What mathematical model is suitable for describing the orbital motion of a spacecraft?

Question

C++ / C#

What are the mathematical models that describe the orbital motion of a spacecraft (for example, Soyuz), except for SGP4, which can accurately describe the OD, as well as the angular position of the spacecraft (6DOF).

Answer 1

In addition to SGP4, there is also SDP4 (only for high orbits) and newer versions of SGP8 and SDP8, but for some reason no one uses the eighth versions in practice. Like, space is conservative. "We have been using SGP4 and SDP4 for a long time, they show good accuracy, but we have not tested SGP8 and SDP8 and do not even want to spend time on testing." Well, I understand. So you have a chance to test SGP8 and SDP8, prove that they are better than the fourth versions and convince everyone to use them ( if they are really better, I don't know).