This package compiles the official C++ code from Revisiting Spacetrack Report #3_ (AIAA 2006-6753) — specifically, the 2023 May 09 release
from David Vallado’s Fundamentals of Astrodynamics and Applications_
webpage — 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 like CelesTrak <https://celestrak.com/>_.

.. _Revisiting Spacetrack Report #3: https://celestrak.org/publications/AIAA/2006-6753/

.. _Fundamentals of Astrodynamics and Applications: https://celestrak.org/software/vallado-sw.php

What we today call ‘SGP4’ in fact merges together what in the 1970s were
originally two separate satellite propagation routines, but which are
now selected automatically:

SGP4 — the ‘Simplified General Perturbations' model is used for
satellites close enough to Earth that their orbit takes less than
225 minutes (3 hours 45 minutes) to complete.
SDP4 — the ‘Simplified Deep Space Perturbations' model is used for
satellites farther from Earth, which take 225 minutes or longer to
compete an orbit.

If your machine can’t install or compile the C++ code, then this package
falls back to using a slower pure-Python implementation of the library.
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 <https://rhodesmill.org/skyfield/>_ library that is built atop this one
(see the section on Earth satellites <https://rhodesmill.org/skyfield/earth-satellites.html>_ 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 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 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 are 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, 20, 42, 0)
jd
2458826.5

fr
0.8625

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” <https://celestrak.com/NORAD/documentation/gp-data-formats.php>_ 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. The fastest and most efficient format is usually
CSV, since the column names are only given once, on the first line:

with open('sample_omm.csv') as f:
... for fields in omm.parse_csv(f):
... sat = Satrec()
... omm.initialize(sat, fields)

The JSON format is more verbose because it repeats the field names over
again in every single record:

import json
with open('sample_omm.json') as f:
... record_list = json.load(f)

for fields in record_list:
... sat = Satrec()
... omm.initialize(sat, fields)

The most verbose format is XML:

with open('sample_omm.xml') as f:
... for fields in omm.parse_xml(f):
... sat = Satrec()
... omm.initialize(sat, fields)

Either way, the satellite object should wind up properly initialized and
ready to start producing positions.

The omm.initialize() routine uses the standard WGS72 gravity model
by default. To make your own choice of model, supply a third argument
that is one of the three constants WGS72OLD, WGS72, or WGS84
(which are shown below in the section on ‘Gravity’).

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..2pi)
... 0.9013560935706996, # inclo: inclination (radians 0..pi)
... 1.4946964807494398, # mo: mean anomaly (radians 0..2pi)
... 0.06763602333248933, # no_kozai: mean motion (radians/minute)
... 3.686137125541276, # nodeo: R.A. of ascending node (radians 0..2pi)
... )

You might notice that these numbers don’t look the same as the numbers
in the TLE above. For example, the inclination was 51.6439 in the TLE,
but is 0.901356 here. That’s because sgp4init() uses different
units than the TLE format: angles are in radians rather than degrees.
But this is the same orbit and will produce the same positions.

If you want to double-check that your elements are valid, you can run
the function check_satrec(), which will raise a ValueError with
an informative error message if any of the angles are out of bounds. If
the satellite is fine, it simply returns, without raising an exception:

from sgp4.conveniences import check_satrec
check_satrec(satellite2)

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 0 ≤ i < pi).
| nodeo — Right ascension of ascending node (radians 0 ≤ Ω < 2pi).
| ecco — Eccentricity.
| argpo — Argument of perigee (radians 0 ≤ ω < 2pi).
| mo — Mean anomaly (radians 0 ≤ M < 2pi).
| 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:

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 Propagation

Each time the SGP4 routine generates a satellite position, it also saves
a set of “singly averaged mean elements” that describe shape of the
satellite's orbit at that moment. 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 <https://www.celestrak.com/publications/AIAA/2006-6753/>. You can
always download the latest version of their code for comparison against
this Python module (or other implementations) at AIAA-2006-6753.zip <https://www.celestrak.com/publications/AIAA/2006-6753/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

Not yet released — 2.25

Added a gravconst parameter to the omm.initialize() routine.

2024-02-15 — 2.24

The documentation now specifies the acceptable range for orbital
element angles like inclination and mean anomaly, and a new function
check_satrec(sat) will tell the caller if any of the angles are
out of bounds.
The documentation now gives an example of loading elements from JSON.
Tweaked the fallback Python code to accept TLE lines without a final
checksum character in the 69th column, to match the C++ code.

2023-10-01 — 2.23

Tweaked tests to resolve breakage introduced by Python 3.12.

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

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