Python coordinate transformation ECI to ECEF

Question

I am using sgp4 python package (developed by Brandon Rhodes); I am inputting the TLE information for ISS(Zarya). I get the position of the satellite at a certain date, in the in ECI coordinate system. However, I want to convert it to ECEF coordinate system.

There are at least two instances of matlab functions implemented (ecitoecef, eci2ecef) and a C function (eci2ecef) implemented for the RTKLIB project.( I can't post links because I have a restriction of two links per question since this is my first question and I have reputation 1)

I was not able to find a python function implemented. However, in this previous question, Python satellite tracking with spg4, pyephem- positions not matching the user says "I found atleast part of the issue. spg84.propagate() returns the location in ECI, not ECEF. Quick run through eci2ecef and it lines up perfectly with the predict response."

Is that eci2ecef referring to a python implementation? Is this available online? Is there a document online that explains exactly the step needed to be done if I were to implemented by myself? In this question How do I convert ECI coordinates to longitude latitude and altitude to display on a Map? in a comment they say "They differ by the Earth's rotation rate so the transformation is just a 2-D cos sin; -sin cos type transform. ". What is the angle of the transform? Is it the Greenwhich Sideral Time? When we use sgp4, is it also the GST that we specify, or other time?

Thank you so much for your help!

Answer 1

First I studied the paper AIAA 2006-6753 which is online at CelesTrak, and which formed the basis for making the sgp4 library available in Python in the first place:

https://celestrak.org/publications/AIAA/2006-6753/

Based on its recommendations — and in particular on the information in its Appendix — I am attempting to integrate Earth satellites into my new Skyfield astronomy library. A new release with this work should be out soon, but in the meantime you can study the transformations that I am using (based on the above paper) at:

https://github.com/brandon-rhodes/python-skyfield/blob/master/skyfield/sgp4lib.py

I am not sure that I have the transforms correct, but will be checking the results against as many official sources of positions as I can find to determine whether I have made any systematic error.

Answer 2

Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8, and SDP8) used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system. This set of models is often referred to collectively as SGP4 due to the frequency of use of that model particularly with two-line element sets produced by NORAD and NASA. These models predict the effect of perturbations caused by the Earth’s shape, drag, radiation, and gravitation effects from other bodies such as the sun and moon. Simplified General Perturbations (SGP) models apply to near-earth objects with an orbital period of fewer than 225 minutes. Simplified Deep Space Perturbations (SDP) models apply to objects with an orbital period greater than 225 minutes, which corresponds to an altitude of 5,877.5 km, assuming a circular orbit. The SGP4 model was developed by Ken Cranford in 1970. This model was obtained by simplification of the more extensive analytical theory of Lane and Cranford which uses the solution of Brouwer for its gravitational model and a power density function for its atmospheric model. The SGP4 MATLAB version returns the satellite's state vector in four coordinate systems i.e. TEME, ITRS, GCRS, and TOD. The SGP4 Python version returns the satellite's state vector in three coordinate systems i.e. TEME, ITRS, and GCRS. You can use my Python version of SGP4 from the following link: https://www.researchgate.net/publication/358351066_SGP4_Python_code or you can use my MATLAB version of SGP4 from the following link: https://www.researchgate.net/publication/346217793_SGP4_MATLAB_code

Answer 3

The ECI to ECEF transformation is also implemented in satellite-js which is derived from PyEphem.

You may have to check it's correctness.