Package: sgp4
This package compiles the official C++ code fromRevisiting Spacetrack
Report #3(AIAA 2006-6753) — specifically, the 2023 May 09 release
from David Vallado’sFundamentals of Astrodynamics and Applicationswebpage — and uses it to compute the positions of satellites in Earth
orbit.  Satellite orbital elements can be loaded from either a legacy
TLE file or from a modern OMM element set, both of which you can fetch
from a site likeCelesTrak.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 positionsagree to within 0.1 mmwith 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 rawx,y,zCartesian 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 theSkyfieldlibrary that is built atop this one
(see thesection on Earth satellitesin its
documentation).UsageYou 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)
TrueThis 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 20:42:00 on 2019 December 9:>>> 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 = 2458826.5, 0.8625
>>> e, r, v = satellite.sgp4(jd, fr)
>>> e
0
>>> print(r)  # True Equator Mean Equinox position (km)
(-6088.92..., -936.13..., -2866.44...)
>>> print(v)  # True Equator Mean Equinox velocity (km/s)
(-1.525..., -5.538..., 5.068...)As input, you can provide either:A simple floating-point Julian Date forjdand the value 0.0 forfr, 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 datejdplus a very precise fractionfrthat 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 asjdand the
fraction asfr; another is to havejdcarry 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:ewill be a non-zero error code if the satellite position could
not be computed for the given date.  You canfrom sgp4.api import SGP4_ERRORSto access a dictionary mapping error codes to error
messages explaining what each code means.rmeasures the satellite position inkilometersfrom the
center of the earth in the idiosyncratic True Equator Mean Equinox
coordinate frame used by SGP4.vvelocity is the rate at which the position is changing,
expressed inkilometers per second.If your application does not natively handle Julian dates, you can
computejdandfrfrom calendar dates usingjday().>>> from sgp4.api import jday
>>> jd, fr = jday(2019, 12, 9, 20, 42, 0)
>>> jd
2458826.5
>>> fr
0.8625Double-checking your TLE linesBecause 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 oftwoline2rv(), 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 aValueError.Using OMM elements instead of TLEThe 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 ommReading 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.EpochOver 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
343.69339541Because 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 thedays2mdhms()function.>>> from sgp4.api import days2mdhms
>>> month, day, hour, minute, second = days2mdhms(19, 343.69339541)
>>> month
12
>>> day
9
>>> hour
16
>>> minute
38
>>> second
29.363424The 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
0.69339541Finally, a convenience function is available in the library if you need
the epoch date and time as Pythondatetime.>>> from sgp4.conveniences import sat_epoch_datetime
>>> sat_epoch_datetime(satellite)
datetime.datetime(2019, 12, 9, 16, 38, 29, 363423, tzinfo=UTC)Array AccelerationTo 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)
TrueTo call the array routine, make NumPy arrays forjdandfrthat
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 aSatrecArrayfrom several individual satellites.  Itssgp4()method will expect bothjdandfrto 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]]
<BLANKLINE>
 [[ 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 ]]
<BLANKLINE>
 [[-3.73  6.33 -1.91]
  [-3.79  6.3  -1.88]
  [-3.85  6.28 -1.85]
  [-3.91  6.25 -1.83]]]ExportIf you have aSatrecyou 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)
TrueAnother 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'}GravityThe 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, thetwoline2rv()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 elementsIf instead of parsing a TLE you want to specify orbital elements
directly, you can pass them as floating point numbers to a satellite
object’ssgp4init()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
underlyingsgp4init()routine uses different units: radians rather
than degrees.  But this is the same orbit and will produce the same
positions.Note thatndotandnddotare ignored by the SGP4 propagator, so
you can leave them0.0without 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 underlyingsgp4init()routine leaves the attributesepochyr,epochdays,jdsatepoch, andjdsatepochFunset,
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.AttributesThere are several dozenSatrecattributes that expose data from the
underlying C++ SGP4 record.  They fall into the following categories.IdentificationThese 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 be0in published TLEs.elnum— Element set number.revnum— Satellite’s revolution number at the moment of the epoch,
presumably counting from 1 following launch.Orbital ElementsThese 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 forno_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 PropertiesThese 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 Modeoperationmode— 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 Propagationt—
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 possibleerrorcodes are:No error.Mean eccentricity is outside the range 0 ≤ e < 1.Mean motion has fallen below zero.Perturbed eccentricity is outside the range 0 ≤ e ≤ 1.Length of the orbit’s semi-latus rectum has fallen below zero.(No longer used.)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 PropagationPartway 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 ParametersWhen 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 oftumin.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 attributesIf 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 algorithmThis 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 isavailable online.  You can
always download the latest version of their code for comparison against
this Python module (or other implementations) atAIAA-2006-6753.zip.For developersDevelopers can check out this full project from GitHub:https://github.com/brandon-rhodes/python-sgp4To run its unit tests, install Python 2, Python 3, and thetoxtesting 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
toxLegacy APIBefore 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/Changelog2023-10-01 — 2.23Tweaked tests to resolve breakage introduced by Python 3.12.2023-04-27 — 2.22Added asatnum_strattribute, exposing the fact that the C++ now
stores the satellite number as a string; and check thatsatnumis
never greater than 339999.Fixed the units of thenddotattribute 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 oftwoline2rv()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’sclassification, it now
defaults to'U'for ‘unclassified’.2022-04-06 — 2.21Addeddump_satrec()to thesgp4.conveniencesmodule.Fixed theSatrecattribute.error, which was previously
building a nonsense integer from the wrong data in memory.Removed.whichconstfrom PythonSatrec, to help users avoid
writing code that will break when the C++ extension is available.2021-07-01 — 2.20Taughtsgp4init()to round bothepochdaysandjdsatepochFto the same 8 decimal places used for the date fraction in a TLE, if
the user-suppliedepochitself 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 howexport_tle()formats the BSTAR field when its value, if
written in scientific notation, has a positive exponent.Fixed theepochyrassigned bysgp4init()so years before 2000
have two digits instead of three (for example, so that 1980 produces
anepochyrof 80 instead of 980).2021-04-22 — 2.19Extended the documentation on the Python Package Index and in the
module docstring so it lists everySatrecattribute that this
library exposes; even the more obscure ones might be useful to folks
working to analyze satellite orbits.2021-03-08 — 2.18If 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.TheSatrecattributesjdsatepoch,jdsatepochF,epochyr, andepochdaysare now writeable, so users can adjust
their values manually — which should make up for the fact that thesgp4init()method can’t set them with full floating point
precision.2021-02-17 — 2.17 — Fixed where in the output array thesgp4_array()method writes NaN values when an SGP4 propagation fails.2021-02-12 — 2.16 — Fixeddays2mdhms()rounding to always match TLE epoch.2021-01-08 — 2.15 — Fixed parsing of thesatnumTLE 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 — Enhancedsgp4init()with custom code that also sets theepochdaysandepochyrsatellite attributes.2020-05-28 — 2.12 — Moved the decision of whether to set the locale duringtwoline2rv()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 toCduring the C++ acceleratedtwoline2rv(), since it does not protect itssscanf()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 — Addedsat_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 theSatrec.epochattribute from Python fallback code to better match the C++ version.2020-05-07 — 2.8 — New functionjday_datetime()is now available in thesgp4.conveniencesmodule, thanks to Egemen Imre.2020-04-24 — 2.7 — New methodsgp4init()(thank you, Chris Lewicki!) is available.2020-04-20 — 2.6 — New routineexport_tle()(thank you, Egemen Imre!) is available. Improved how the accelerated C++ backend parses theintldesgstring and therevnuminteger.2020-03-22 — 2.5 — Gave the new acceleratedtwoline2rv()an optional argument that lets the user choose a non-standard set of gravity constants.2020-02-25 — 2.4 — Improved thejday()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.epochyrattribute 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.noavailable in the Python fallback case as well.2020-02-02 — 2.1 — Add vectorized array method to Satrec object; add.noattribute 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; makegstime()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_message2013-11-29 — 1.2 — Madeepochyr4 digits; adddatetimefor.epoch2012-11-22 — 1.1 — Python 3 compatibility; more documentation2012-08-27 — 1.0 — Initial release