# -*- coding: utf-8 -*-
"""Track Earth satellites given TLE data, using up-to-date 2020 SGP4 routines.

This Python package computes the position and velocity of an
earth-orbiting satellite, given the satellite's TLE orbital elements
from a source like `CelesTrak <https://celestrak.com/>`_.  It implements
the most recent version of SGP4, and is regularly run against the SGP4
test suite to make sure that its satellite position predictions **agree
to within 0.1 mm** with the predictions of the standard distribution of
the algorithm.  This error is far less than the 1–3 km/day by which
satellites themselves deviate from the ideal orbits described in TLE
files.

* If your platform supports it, this package compiles and uses the
  verbatim source code from the official C++ version of SGP4.

* Otherwise, a slower but reliable Python implementation of SGP4 is used
  instead.

* If, instead of asking for the position of a single satellite at a
  single time, you supply this library with an array of satellites and
  an array of times, then the arrays can be processed using machine code
  instead of requiring you to run a slow Python loop over them.

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 ICRF; nor to convert positions into any Earth-centered
Earth-fixed (ECEF) frames like the ITRS; nor to convert them to
latitudes and longitudes through an Earth ellipsoid like WGS84.

For conversions into other coordinate frames, look for a comprehensive
astronomy library that is built atop this one, like the `Skyfield
<https://rhodesmill.org/skyfield/>`_ library:

https://rhodesmill.org/skyfield/earth-satellites.html

Usage
-----

This library uses the same function names as the official C++ code, to
help users who may already be 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

OMM
---

The industry is making adjustments because the fixed-width TLE format
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 now 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.  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 Python loops when you have many dates, you can
pass them as arrays to another method that understands NumPy:

>>> 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]]
<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]]]

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 (revs/day)
...     0.0,                  # nddot: mean motion 2nd derivative (revs/day^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`` — Unique number assigned to the satellite.
| ``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
<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
---------

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__ = '2.21'
