sgp4 1.1

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. 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 of the predictions of the standard C++ implementation 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.

The C++ function names have been retained, since users may already be familiar with this library in other languages. Here is how to compute the x,y,z position and velocity for Vanguard 1 at 12:50:19 on 29 June 2000:

>>> from sgp4.earth_gravity import wgs72
>>> from sgp4.io import twoline2rv
>>>
>>> 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')
>>>
>>> satellite = twoline2rv(line1, line2, wgs72)
>>> position, velocity = satellite.propagate(
...     2000, 6, 29, 12, 50, 19)
>>>
>>> position
[5576.056952400586, -3999.371134576452, -1521.9571594376037]
>>> velocity
[4.772627303379319, 5.119817120959591, 4.275553909172126]

The position vector measures the satellite position in kilometers from the center of the earth. The velocity is the rate at which those three parameters are changing, expressed in kilometers per second.

There are three gravity models available that you can import from the earth_gravity module:

• wgs72

• wgs72old

• wgs84

The wgs72 model seems to be the most commonly used in the satellite tracking community, and is probably the model behind most TLE elements that are available for download.

The twoline2rv() function returns a Satellite object whose attributes carry the data loaded from the TLE entry. Most of this class’s hundred-plus attributes are intermediate values of interest only to the propagation algorithm itself. Here are the attributes set by sgp4.io.twoline2rv() in which users are likely to be interested:

satnum

Unique satellite number given in the TLE file.

epochyr

Full four-digit year of this element set’s epoch moment.

epochdays

Fractional days into the year of the epoch moment.

jdsatepoch

Julian date of the epoch (computed from epochyr and epochdays).

ndot

First time derivative of the mean motion (ignored by SGP4).

nddot

Second time derivative of the mean motion (ignored by SGP4).

bstar

Ballistic drag coefficient B* in inverse earth radii.

inclo

Inclination in radians.

nodeo

Right ascension of ascending node in radians.

ecco

Eccentricity.

argpo

Argument of perigee in radians.

mo

Mean anomaly in radians.

no

Mean motion in radians per minute.

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.

This module was adapted from Vallado’s C++ code since its revision date was the most recently updated SGP4 implementation in their zip file:

• C++, August 2010

• Fortran, August 2008

• Pascal, August 2008

• Matlab, May 2008

• Java, July 2005