.56701 100.27265 301.43353 213.39892 352.50827 2009 7 2 12:10: 0.000286
1844235.00000000 -8907.12176784 -37478.81060673 4595.73858344 2.224624089 3.345794555 -0.828708674 107191.868720 0.962745 16.56735 100.27300 301.43305 214.01991 352.81724 2009 7 2 12:15: 0.000268
1844240.00000000 -8236.21330715 -36462.68000983 4345.60076943 2.242988067 3.425064297 -0.838313893 107187.670970 0.962742 16.56768 100.27339 301.43254 214.67894 353.12622 2009 7 2 12:20: 0.000250
1844245.00000000 -7559.75771067 -35421.96263240 4092.52889178 2.261565621 3.509685388 -0.848267260 107183.132658 0.962739 16.56803 100.27382 301.43201 215.38035 353.43520 2009 7 2 12:25: 0.000273
1844250.00000000 -6877.69949423 -34354.95691398 3836.41626403 2.280296205 3.600307848 -0.858585776 107178.207951 0.962736 16.56837 100.27430 301.43143 216.12924 353.74418 2009 7 2 12:30: 0.000255
1844255.00000000 -6190.00479593 -33259.74931042 3577.15125966 2.299095084 3.697697981 -0.869285578 107172.842155 0.962732 16.56873 100.27483 301.43082 216.93161 354.05317 2009 7 2 12:35: 0.000277
1844260.00000000 -5496.66989517 -32134.17535485 3314.61773512 2.317844446 3.802766452 -0.880380840 107166.969427 0.962729 16.56909 100.27542 301.43016 217.79460 354.36217 2009 7 2 12:40: 0.000259
1844265.00000000 -4797.73291806 -30975.77105656 3048.69587160 2.336380825 3.916605048 -0.891882055 107160.509727 0.962725 16.56946 100.27609 301.42945 218.72678 354.67118 2009 7 2 12:45: 0.000282
1844270.00000000 -4093.29008842 -29781.71155368 2779.26366928 2.354477016 4.040535491 -0.903793358 107153.364709 0.962721 16.56984 100.27684 301.42867 219.73855 354.98019 2009 7 2 12:50: 0.000264
1844275.00000000 -3383.51857112 -28548.73271713 2506.19946418 2.371815647 4.176175206 -0.916108304 107145.412070 0.962717 16.57022 100.27769 301.42781 220.84268 355.28921 2009 7 2 12:55: 0.000286
1844280.00000000 -2668.70904438 -27273.02958541 2229.38606006 2.387949818 4.325527393 -0.928803170 107136.497643 0.962712 16.57061 100.27865 301.42686 222.05501 355.59824 2009 7 2 13: 0: 0.000268
1844285.00000000 -1949.31292724 -25950.12276772 1948.71744545 2.402243201 4.491106668 -0.941826145 107126.424100 0.962707 16.57101 100.27976 301.42580 223.39556 355.90729 2009 7 2 13: 5: 0.000250
1844290.00000000 -1226.01219539 -24574.67969914 1664.10971973 2.413776635 4.676117853 -0.955079559 107114.934413 0.962702 16.57141 100.28105 301.42459 224.88998 356.21634 2009 7 2 13:10: 0.000273
1844295.00000000 -499.82494656 -23140.27088532 1375.51902292 2.421198325 4.884716234 -0.968389967 107101.686955 0.962696 16.57181 100.28254 301.42322 226.57181 356.52541 2009 7 2 13:15: 0.000255
1844300.00000000 227.73070622 -21639.03026438 1082.97143381 2.422475651 5.122396027 -0.981456298 107086.216827 0.962689 16.57221 100.28430 301.42162 228.48591 356.83450 2009 7 2 13:20: 0.000277
1844305.00000000 954.37414156 -20061.17032355 786.61399449 2.414468102 5.396586724 -0.993756776 107067.873450 0.962681 16.57260 100.28640 301.41975 230.69381 357.14360 2009 7 2 13:25: 0.000259
1844310.00000000 1676.62598578 -18394.27054334 486.80451896 2.392158864 5.717597475 -1.004374559 107045.715250 0.962672 16.57296 100.28892 301.41751 233.28265 357.45273 2009 7 2 13:30: 0.000282
1844315.00000000 2389.05019358 -16622.20037093 184.27608369 2.347196726 6.100163738 -1.011653737 107018.321932 0.962661 16.57327 100.29202 301.41479 236.38060 357.76188 2009 7 2 13:35: 0.000264
1844320.00000000 3082.86422007 -14723.43238400 -119.54602920 2.264946104 6.566068142 -1.012476101 106983.436286 0.962647 16.57347 100.29586 301.41142 240.18503 358.07107 2009 7 2 13:40: 0.000286
1844325.00000000 3743.21501841 -12668.30537300 -421.89289454 2.118033246 7.148704873 -1.000616134 106937.218867 0.962629 16.57346 100.30071 301.40718 245.01826 358.38030 2009 7 2 13:45: 0.000268
1844330.00000000 4343.37719213 -10414.45480896 -717.19751285 1.850804312 7.900986048 -0.962613657 106872.512649 0.962605 16.57303 100.30687 301.40176 251.44720 358.68960 2009 7 2 13:50: 0.000250
1844335.00000000 4831.03777566 -7899.26116450 -993.48392108 1.337297849 8.906916366 -0.866084974 106774.174776 0.962568 16.57169 100.31447 301.39505 260.56996 358.99898 2009 7 2 13:55: 0.000273
1844340.00000000 5091.55546380 -5030.01134361 -1222.14210549 0.252792005 10.276493768 -0.621814132 106604.437813 0.962507 16.56837 100.32203 301.38830 274.78802 359.30853 2009 7 2 14: 0: 0.000255
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/tests.py 0000644 0001751 0000173 00000075637 14422467341 014337 0 ustar 00runner docker """Test suite for SGP4."""
try:
from unittest2 import TestCase, main
except:
from unittest import TestCase, main
import datetime as dt
import re
import os
import sys
from doctest import DocTestSuite, ELLIPSIS
from math import pi, isnan
from pkgutil import get_data
try:
from io import StringIO
except ImportError:
from StringIO import StringIO
import numpy as np
from sgp4.api import WGS72OLD, WGS72, WGS84, Satrec, jday
from sgp4.earth_gravity import wgs72
from sgp4.ext import invjday, newtonnu, rv2coe
from sgp4.functions import days2mdhms, _day_of_year_to_month_day
from sgp4.propagation import sgp4, sgp4init
from sgp4 import api, conveniences, io, omm
from sgp4.exporter import export_omm, export_tle
import sgp4.model as model
_testcase = TestCase('setUp')
_testcase.maxDiff = 9999
assertEqual = _testcase.assertEqual
assertAlmostEqual = _testcase.assertAlmostEqual
assertRaises = _testcase.assertRaises
assertRaisesRegex = getattr(_testcase, 'assertRaisesRegex',
_testcase.assertRaisesRegexp)
error = 2e-7
rad = 180.0 / pi
LINE1 = '1 00005U 58002B 00179.78495062 .00000023 00000-0 28098-4 0 4753'
LINE2 = '2 00005 34.2682 348.7242 1859667 331.7664 19.3264 10.82419157413667'
BAD2 = '2 00007 34.2682 348.7242 1859667 331.7664 19.3264 10.82419157413669'
VANGUARD_ATTRS = {
# Identity
'satnum': 5,
'satnum_str': '00005',
'classification': 'U',
'operationmode': 'i',
# Time
'epochyr': 0,
'epochdays': 179.78495062,
'jdsatepoch': 2451722.5,
'jdsatepochF': 0.78495062,
# Orbit
'bstar': 2.8098e-05,
'ndot': 6.96919666594958e-13,
'nddot': 0.0,
'ecco': 0.1859667,
'argpo': 5.790416027488515,
'inclo': 0.5980929187319208,
'mo': 0.3373093125574321,
'no_kozai': 0.04722944544077857,
'nodeo': 6.08638547138321,
}
VANGUARD_EPOCH = 18441.78495062
# Handle deprecated assertRaisesRegexp, but allow its use Python 2.6 and 2.7
if sys.version_info[:2] == (2, 7) or sys.version_info[:2] == (2, 6):
TestCase.assertRaisesRegex = TestCase.assertRaisesRegexp
# ------------------------------------------------------------------------
# Core Attributes
#
def test_satrec_built_with_twoline2rv():
sat = Satrec.twoline2rv(LINE1, LINE2)
verify_vanguard_1(sat)
def test_legacy_built_with_twoline2rv():
sat = io.twoline2rv(LINE1, LINE2, wgs72)
verify_vanguard_1(sat, legacy=True)
def test_satrec_initialized_with_sgp4init():
sat = Satrec()
sat.sgp4init(
WGS72,
'i',
VANGUARD_ATTRS['satnum'],
VANGUARD_EPOCH,
*sgp4init_args(VANGUARD_ATTRS)
)
verify_vanguard_1(sat)
def test_satrec_initialized_with_sgp4init_in_afspc_mode():
sat = Satrec()
sat.sgp4init(
WGS72,
'a',
VANGUARD_ATTRS['satnum'],
VANGUARD_EPOCH,
*sgp4init_args(VANGUARD_ATTRS)
)
assertEqual(sat.operationmode, 'a')
def test_legacy_initialized_with_sgp4init():
sat = model.Satellite()
sgp4init(
wgs72, 'i', VANGUARD_ATTRS['satnum'], VANGUARD_EPOCH,
*sgp4init_args(VANGUARD_ATTRS) + (sat,)
)
verify_vanguard_1(sat, legacy=True)
# ------------------------------------------------------------------------
# Test array API
def test_whether_array_logic_writes_nan_values_to_correct_row():
# https://github.com/brandon-rhodes/python-sgp4/issues/87
l1 = "1 44160U 19006AX 20162.79712247 +.00816806 +19088-3 +34711-2 0 9997"
l2 = "2 44160 095.2472 272.0808 0216413 032.6694 328.7739 15.58006382062511"
sat = Satrec.twoline2rv(l1, l2)
jd0 = np.array([2459054.5, 2459055.5])
jd1 = np.array([0.79712247, 0.79712247])
e, r, v = sat.sgp4_array(jd0, jd1)
assert list(e) == [6, 1]
assert np.isnan(r).tolist() == [[False, False, False], [True, True, True]]
assert np.isnan(v).tolist() == [[False, False, False], [True, True, True]]
# ------------------------------------------------------------------------
# Other Officially Supported Routines
#
def test_days2mdhms():
# See https://github.com/brandon-rhodes/python-sgp4/issues/64
tup = days2mdhms(2020, 133.35625)
assertEqual(tup, (5, 12, 8, 33, 0.0))
def test_jday2():
jd, fr = jday(2019, 10, 9, 16, 57, 15)
assertEqual(jd, 2458765.5)
assertAlmostEqual(fr, 0.7064236111111111)
def test_jday_datetime():
# define local time
# UTC equivalent: 2011-11-03 20:05:23+00:00
class UTC_plus_4(dt.tzinfo):
'UTC'
offset = dt.timedelta(hours=4)
def utcoffset(self, datetime):
return self.offset
def tzname(self, datetime):
return 'UTC plus 4'
def dst(self, datetime):
return self.offset
datetime_local = dt.datetime(2011, 11, 4, 0, 5, 23, 0, UTC_plus_4())
jd, fr = conveniences.jday_datetime(datetime_local)
# jd of this date is 2455868.5 + 0.8370717592592593
assertEqual(jd, 2455868.5)
assertAlmostEqual(fr, 0.8370717592592593)
def test_sat_epoch_datetime():
sat = Satrec.twoline2rv(LINE1, LINE2)
datetime = conveniences.sat_epoch_datetime(sat)
zone = conveniences.UTC
assertEqual(datetime, dt.datetime(2000, 6, 27, 18, 50, 19, 733568, zone))
def test_good_tle_checksum():
for line in LINE1, LINE2:
checksum = int(line[-1])
assertEqual(io.compute_checksum(line), checksum)
assertEqual(io.fix_checksum(line[:68]), line)
io.verify_checksum(line)
def test_bad_tle_checksum():
checksum = LINE1[-1]
assertEqual(checksum, '3')
bad = LINE1[:68] + '7'
assertRaises(ValueError, io.verify_checksum, bad)
assertEqual(io.fix_checksum(bad), LINE1)
def test_tle_export():
"""Check `export_tle()` round-trip using all the TLEs in the test file.
This iterates through the satellites in "SGP4-VER.TLE",
generates `Satrec` objects and exports the TLEs. These exported
TLEs are then compared to the original TLE, closing the loop (or
the round-trip).
"""
data = get_data(__name__, 'SGP4-VER.TLE')
tle_lines = iter(data.decode('ascii').splitlines())
# Skip these lines, known errors
# Resulting TLEs are equivalent (same values in the Satrec object), but they are not the same
# 25954: BSTAR = 0 results in a negative exp, not positive
# 29141: BSTAR = 0.13519 results in a negative exp, not positive
# 33333: Checksum error as expected on both lines
# 33334: Checksum error as expected on line 1
# 33335: Checksum error as expected on line 1
expected_errs_line1 = set([25954, 29141, 33333, 33334, 33335])
expected_errs_line2 = set([33333, 33335])
# Non-standard: omits the ephemeris type integer.
expected_errs_line1.add(11801)
for line1 in tle_lines:
if not line1.startswith('1'):
continue
line2 = next(tle_lines)
# trim lines to normal TLE string size
line1 = line1[:69]
line2 = line2[:69]
satrec = Satrec.twoline2rv(line1, line2)
satrec_old = io.twoline2rv(line1, line2, wgs72)
# Generate TLE from satrec
actual_line1, actual_line2 = export_tle(satrec)
actual_line1_old, actual_line2_old = export_tle(satrec_old)
if satrec.satnum not in expected_errs_line1:
assertEqual(actual_line1, line1)
assertEqual(actual_line1_old, line1)
if satrec.satnum not in expected_errs_line2:
assertEqual(actual_line2, line2)
assertEqual(actual_line2_old, line2)
def test_export_tle_raises_error_for_out_of_range_angles():
# See https://github.com/brandon-rhodes/python-sgp4/issues/70
for angle in 'inclo', 'nodeo', 'argpo', 'mo':
sat = Satrec()
wrong_vanguard_attrs = VANGUARD_ATTRS.copy()
wrong_vanguard_attrs[angle] = -1.0
sat.sgp4init(
WGS84, 'i', wrong_vanguard_attrs['satnum'], VANGUARD_EPOCH,
*sgp4init_args(wrong_vanguard_attrs)
)
assertRaises(ValueError, export_tle, sat)
def test_tle_import_export_round_trips():
for line1, line2 in [(
'1 44542U 19061A 21180.78220369 -.00000015 00000-0 -66561+1 0 9997',
'2 44542 54.7025 244.1098 0007981 318.8601 283.5781 1.86231125 12011',
)]:
sat = Satrec.twoline2rv(line1, line2)
outline1, outline2 = export_tle(sat)
assertEqual(line1, outline1)
assertEqual(line2, outline2)
def test_all_three_gravity_models_with_twoline2rv():
# The numbers below are those produced by Vallado's C++ code.
# (Why does the Python version not produce the same values to
# high accuracy, instead of agreeing to only 4 places?)
assert_wgs72old(Satrec.twoline2rv(LINE1, LINE2, WGS72OLD))
assert_wgs72(Satrec.twoline2rv(LINE1, LINE2, WGS72))
assert_wgs84(Satrec.twoline2rv(LINE1, LINE2, WGS84))
# Not specifying a gravity model should select WGS72.
assert_wgs72(Satrec.twoline2rv(LINE1, LINE2))
def test_all_three_gravity_models_with_sgp4init():
# Gravity models specified with sgp4init() should also change the
# positions generated.
sat = Satrec()
args = sgp4init_args(VANGUARD_ATTRS)
sat.sgp4init(WGS72OLD, 'i', VANGUARD_ATTRS['satnum'], VANGUARD_EPOCH, *args)
assert_wgs72old(sat)
sat.sgp4init(WGS72, 'i', VANGUARD_ATTRS['satnum'], VANGUARD_EPOCH, *args)
assert_wgs72(sat)
sat.sgp4init(WGS84, 'i', VANGUARD_ATTRS['satnum'], VANGUARD_EPOCH, *args)
assert_wgs84(sat)
GRAVITY_DIGITS = (
# Why don't Python and C agree more closely?
4 if not api.accelerated
# Otherwise, try 10 digits. Note that at least 6 digits past the
# decimal point are necessary to let the test distinguish between
# WSG72OLD and WGS72. See:
# https://github.com/conda-forge/sgp4-feedstock/pull/19
# https://github.com/brandon-rhodes/python-sgp4/issues/69
else 10
)
def assert_wgs72old(sat):
e, r, v = sat.sgp4_tsince(309.67110720001529)
assertAlmostEqual(r[0], -3754.251473242793, GRAVITY_DIGITS)
assertAlmostEqual(r[1], 7876.346815095482, GRAVITY_DIGITS)
assertAlmostEqual(r[2], 4719.220855042922, GRAVITY_DIGITS)
def assert_wgs72(sat):
e, r, v = sat.sgp4_tsince(309.67110720001529)
assertAlmostEqual(r[0], -3754.2514743216166, GRAVITY_DIGITS)
assertAlmostEqual(r[1], 7876.346817439062, GRAVITY_DIGITS)
assertAlmostEqual(r[2], 4719.220856478582, GRAVITY_DIGITS)
def assert_wgs84(sat):
e, r, v = sat.sgp4_tsince(309.67110720001529)
assertAlmostEqual(r[0], -3754.2437675772426, GRAVITY_DIGITS)
assertAlmostEqual(r[1], 7876.3549956188945, GRAVITY_DIGITS)
assertAlmostEqual(r[2], 4719.227897029576, GRAVITY_DIGITS)
# ------------------------------------------------------------------------
# Special Cases
#
def test_satnum_leading_spaces():
# https://github.com/brandon-rhodes/python-sgp4/issues/81
# https://github.com/brandon-rhodes/python-sgp4/issues/90
l1 = '1 4859U 21001A 21007.63955392 .00000000 00000+0 00000+0 0 9990'
l2 = '2 4859 000.0000 000.0000 0000000 000.0000 000.0000 01.00000000 09'
sat = Satrec.twoline2rv(l1, l2)
assertEqual(sat.satnum, 4859)
assertEqual(sat.classification, 'U')
assertEqual(sat.intldesg, '21001A')
def test_satnum_alpha5_encoding():
def make_sat(satnum_string):
return Satrec.twoline2rv(LINE1.replace('00005', satnum_string),
LINE2.replace('00005', satnum_string))
# Test cases from https://www.space-track.org/documentation#tle-alpha5
cases = [(100000, 'A0000'),
(148493, 'E8493'),
(182931, 'J2931'),
(234018, 'P4018'),
(301928, 'W1928'),
(339999, 'Z9999')]
for satnum, satnum_string in cases:
sat = make_sat(satnum_string)
assertEqual(sat.satnum, satnum)
assertEqual(sat.satnum_str, satnum_string)
args = sgp4init_args(VANGUARD_ATTRS)
for satnum, satnum_string in cases:
sat.sgp4init(WGS72, 'i', satnum, VANGUARD_EPOCH, *args)
assertEqual(sat.satnum, satnum)
def test_satnum_that_is_too_large():
sat = Satrec()
with assertRaisesRegex(ValueError, 'cannot exceed 339999'):
sat.sgp4init(
WGS72,
'i',
340000,
VANGUARD_EPOCH,
*sgp4init_args(VANGUARD_ATTRS)
)
def test_intldesg_with_6_characters():
sat = Satrec.twoline2rv(LINE1, LINE2)
assertEqual(sat.intldesg, '58002B')
def test_intldesg_with_7_characters():
sat = Satrec.twoline2rv(
'1 39444U 13066AE 20110.89708219 .00000236 00000-0'
' 35029-4 0 9992',
'2 39444 97.5597 114.3769 0059573 102.0933 258.6965 '
'14.82098949344697',
)
assertEqual(sat.intldesg, '13066AE')
def test_1990s_satrec_initialized_with_sgp4init():
sat = Satrec()
sat.sgp4init(
WGS72,
'i',
VANGUARD_ATTRS['satnum'],
VANGUARD_EPOCH - 365.0, # change year 2000 to 1999
*sgp4init_args(VANGUARD_ATTRS)
)
assertEqual(sat.epochyr, 99)
def test_setters():
sat = Satrec()
sat.classification = 'S'
assert sat.classification == 'S'
sat.intldesg = 'abcdefg'
assert sat.intldesg == 'abcdefg'
sat.ephtype = 23
assert sat.ephtype == 23
sat.elnum = 123
assert sat.elnum == 123
sat.revnum = 1234
assert sat.revnum == 1234
sat.satnum_str = 'abcde'
assert sat.satnum_str == 'abcde'
def test_hyperbolic_orbit():
# Exercise the newtonnu() code path with asinh() to see whether
# we can replace it with the one from Python's math module.
e0, m = newtonnu(1.0, 2.9) # parabolic
assertAlmostEqual(e0, 8.238092752965605, places=12)
assertAlmostEqual(m, 194.60069989482898, places=12)
e0, m = newtonnu(1.1, 2.7) # hyperbolic
assertAlmostEqual(e0, 4.262200676156417, places=12)
assertAlmostEqual(m, 34.76134082028372, places=12)
def test_correct_epochyr():
# Make sure that the non-standard four-digit epochyr I switched
# to in the Python version of SGP4 is reverted back to the
# official behavior when that code is used behind Satrec.
sat = Satrec.twoline2rv(LINE1, LINE2)
assertEqual(sat.epochyr, 0)
def test_legacy_epochyr():
# Apparently I saw fit to change the meaning of this attribute
# in the Python version of SGP4.
sat = io.twoline2rv(LINE1, LINE2, wgs72)
assertEqual(sat.epochyr, 2000)
def test_support_for_old_no_attribute():
s = io.twoline2rv(LINE1, LINE2, wgs72)
assert s.no == s.no_kozai
def test_months_and_days():
# Make sure our hand-written months-and-days routine is perfect.
month_lengths = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
day_of_year = 1
for month, length in enumerate(month_lengths, 1):
for day in range(1, length + 1):
tup = _day_of_year_to_month_day(day_of_year, False)
assertEqual((month, day), tup)
day_of_year += 1
month_lengths[1] = 29 # February, during a leap year
day_of_year = 1
for month, length in enumerate(month_lengths, 1):
for day in range(1, length + 1):
tup = _day_of_year_to_month_day(day_of_year, True)
assertEqual((month, day), tup)
day_of_year += 1
def test_december_32():
# ISS [Orbit 606], whose date is 2019 plus 366.82137887 days.
# The core SGP4 routines handled this fine, but my hamfisted
# attempt to provide a Python datetime for "convenience" ran
# into an overflow.
a = '1 25544U 98067A 19366.82137887 .00016717 00000-0 10270-3 0 9129'
b = '2 25544 51.6392 96.6358 0005156 88.7140 271.4601 15.49497216 6061'
correct_epoch = dt.datetime(2020, 1, 1, 19, 42, 47, 134368)
# Legacy API.
sat = io.twoline2rv(a, b, wgs72)
assertEqual(sat.epoch, correct_epoch)
correct_epoch = correct_epoch.replace(tzinfo=conveniences.UTC)
# Modern API.
sat = Satrec.twoline2rv(a, b)
assertEqual(conveniences.sat_epoch_datetime(sat), correct_epoch)
def test_non_ascii_first_line():
if sys.version_info < (3,):
return
with assertRaisesRegex(ValueError, re.escape("""your TLE lines are broken because they contain non-ASCII characters:
1 00005U 58002B 00179.78495062 .00000023\\xa0 00000-0 28098-4 0 4753
2 00005 34.2682 348.7242 1859667 331.7664 19.3264 10.82419157413667""")):
io.twoline2rv(LINE1.replace('23 ', '23\xa0'), LINE2, wgs72)
def test_non_ascii_second_line():
if sys.version_info < (3,):
return
with assertRaisesRegex(ValueError, re.escape("""your TLE lines are broken because they contain non-ASCII characters:
1 00005U 58002B 00179.78495062 .00000023 00000-0 28098-4 0 4753
2 00005 \\xa034.2682\\xa0348.7242 1859667 331.7664 19.3264 10.82419157413667\
""")):
io.twoline2rv(LINE1, LINE2.replace(' 34', '\xa034'), wgs72)
def test_bad_first_line():
with assertRaisesRegex(ValueError, re.escape("""TLE format error
The Two-Line Element (TLE) format was designed for punch cards, and so
is very strict about the position of every period, space, and digit.
Your line does not quite match. Here is the official format for line 1
with an N where each digit should go, followed by the line you provided:
1 NNNNNC NNNNNAAA NNNNN.NNNNNNNN +.NNNNNNNN +NNNNN-N +NNNNN-N N NNNNN
1 00005U 58002B 00179.78495062 .000000234 00000-0 28098-4 0 4753""")):
io.twoline2rv(LINE1.replace('23 ', '234'), LINE2, wgs72)
def test_bad_second_line():
with assertRaisesRegex(ValueError, re.escape("""TLE format error
The Two-Line Element (TLE) format was designed for punch cards, and so
is very strict about the position of every period, space, and digit.
Your line does not quite match. Here is the official format for line 2
with an N where each digit should go, followed by the line you provided:
2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN
2 00005 34 .268234 8.7242 1859667 331.7664 19.3264 10.82419157413667""")):
io.twoline2rv(LINE1, LINE2.replace(' 34', '34 '), wgs72)
def test_mismatched_lines():
msg = "Object numbers in lines 1 and 2 do not match"
with assertRaisesRegex(ValueError, re.escape(msg)):
io.twoline2rv(LINE1, BAD2, wgs72)
# ------------------------------------------------------------------------
# Helper routines
#
def verify_vanguard_1(sat, legacy=False):
attrs = VANGUARD_ATTRS
if legacy:
attrs = attrs.copy()
del attrs['epochyr']
del attrs['epochdays']
del attrs['jdsatepoch']
del attrs['jdsatepochF']
for name, value in attrs.items():
try:
assertEqual(getattr(sat, name), value)
except AssertionError as e:
message, = e.args
e.args = ('for attribute %s, %s' % (name, message),)
raise e
def sgp4init_args(d):
"""Given a dict of orbital parameters, return them in sgp4init order."""
return (d['bstar'], d['ndot'], d['nddot'], d['ecco'], d['argpo'],
d['inclo'], d['mo'], d['no_kozai'], d['nodeo'])
# ----------------------------------------------------------------------
# INTEGRATION TEST
#
# This runs both new and old satellite objects against every example
# computation in the official `tcppver.out` test case file. Instead of
# trying to parse the file, it instead re-generates it using Python
# satellite objects, then compares the resulting text with the file.
def test_satrec_against_tcppver_using_julian_dates():
def invoke(satrec, tsince):
whole, fraction = divmod(tsince / 1440.0, 1.0)
jd = satrec.jdsatepoch + whole
fr = satrec.jdsatepochF + fraction
e, r, v = satrec.sgp4(jd, fr)
assert e == satrec.error
return e, r, v
run_satellite_against_tcppver(Satrec.twoline2rv, invoke, [1,1,6,6,4,3,6])
def test_satrec_against_tcppver_using_tsince():
def invoke(satrec, tsince):
e, r, v = satrec.sgp4_tsince(tsince)
assert e == satrec.error
return e, r, v
run_satellite_against_tcppver(Satrec.twoline2rv, invoke, [1,1,6,6,4,3,6])
def test_legacy_against_tcppver():
def make_legacy_satellite(line1, line2):
sat = io.twoline2rv(line1, line2, wgs72)
return sat
def run_legacy_sgp4(satrec, tsince):
r, v = sgp4(satrec, tsince)
return (satrec.error, satrec.error_message), r, v
errs = [
(1, 'mean eccentricity -0.001329 not within range 0.0 <= e < 1.0'),
(1, 'mean eccentricity -0.001208 not within range 0.0 <= e < 1.0'),
(6, 'mrt 0.996159 is less than 1.0'
' indicating the satellite has decayed'),
(6, 'mrt 0.996252 is less than 1.0'
' indicating the satellite has decayed'),
(4, 'semilatus rectum -0.103223 is less than zero'),
(3, 'perturbed eccentricity -122.217193'
' not within range 0.0 <= e <= 1.0'),
(6, 'mrt 0.830534 is less than 1.0'
' indicating the satellite has decayed'),
]
run_satellite_against_tcppver(make_legacy_satellite, run_legacy_sgp4, errs)
def run_satellite_against_tcppver(twoline2rv, invoke, expected_errors):
# Check whether this library can produce (at least roughly) the
# output in tcppver.out.
data = get_data(__name__, 'tcppver.out')
data = data.replace(b'\r', b'')
tcppver_lines = data.decode('ascii').splitlines(True)
error_list = []
actual_lines = list(generate_test_output(twoline2rv, invoke, error_list))
assert len(tcppver_lines) == len(actual_lines) == 700
previous_data_line = None
linepairs = zip(tcppver_lines, actual_lines)
for lineno, (expected_line, actual_line) in enumerate(linepairs, start=1):
if actual_line == '(Use previous data line)':
actual_line = (' 0.00000000' +
previous_data_line[17:107])
# Compare the lines. The first seven fields are printed
# to very high precision, so we allow a small error due
# to rounding differences; the rest are printed to lower
# precision, and so can be compared textually.
if 'xx' in actual_line:
similar = (actual_line == expected_line)
else:
afields = actual_line.split()
efields = expected_line.split()
actual7 = [ float(a) for a in afields[:7] ]
expected7 = [ float(e) for e in efields[:7] ]
similar = (
len(actual7) == len(expected7)
and
all(
-error < (a - e) < error
for a, e in zip(actual7, expected7)
)
and
afields[7:] == efields[7:] # just compare text
)
if not similar:
raise ValueError(
'Line %d of output does not match:\n'
'\n'
'Expected: %r\n'
'Got back: %r'
% (lineno, expected_line, actual_line))
if 'xx' not in actual_line:
previous_data_line = actual_line
# Make sure we produced the correct list of errors.
assertEqual(error_list, expected_errors)
def generate_test_output(twoline2rv, invoke, error_list):
"""Generate lines like those in the test file tcppver.out.
This iterates through the satellites in "SGP4-VER.TLE", which are
each supplemented with a time start/stop/step over which we are
supposed to print results.
"""
data = get_data(__name__, 'SGP4-VER.TLE')
tle_lines = iter(data.decode('ascii').splitlines())
for line1 in tle_lines:
if not line1.startswith('1'):
continue
line2 = next(tle_lines)
satrec = twoline2rv(line1, line2)
yield '%ld xx\n' % (satrec.satnum,)
for line in generate_satellite_output(
satrec, invoke, line2, error_list):
yield line
def generate_satellite_output(satrec, invoke, line2, error_list):
"""Print a data line for each time in line2's start/stop/step field."""
mu = wgs72.mu
e, r, v = invoke(satrec, 0.0)
if isnan(r[0]) and isnan(r[1]) and isnan(r[2]):
error_list.append(e)
yield '(Use previous data line)'
return
yield format_short_line(0.0, r, v)
tstart, tend, tstep = (float(field) for field in line2[69:].split())
tsince = tstart
while tsince <= tend:
if tsince == tstart == 0.0:
tsince += tstep
continue # avoid duplicating the first line
e, r, v = invoke(satrec, tsince)
if e != 0 and e != (0, None):
error_list.append(e)
return
yield format_long_line(satrec, tsince, mu, r, v)
tsince += tstep
if tsince - tend < tstep - 1e-6: # do not miss last line!
e, r, v = invoke(satrec, tend)
if e != 0 and e != (0, None):
error_list.append(e)
return
yield format_long_line(satrec, tend, mu, r, v)
def format_short_line(tsince, r, v):
"""Short line, using the same format string that testcpp.cpp uses."""
return ' %16.8f %16.8f %16.8f %16.8f %12.9f %12.9f %12.9f\n' % (
tsince, r[0], r[1], r[2], v[0], v[1], v[2])
def format_long_line(satrec, tsince, mu, r, v):
"""Long line, using the same format string that testcpp.cpp uses."""
short = format_short_line(tsince, r, v).strip('\n')
jd = satrec.jdsatepoch + satrec.jdsatepochF + tsince / 1440.0
year, mon, day, hr, minute, sec = invjday(jd)
(p, a, ecc, incl, node, argp, nu, m, arglat, truelon, lonper
) = rv2coe(r, v, mu)
return short + (
' %14.6f %8.6f %10.5f %10.5f %10.5f %10.5f %10.5f'
' %5i%3i%3i %2i:%2i:%9.6f\n'
) % (
a, ecc, incl*rad, node*rad, argp*rad, nu*rad,
m*rad, year, mon, day, hr, minute, sec,
)
# ----------------------------------------------------------------------
# NEW "OMM" FORMAT TESTS
# https://celestrak.com/satcat/tle.php?CATNR=5
VANGUARD_TLE = """\
VANGUARD 1 \n\
1 00005U 58002B 20287.20333880 -.00000016 00000-0 -22483-4 0 9998
2 00005 34.2443 225.5254 1845686 162.2516 205.2356 10.84869164218149
"""
# The MARIO satellite was chosen by reading through stations.txt looking
# for an element set with every field nonzero, since a zero in any field
# would hide errors in our unit conversion: zero times any conversion
# factor is zero.
MARIO_TLE = """\
MARIO \n\
1 55123U 98067UQ 23115.44827133 .00787702 29408-3 15680-2 0 9999
2 55123 51.6242 216.2930 0014649 331.8976 28.1241 15.99081912 18396
"""
# https://celestrak.org/NORAD/elements/gp.php?CATNR=55123&FORMAT=XML
MARIO_XML = """\
MARIO1998-067UQEARTHTEMEUTCSGP42023-04-25T10:45:30.64291215.99081912.001464951.6242216.2930331.897628.12410U551239991839.1568E-2.787702E-2.29408E-3
"""
# https://celestrak.com/NORAD/elements/gp.php?CATNR=55123&FORMAT=CSV
MARIO_CSV = """\
OBJECT_NAME,OBJECT_ID,EPOCH,MEAN_MOTION,ECCENTRICITY,INCLINATION,RA_OF_ASC_NODE,ARG_OF_PERICENTER,MEAN_ANOMALY,EPHEMERIS_TYPE,CLASSIFICATION_TYPE,NORAD_CAT_ID,ELEMENT_SET_NO,REV_AT_EPOCH,BSTAR,MEAN_MOTION_DOT,MEAN_MOTION_DDOT
MARIO,1998-067UQ,2023-04-25T10:45:30.642912,15.99081912,.0014649,51.6242,216.2930,331.8976,28.1241,0,U,55123,999,1839,.1568E-2,.787702E-2,.29408E-3
"""
def test_omm_xml_matches_old_tle():
line0, line1, line2 = MARIO_TLE.splitlines()
sat1 = Satrec.twoline2rv(line1, line2)
fields = next(omm.parse_xml(StringIO(MARIO_XML)))
sat2 = Satrec()
omm.initialize(sat2, fields)
assert_satellites_match(sat1, sat2)
def test_omm_csv_matches_old_tle():
line0, line1, line2 = MARIO_TLE.splitlines()
sat1 = Satrec.twoline2rv(line1, line2)
fields = next(omm.parse_csv(StringIO(MARIO_CSV)))
sat2 = Satrec()
omm.initialize(sat2, fields)
assert_satellites_match(sat1, sat2)
def assert_satellites_match(sat1, sat2):
for attr in dir(sat1):
if attr.startswith('_'):
continue
value1 = getattr(sat1, attr, None)
if value1 is None:
continue
if callable(value1):
continue
value2 = getattr(sat2, attr)
assertEqual(value1, value2, '%s %r != %r' % (attr, value1, value2))
# Live example of OMM:
# https://celestrak.com/NORAD/elements/gp.php?INTDES=2020-025&FORMAT=JSON-PRETTY
def test_omm_export():
line0, line1, line2 = VANGUARD_TLE.splitlines()
sat = Satrec.twoline2rv(line1, line2)
fields = export_omm(sat, 'VANGUARD 1')
assertEqual(fields, {
'ARG_OF_PERICENTER': 162.2516,
'BSTAR': -2.2483e-05,
'CENTER_NAME': 'EARTH',
'CLASSIFICATION_TYPE': 'U',
'ECCENTRICITY': 0.1845686,
'ELEMENT_SET_NO': 999,
'EPHEMERIS_TYPE': 0,
'EPOCH': '2020-10-13T04:52:48.472320',
'INCLINATION': 34.2443,
'MEAN_ANOMALY': 205.2356,
'MEAN_ELEMENT_THEORY': 'SGP4',
'MEAN_MOTION': 10.84869164,
'MEAN_MOTION_DDOT': 0.0,
'MEAN_MOTION_DOT': -1.6e-07,
'NORAD_CAT_ID': 5,
'OBJECT_ID': '1958-002B',
'OBJECT_NAME': 'VANGUARD 1',
'RA_OF_ASC_NODE': 225.5254,
'REF_FRAME': 'TEME',
'REV_AT_EPOCH': 21814,
'TIME_SYSTEM': 'UTC',
})
# ----------------------------------------------------------------------
def load_tests(loader, tests, ignore):
"""Run our main documentation as a test, plus all test functions."""
from sgp4.wulfgar import add_test_functions
add_test_functions(loader, tests, __name__)
# Python 2.6 formats floating-point numbers a bit differently and
# breaks the doctest, so we only run the doctest on later versions.
if sys.version_info >= (2, 7):
def setUp(suite):
suite.olddir = os.getcwd()
os.chdir(os.path.dirname(__file__))
suite.oldaccel = api.accelerated
api.accelerated = True # so doctest passes under 2.7
def tearDown(suite):
os.chdir(suite.olddir)
api.accelerated = suite.oldaccel
options = dict(optionflags=ELLIPSIS, setUp=setUp, tearDown=tearDown)
tests.addTests(DocTestSuite('sgp4', **options))
tests.addTests(DocTestSuite('sgp4.conveniences', **options))
tests.addTests(DocTestSuite('sgp4.functions', **options))
return tests
if __name__ == '__main__':
main()
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/wrapper.py 0000644 0001751 0000173 00000004353 14422467341 014640 0 ustar 00runner docker from . import vallado_cpp
class Satrec(vallado_cpp.Satrec):
"""High-speed computation of satellite positions and velocities."""
__slots__ = ()
def sgp4_array(self, jd, fr):
"""Compute positions and velocities for the times in a NumPy array.
Given NumPy arrays ``jd`` and ``fr`` of the same length that
supply the whole part and the fractional part of one or more
Julian dates, return a tuple ``(e, r, v)`` of three vectors:
* ``e``: nonzero for any dates that produced errors, 0 otherwise.
* ``r``: position vectors in kilometers.
* ``v``: velocity vectors in kilometers per second.
"""
jd = jd.astype('float64', copy=False)
fr = fr.astype('float64', copy=False)
eshape = jd.shape
fshape = eshape[0], 3
array = type(jd)
e = array(eshape, 'uint8')
r = array(fshape, 'float64')
v = array(fshape, 'float64')
self._sgp4(jd, fr, e, r, v)
return e, r, v
class SatrecArray(vallado_cpp.SatrecArray):
"""High-speed satellite array for computing positions and velocities."""
__slots__ = ()
def sgp4(self, jd, fr):
"""Compute positions and velocities for the satellites in this array.
Given NumPy scalars or arrays ``jd`` and ``fr`` supplying the
whole part and the fractional part of one or more Julian dates,
return a tuple ``(e, r, v)`` of three vectors:
* ``e``: nonzero for any dates that produced errors, 0 otherwise.
* ``r``: position vectors in kilometers.
* ``v``: velocity vectors in kilometers per second.
The first dimension of each output vector has the same length as
this satellite array, the second dimension the same length as
the input date arrays, and the third dimension has length 3.
"""
jd = jd.astype('float64', copy=False)
fr = fr.astype('float64', copy=False)
ilength = len(self)
jlength, = jd.shape
eshape = ilength, jlength
fshape = ilength, jlength, 3
array = type(jd)
e = array(eshape, 'uint8')
r = array(fshape, 'float64')
v = array(fshape, 'float64')
self._sgp4(jd, fr, e, r, v)
return e, r, v
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599649.0
sgp4-2.22/sgp4/wulfgar.py 0000644 0001751 0000173 00000001457 14422467341 014631 0 ustar 00runner docker """Support test functions, in a module small enough to carry inline."""
from importlib import import_module
from unittest import TestCase
__unittest = 1 # Tell unittest not to include run() in test tracebacks.
def add_test_functions(loader, tests, module_name):
"""Run our main documentation as a test and test functions in this file."""
def wrap_test_function(test):
def run(self):
return test()
return run
module = import_module(module_name)
test_methods = dict((name, wrap_test_function(getattr(module, name)))
for name in dir(module) if name.startswith('test_'))
TestFunctions = type('TestFunctions', (TestCase,), test_methods)
TestFunctions.__module__ = module_name
tests.addTest(loader.loadTestsFromTestCase(TestFunctions))
././@PaxHeader 0000000 0000000 0000000 00000000034 00000000000 010212 x ustar 00 28 mtime=1682599655.3394356
sgp4-2.22/sgp4.egg-info/ 0000755 0001751 0000173 00000000000 14422467347 014301 5 ustar 00runner docker ././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599655.0
sgp4-2.22/sgp4.egg-info/PKG-INFO 0000644 0001751 0000173 00000074373 14422467347 015414 0 ustar 00runner docker Metadata-Version: 2.1
Name: sgp4
Version: 2.22
Summary: Track Earth satellites given TLE data, using up-to-date 2020 SGP4 routines.
Home-page: https://github.com/brandon-rhodes/python-sgp4
Author: Brandon Rhodes
Author-email: brandon@rhodesmill.org
License: MIT
Classifier: Development Status :: 5 - Production/Stable
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: MIT License
Classifier: Programming Language :: Python :: 2
Classifier: Programming Language :: Python :: 2.6
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.3
Classifier: Programming Language :: Python :: 3.4
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
Classifier: Programming Language :: Python :: 3.9
Classifier: Topic :: Scientific/Engineering :: Astronomy
License-File: LICENSE
This package compiles the official C++ code from `Revisiting Spacetrack
Report #3 `_ (AIAA
2006-6753) and uses it to compute the positions of satellites in Earth
orbit. Orbital elements can be read from either a legacy TLE file or
from a modern OMM element set, both of which you can fetch from a site
like `CelesTrak `_.
If your machine can’t install or compile the C++ code, then this package
falls back to using a slower pure-Python implementation of SGP4. Tests
make sure that its positions **agree to within 0.1 mm** with the
standard version of the algorithm — an error far less than the
1–3 km/day by which satellites themselves deviate from the ideal orbits
described in TLE files.
An accelerated routine is available that, given a series of times and of
satellites, computes a whole array of output positions using a fast C++
loop. See the “Array Acceleration” section below.
Note that the SGP4 propagator returns raw *x,y,z* Cartesian coordinates
in a “True Equator Mean Equinox” (TEME) reference frame that’s centered
on the Earth but does not rotate with it — an “Earth centered inertial”
(ECI) reference frame. The SGP4 propagator itself does not implement
the math to convert these positions into more official ECI frames like
J2000 or the ICRS, nor into any Earth-centered Earth-fixed (ECEF) frames
like the ITRS, nor into latitudes and longitudes through an Earth
ellipsoid like WGS84. For conversions into these other coordinate
frames, look for a comprehensive astronomy library, like the `Skyfield
`_ library that is built atop this one
(see the `section on Earth satellites
`_ in its
documentation).
Usage
-----
You will probably first want to to check whether your machine has
successfully installed the fast SGP4 C++ code, or is using the slow
Python version (in which case this value will be false):
>>> from sgp4.api import accelerated
>>> print(accelerated)
True
This library uses the same function names as the official C++ code, to
help users who are already familiar with SGP4 in other languages. Here
is how to compute the x,y,z position and velocity for the International
Space Station at 12:50:19 on 29 June 2000:
>>> from sgp4.api import Satrec
>>>
>>> s = '1 25544U 98067A 19343.69339541 .00001764 00000-0 38792-4 0 9991'
>>> t = '2 25544 51.6439 211.2001 0007417 17.6667 85.6398 15.50103472202482'
>>> satellite = Satrec.twoline2rv(s, t)
>>>
>>> jd, fr = 2458827, 0.362605
>>> e, r, v = satellite.sgp4(jd, fr)
>>> e
0
>>> print(r) # True Equator Mean Equinox position (km)
(-6102.44..., -986.33..., -2820.31...)
>>> print(v) # True Equator Mean Equinox velocity (km/s)
(-1.45..., -5.52..., 5.10...)
As input, you can provide either:
* A simple floating-point Julian Date for ``jd`` and the value 0.0 for
``fr``, if you are happy with the precision of a 64-bit floating point
number. Note that modern Julian Dates are greater than 2,450,000
which means that nearly half of the precision of a 64-bit float will
be consumed by the whole part that specifies the day. The remaining
digits will provide a precision for the fraction of around 20.1 µs.
This should be no problem for the accuracy of your result — satellite
positions usually off by a few kilometers anyway, far less than a
satellite moves in 20.1 µs — but if you run a solver that dives down
into the microseconds while searching for a rising or setting time,
the solver might be bothered by the 20.1 µs plateau between each jump
in the satellite’s position.
* Or, you can provide a coarse date ``jd`` plus a very precise fraction
``fr`` that supplies the rest of the value. The Julian Date for which
the satellite position is computed is the sum of the two values. One
common practice is to provide the whole number as ``jd`` and the
fraction as ``fr``; another is to have ``jd`` carry the fraction 0.5
since UTC midnight occurs halfway through each Julian Date. Either
way, splitting the value allows a solver to run all the way down into
the nanoseconds and still see SGP4 respond smoothly to tiny date
adjustments with tiny changes in the resulting satellite position.
Here is how to intrepret the results:
* ``e`` will be a non-zero error code if the satellite position could
not be computed for the given date. You can ``from sgp4.api import
SGP4_ERRORS`` to access a dictionary mapping error codes to error
messages explaining what each code means.
* ``r`` measures the satellite position in **kilometers** from the
center of the earth in the idiosyncratic True Equator Mean Equinox
coordinate frame used by SGP4.
* ``v`` velocity is the rate at which the position is changing,
expressed in **kilometers per second**.
If your application does not natively handle Julian dates, you can
compute ``jd`` and ``fr`` from calendar dates using ``jday()``.
>>> from sgp4.api import jday
>>> jd, fr = jday(2019, 12, 9, 12, 0, 0)
>>> jd
2458826.5
>>> fr
0.5
Double-checking your TLE lines
------------------------------
Because TLE is an old punch-card fixed-width format, it’s very sensitive
to whether exactly the right number of spaces are positioned in exactly
the right columns. If you suspect that your satellite elements aren’t
getting loaded correctly, try calling the slow pure-Python version of
``twoline2rv()``, which performs extra checks that the fast C++ doesn’t:
>>> from sgp4.earth_gravity import wgs72
>>> from sgp4.io import twoline2rv
>>> assert twoline2rv(s, t, wgs72)
Any TLE formatting errors will be raised as a ``ValueError``.
Using OMM elements instead of TLE
---------------------------------
The industry is migrating away from the original TLE format, because it
will soon run out of satellite numbers.
* Some TLE files now use a new “Alpha-5” convention that expands the
range of satellite numbers by using an initial letter; for example,
“E8493” means satellite 148493. This library supports the Alpha-5
convention and should return the correct integer in Python.
* Some authorities are now distributing satellite elements in an “OMM”
Orbit Mean Elements Message format that replaces the TLE format. You
can learn about OMM in Dr. T.S. Kelso’s `“A New Way to Obtain GP Data”
`_ at
the CelesTrak site.
You can already try out experimental support for OMM:
>>> from sgp4 import omm
Reading OMM data takes two steps, because OMM supports several different
text formats. First, parse the input text to recover the field names
and values that it stores; second, build a Python satellite object from
those field values. For example, to load OMM from XML:
>>> with open('sample_omm.xml') as f:
... fields = next(omm.parse_xml(f))
>>> sat = Satrec()
>>> omm.initialize(sat, fields)
Or, to load OMM from CSV:
>>> with open('sample_omm.csv') as f:
... fields = next(omm.parse_csv(f))
>>> sat = Satrec()
>>> omm.initialize(sat, fields)
Either way, the satellite object should wind up properly initialized and
ready to start producing positions.
If you are interested in saving satellite parameters using the new OMM
format, then read the section on “Export” below.
Epoch
-----
Over a given satellite’s lifetime, dozens or hundreds of different TLE
records will be produced as its orbit evolves. Each TLE record
specifies the “epoch date” for which it is most accurate. Typically a
TLE is only useful for a couple of weeks to either side of its epoch
date, beyond which its predictions become unreliable.
Satellite objects natively provide their epoch as a two-digit year and
then a fractional number of days into the year:
>>> satellite.epochyr
19
>>> satellite.epochdays
343.69339541
Because Sputnik was launched in 1957, satellite element sets will never
refer to an earlier year, so years 57 through 99 mean 1957–1999 while 0
through 56 mean 2000–2056. The TLE format will presumably be obsolete
in 2057 and have to be upgraded to 4-digit years.
To turn the number of days and its fraction into a calendar date and
time, use the ``days2mdhms()`` function.
>>> from sgp4.api import days2mdhms
>>> month, day, hour, minute, second = days2mdhms(19, 343.69339541)
>>> month
12
>>> day
9
>>> hour
16
>>> minute
38
>>> second
29.363424
The SGP4 library also translates those two numbers into a Julian date
and fractional Julian date, since Julian dates are more commonly used in
astronomy.
>>> satellite.jdsatepoch
2458826.5
>>> satellite.jdsatepochF
0.69339541
Finally, a convenience function is available in the library if you need
the epoch date and time as Python ``datetime``.
>>> from sgp4.conveniences import sat_epoch_datetime
>>> sat_epoch_datetime(satellite)
datetime.datetime(2019, 12, 9, 16, 38, 29, 363423, tzinfo=UTC)
Array Acceleration
------------------
To avoid the expense of running a Python loop when you have many dates
and times for which you want a position, you can pass your Julian dates
as arrays. The array routine is only faster if your machine has
successfully installed or compiled the SGP4 C++ code, so you might want
to check first:
>>> from sgp4.api import accelerated
>>> print(accelerated)
True
To call the array routine, make NumPy arrays for ``jd`` and ``fr`` that
are the same length:
>>> import numpy as np
>>> np.set_printoptions(precision=2)
>>> jd = np.array((2458826, 2458826, 2458826, 2458826))
>>> fr = np.array((0.0001, 0.0002, 0.0003, 0.0004))
>>> e, r, v = satellite.sgp4_array(jd, fr)
>>> print(e)
[0 0 0 0]
>>> print(r)
[[-3431.31 2620.15 -5252.97]
[-3478.86 2575.14 -5243.87]
[-3526.09 2529.89 -5234.28]
[-3572.98 2484.41 -5224.19]]
>>> print(v)
[[-5.52 -5.19 1.02]
[-5.49 -5.22 1.08]
[-5.45 -5.25 1.14]
[-5.41 -5.28 1.2 ]]
To avoid the expense of Python loops when you have many satellites and
dates, build a ``SatrecArray`` from several individual satellites. Its
``sgp4()`` method will expect both ``jd`` and ``fr`` to be NumPy arrays,
so if you only have one date, be sure to provide NumPy arrays of length
one. Here is a sample computation for 2 satellites and 4 dates:
>>> u = '1 20580U 90037B 19342.88042116 .00000361 00000-0 11007-4 0 9996'
>>> w = '2 20580 28.4682 146.6676 0002639 185.9222 322.7238 15.09309432427086'
>>> satellite2 = Satrec.twoline2rv(u, w)
>>> from sgp4.api import SatrecArray
>>> a = SatrecArray([satellite, satellite2])
>>> e, r, v = a.sgp4(jd, fr)
>>> np.set_printoptions(precision=2)
>>> print(e)
[[0 0 0 0]
[0 0 0 0]]
>>> print(r)
[[[-3431.31 2620.15 -5252.97]
[-3478.86 2575.14 -5243.87]
[-3526.09 2529.89 -5234.28]
[-3572.98 2484.41 -5224.19]]
[[ 5781.85 2564. -2798.22]
[ 5749.36 2618.59 -2814.63]
[ 5716.35 2672.94 -2830.78]
[ 5682.83 2727.05 -2846.68]]]
>>> print(v)
[[[-5.52 -5.19 1.02]
[-5.49 -5.22 1.08]
[-5.45 -5.25 1.14]
[-5.41 -5.28 1.2 ]]
[[-3.73 6.33 -1.91]
[-3.79 6.3 -1.88]
[-3.85 6.28 -1.85]
[-3.91 6.25 -1.83]]]
Export
------
If you have a ``Satrec`` you want to share with friends or persist to a
file, there’s an export routine that will turn it back into a TLE:
>>> from sgp4 import exporter
>>> line1, line2 = exporter.export_tle(satellite)
>>> line1
'1 25544U 98067A 19343.69339541 .00001764 00000-0 38792-4 0 9991'
>>> line2
'2 25544 51.6439 211.2001 0007417 17.6667 85.6398 15.50103472202482'
Happily, these are exactly the two TLE lines that we used to create this
satellite object:
>>> (s == line1) and (t == line2)
True
Another export routine is available that produces the fields defined by
the new OMM format (see the “OMM” section above):
>>> from pprint import pprint
>>> fields = exporter.export_omm(satellite, 'ISS (ZARYA)')
>>> pprint(fields)
{'ARG_OF_PERICENTER': 17.6667,
'BSTAR': 3.8792e-05,
'CENTER_NAME': 'EARTH',
'CLASSIFICATION_TYPE': 'U',
'ECCENTRICITY': 0.0007417,
'ELEMENT_SET_NO': 999,
'EPHEMERIS_TYPE': 0,
'EPOCH': '2019-12-09T16:38:29.363423',
'INCLINATION': 51.6439,
'MEAN_ANOMALY': 85.6398,
'MEAN_ELEMENT_THEORY': 'SGP4',
'MEAN_MOTION': 15.501034720000002,
'MEAN_MOTION_DDOT': 0.0,
'MEAN_MOTION_DOT': 1.764e-05,
'NORAD_CAT_ID': 25544,
'OBJECT_ID': '1998-067A',
'OBJECT_NAME': 'ISS (ZARYA)',
'RA_OF_ASC_NODE': 211.2001,
'REF_FRAME': 'TEME',
'REV_AT_EPOCH': 20248,
'TIME_SYSTEM': 'UTC'}
Gravity
-------
The SGP4 algorithm operates atop a set of constants specifying how
strong the Earth’s gravity is. The most recent official paper on SGP4
(see below) specifies that “We use WGS-72 as the default value”, so this
Python module uses the same default. But in case you want to use either
the old legacy version of the WGS-72 constants, or else the non-standard
but more modern WGS-84 constants, the ``twoline2rv()`` constructor takes
an optional argument:
>>> from sgp4.api import WGS72OLD, WGS72, WGS84
>>> satellite3 = Satrec.twoline2rv(s, t, WGS84)
You will in general get less accurate results if you choose WGS-84.
Even though it reflects more recent and accurate measures of the Earth,
satellite TLEs across the industry are most likely generated with WGS-72
as their basis. The positions you generate will better agree with the
real positions of each satellite if you use the same underlying gravity
constants as were used to generate the TLE.
Providing your own elements
---------------------------
If instead of parsing a TLE you want to specify orbital elements
directly, you can pass them as floating point numbers to a satellite
object’s ``sgp4init()`` method. For example, here’s how to build the
same International Space Station orbit that we loaded from a TLE in the
first code example above:
>>> satellite2 = Satrec()
>>> satellite2.sgp4init(
... WGS72, # gravity model
... 'i', # 'a' = old AFSPC mode, 'i' = improved mode
... 25544, # satnum: Satellite number
... 25545.69339541, # epoch: days since 1949 December 31 00:00 UT
... 3.8792e-05, # bstar: drag coefficient (1/earth radii)
... 0.0, # ndot: ballistic coefficient (radians/minute^2)
... 0.0, # nddot: mean motion 2nd derivative (radians/minute^3)
... 0.0007417, # ecco: eccentricity
... 0.3083420829620822, # argpo: argument of perigee (radians)
... 0.9013560935706996, # inclo: inclination (radians)
... 1.4946964807494398, # mo: mean anomaly (radians)
... 0.06763602333248933, # no_kozai: mean motion (radians/minute)
... 3.686137125541276, # nodeo: R.A. of ascending node (radians)
... )
These numbers don’t look the same as the numbers in the TLE, because the
underlying ``sgp4init()`` routine uses different units: radians rather
than degrees. But this is the same orbit and will produce the same
positions.
Note that ``ndot`` and ``nddot`` are ignored by the SGP4 propagator, so
you can leave them ``0.0`` without any effect on the resulting satellite
positions. But they do at least get saved to the satellite object, and
written out if you write the parameters to a TLE or OMM file (see the
“Export” section, above).
To compute the “epoch” argument, take the epoch’s Julian date and
subtract 2433281.5 days.
While the underlying ``sgp4init()`` routine leaves the attributes
``epochyr``, ``epochdays``, ``jdsatepoch``, and ``jdsatepochF`` unset,
this library goes ahead and sets them anyway for you, using the epoch
you provided.
See the next section for the complete list of attributes that are
available from the satellite record once it has been initialized.
Attributes
----------
There are several dozen ``Satrec`` attributes that expose data from the
underlying C++ SGP4 record. They fall into the following categories.
*Identification*
These are copied directly from the TLE record but aren’t used by the
propagation math.
| ``satnum_str`` — Satellite number, as a 5-character string.
| ``satnum`` — Satellite number, converted to an integer.
| ``classification`` — ``'U'``, ``'C'``, or ``'S'``
indicating the element set is Unclassified, Classified, or Secret.
| ``ephtype`` — Integer “ephemeris type”, used internally by space
agencies to mark element sets that are not ready for publication;
this field should always be ``0`` in published TLEs.
| ``elnum`` — Element set number.
| ``revnum`` — Satellite’s revolution number at the moment of the epoch,
presumably counting from 1 following launch.
*Orbital Elements*
These are the orbital parameters, copied verbatim from the text of the
TLE record. They describe the orbit at the moment of the TLE’s epoch
and so remain constant even as the satellite record is used over and
over again to propagate positions for different times.
| ``epochyr`` — Epoch date: the last two digits of the year.
| ``epochdays`` — Epoch date: the number of days into the year,
including a decimal fraction for the UTC time of day.
| ``ndot`` — First time derivative of the mean motion
(loaded from the TLE, but otherwise ignored).
| ``nddot`` — Second time derivative of the mean motion
(loaded from the TLE, but otherwise ignored).
| ``bstar`` — Ballistic drag coefficient B* (1/earth radii).
| ``inclo`` — Inclination (radians).
| ``nodeo`` — Right ascension of ascending node (radians).
| ``ecco`` — Eccentricity.
| ``argpo`` — Argument of perigee (radians).
| ``mo`` — Mean anomaly (radians).
| ``no_kozai`` — Mean motion (radians/minute).
| ``no`` — Alias for ``no_kozai``, for compatibility with old code.
You can also access the epoch as a Julian date:
| ``jdsatepoch`` — Whole part of the epoch’s Julian date.
| ``jdsatepochF`` — Fractional part of the epoch’s Julian date.
*Computed Orbit Properties*
These are computed when the satellite is first loaded,
as a convenience for callers who might be interested in them.
They aren’t used by the SGP4 propagator itself.
| ``a`` — Semi-major axis (earth radii).
| ``altp`` — Altitude of the satellite at perigee
(earth radii, assuming a spherical Earth).
| ``alta`` — Altitude of the satellite at apogee
(earth radii, assuming a spherical Earth).
| ``argpdot`` — Rate at which the argument of perigee is changing
(radians/minute).
| ``gsto`` — Greenwich Sidereal Time at the satellite’s epoch (radians).
| ``mdot`` — Rate at which the mean anomaly is changing (radians/minute)
| ``nodedot`` — Rate at which the right ascension of the ascending node
is changing (radians/minute).
*Propagator Mode*
| ``operationmode`` — A single character that directs SGP4
to either operate in its modern ``'i'`` improved mode
or in its legacy ``'a'`` AFSPC mode.
| ``method`` — A single character, chosen automatically
when the orbital elements were loaded, that indicates whether SGP4
has chosen to use its built-in ``'n'`` Near Earth
or ``'d'`` Deep Space mode for this satellite.
*Result of Most Recent Propagation*
| ``t`` —
The time you gave when you most recently asked SGP4
to compute this satellite’s position,
measured in minutes before (negative) or after (positive)
the satellite’s epoch.
| ``error`` —
Error code produced by the most recent SGP4 propagation
you performed with this element set.
The possible ``error`` codes are:
0. No error.
1. Mean eccentricity is outside the range 0 ≤ e < 1.
2. Mean motion has fallen below zero.
3. Perturbed eccentricity is outside the range 0 ≤ e ≤ 1.
4. Length of the orbit’s semi-latus rectum has fallen below zero.
5. (No longer used.)
6. Orbit has decayed: the computed position is underground.
(The position is still returned, in case the vector is helpful
to software that might be searching for the moment of re-entry.)
*Mean Elements From Most Recent Propagation*
Partway through each propagation, the SGP4 routine saves a set of
“singly averaged mean elements” that describe the orbit’s shape at the
moment for which a position is being computed. They are averaged with
respect to the mean anomaly and include the effects of secular gravity,
atmospheric drag, and — in Deep Space mode — of those pertubations from
the Sun and Moon that SGP4 averages over an entire revolution of each of
those bodies. They omit both the shorter-term and longer-term periodic
pertubations from the Sun and Moon that SGP4 applies right before
computing each position.
| ``am`` — Average semi-major axis (earth radii).
| ``em`` — Average eccentricity.
| ``im`` — Average inclination (radians).
| ``Om`` — Average right ascension of ascending node (radians).
| ``om`` — Average argument of perigee (radians).
| ``mm`` — Average mean anomaly (radians).
| ``nm`` — Average mean motion (radians/minute).
*Gravity Model Parameters*
When the satellite record is initialized, your choice of gravity model
results in a slate of eight constants being copied in:
| ``tumin`` — Minutes in one “time unit”.
| ``xke`` — The reciprocal of ``tumin``.
| ``mu`` — Earth’s gravitational parameter (km³/s²).
| ``radiusearthkm`` — Radius of the earth (km).
| ``j2``, ``j3``, ``j4`` — Un-normalized zonal harmonic values J₂, J₃, and J₄.
| ``j3oj2`` — The ratio J₃/J₂.
Printing satellite attributes
-----------------------------
If you want to print out a satellite, this library provides a convenient
“attribute dump” routine that takes a satellite and generates lines that
list its attributes::
from sys import stdout
from sgp4.conveniences import dump_satrec
stdout.writelines(dump_satrec(satellite))
If you want to compare two satellites, then simply pass a second
argument; the second satellite’s attributes will be printed in a second
column next to those of the first. ::
stdout.writelines(dump_satrec(satellite, satellite2))
Validation against the official algorithm
-----------------------------------------
This implementation passes all of the automated tests in the August 2010
release of the reference implementation of SGP4 by Vallado et al., who
originally published their revision of SGP4 in 2006:
Vallado, David A., Paul Crawford, Richard Hujsak, and T.S. Kelso,
“Revisiting Spacetrack Report #3,” presented at the AIAA/AAS
Astrodynamics Specialist Conference, Keystone, CO, 2006 August
21–24.
If you would like to review the paper, it is `available online
`_. You can
always download the latest version of their code for comparison against
this Python module (or other implementations) at `AIAA-2006-6753.zip
`_.
For developers
--------------
Developers can check out this full project from GitHub:
https://github.com/brandon-rhodes/python-sgp4
To run its unit tests, install Python 2, Python 3, and the ``tox``
testing tool. The tests runing in Python 2 will exercise the fallback
pure-Python version of the routines, while Python 3 exercises the fast
new C++ accelerated code::
cd python-sgp4
tox
Legacy API
----------
Before this library pivoted to wrapping Vallado's official C++ code and
was operating in pure Python only, it had a slightly quirkier API, which
is still supported for compatibility with older clients. You can learn
about it by reading the documentation from version 1.4 or earlier:
https://pypi.org/project/sgp4/1.4/
Changelog
---------
2023-04-27 — 2.22
* Added a ``satnum_str`` attribute, exposing the fact that the C++ now
stores the satellite number as a string; and check that ``satnum`` is
never greater than 339999.
* Fixed the units of the ``nddot`` attribute when the value is loaded
from an OMM record. (Since the TLE computation itself ignores this
attribute, this did not affect any satellite positions.)
* Enhanced the fallback Python version of ``twoline2rv()`` to verify
that TLE lines are ASCII, and added documentation using it to
double-check TLEs that might suffer from non-ASCII characters.
* If the user doesn’t set a satellite’s ``classification``, it now
defaults to ``'U'`` for ‘unclassified’.
2022-04-06 — 2.21
* Added ``dump_satrec()`` to the ``sgp4.conveniences`` module.
* Fixed the ``Satrec`` attribute ``.error``, which was previously
building a nonsense integer from the wrong data in memory.
* Removed ``.whichconst`` from Python ``Satrec``, to help users avoid
writing code that will break when the C++ extension is available.
2021-07-01 — 2.20
* Taught ``sgp4init()`` to round both ``epochdays`` and ``jdsatepochF``
to the same 8 decimal places used for the date fraction in a TLE, if
the user-supplied ``epoch`` itself has 8 or fewer digits behind the
decimal point. This should make it easier to build satellites that
round-trip to TLE format with perfect accuracy.
* Fixed how ``export_tle()`` formats the BSTAR field when its value, if
written in scientific notation, has a positive exponent.
* Fixed the ``epochyr`` assigned by ``sgp4init()`` so years before 2000
have two digits instead of three (for example, so that 1980 produces
an ``epochyr`` of 80 instead of 980).
2021-04-22 — 2.19
* Extended the documentation on the Python Package Index and in the
module docstring so it lists every ``Satrec`` attribute that this
library exposes; even the more obscure ones might be useful to folks
working to analyze satellite orbits.
2021-03-08 — 2.18
* If a TLE satellite number lacks the required 5 digits,
``twoline2rv()`` now gives the underlying C++ library a little help so
it can still parse the classification and international designator
correctly.
* The ``Satrec`` attributes ``jdsatepoch``, ``jdsatepochF``,
``epochyr``, and ``epochdays`` are now writeable, so users can adjust
their values manually — which should make up for the fact that the
``sgp4init()`` method can’t set them with full floating point
precision.
| 2021-02-17 — 2.17 — Fixed where in the output array the ``sgp4_array()`` method writes NaN values when an SGP4 propagation fails.
| 2021-02-12 — 2.16 — Fixed ``days2mdhms()`` rounding to always match TLE epoch.
| 2021-01-08 — 2.15 — Fixed parsing of the ``satnum`` TLE field in the Python fallback code, when the field has a leading space; added OMM export routine.
| 2020-12-16 — 2.14 — New data formats: added OMM message support for both XML and CSV, and added support for the new Alpha-5 extension to TLE files.
| 2020-10-14 — 2.13 — Enhanced ``sgp4init()`` with custom code that also sets the ``epochdays`` and ``epochyr`` satellite attributes.
| 2020-05-28 — 2.12 — Moved the decision of whether to set the locale during ``twoline2rv()`` from import time to runtime, for users who change locales after their application is up and running.
| 2020-05-24 — 2.11 — Fixed a regression in how dates are split into hours, minutes, and seconds that would sometimes produce a time whose second=60, crashing the pure-Python version of the library.
| 2020-05-22 — 2.10 — Switch the locale temporarily to ``C`` during the C++ accelerated ``twoline2rv()``, since it does not protect its ``sscanf()`` calls from locales that, like German, expect comma decimal points instead of the period decimal points always used in a TLE.
| 2020-05-21 — 2.9 — Added ``sat_epoch_datetime()``, expanded documentation around converting a satellite epoch to a date and time, and started rounding the epoch to exactly the digits provided in the TLE; and removed the ``Satrec.epoch`` attribute from Python fallback code to better match the C++ version.
| 2020-05-07 — 2.8 — New function ``jday_datetime()`` is now available in the ``sgp4.conveniences`` module, thanks to Egemen Imre.
| 2020-04-24 — 2.7 — New method ``sgp4init()`` (thank you, Chris Lewicki!) is available.
| 2020-04-20 — 2.6 — New routine ``export_tle()`` (thank you, Egemen Imre!) is available. Improved how the accelerated C++ backend parses the ``intldesg`` string and the ``revnum`` integer.
| 2020-03-22 — 2.5 — Gave the new accelerated ``twoline2rv()`` an optional argument that lets the user choose a non-standard set of gravity constants.
| 2020-02-25 — 2.4 — Improved the ``jday()`` docstring; made the old legacy Python resilient if the day of the month is out-of-range (past the end of the month) in a TLE; and Mark Rutten fixed the C++ so it compiles on Windows!
| 2020-02-04 — 2.3 — Removed experimental code that caused performance problems for users with Numba installed.
| 2020-02-02 — 2.2 — A second release on Palindrome Day: fix the Satrec ``.epochyr`` attribute so it behaves the same way in Python as it does in the official C library, where it is only the last 2 digits of the year; and make ``.no`` available in the Python fallback case as well.
| 2020-02-02 — 2.1 — Add vectorized array method to Satrec object; add ``.no`` attribute to new Satrec object to support old code that has not migrated to the new name ``.no_kozai``; gave Python wrapper classes ``__slots__`` to avoid the expense of a per-object attribute dictionary.
| 2020-01-30 — 2.0 — Rewrite API to use genuine Vallado C++ code on those systems where it can be compiled; add accelerated vectorized array interface; make ``gstime()`` a public function; clarify format error message.
| 2015-01-15 — 1.4 — Display detailed help when TLE input does not match format.
| 2014-06-26 — 1.3 — Return ``(NaN,NaN,NaN)`` vectors on error and set ``.error_message``
| 2013-11-29 — 1.2 — Made ``epochyr`` 4 digits; add ``datetime`` for ``.epoch``
| 2012-11-22 — 1.1 — Python 3 compatibility; more documentation
| 2012-08-27 — 1.0 — Initial release
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599655.0
sgp4-2.22/sgp4.egg-info/SOURCES.txt 0000644 0001751 0000173 00000001010 14422467347 016155 0 ustar 00runner docker LICENSE
MANIFEST.in
README.md
setup.py
extension/SGP4.cpp
extension/SGP4.h
extension/wrapper.cpp
sgp4/SGP4-VER.TLE
sgp4/__init__.py
sgp4/alpha5.py
sgp4/api.py
sgp4/conveniences.py
sgp4/earth_gravity.py
sgp4/exporter.py
sgp4/ext.py
sgp4/functions.py
sgp4/io.py
sgp4/model.py
sgp4/omm.py
sgp4/propagation.py
sgp4/sample_omm.csv
sgp4/sample_omm.xml
sgp4/tcppver.out
sgp4/tests.py
sgp4/wrapper.py
sgp4/wulfgar.py
sgp4.egg-info/PKG-INFO
sgp4.egg-info/SOURCES.txt
sgp4.egg-info/dependency_links.txt
sgp4.egg-info/top_level.txt ././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599655.0
sgp4-2.22/sgp4.egg-info/dependency_links.txt 0000644 0001751 0000173 00000000001 14422467347 020347 0 ustar 00runner docker
././@PaxHeader 0000000 0000000 0000000 00000000026 00000000000 010213 x ustar 00 22 mtime=1682599655.0
sgp4-2.22/sgp4.egg-info/top_level.txt 0000644 0001751 0000173 00000000005 14422467347 017026 0 ustar 00runner docker sgp4