I am very confused with regards the simulation and fitting of satellite orbits.

For example, how does one compare the results of a numerically integrated force model with an orbit that has been fitted to laser ranging data??

When you numerically integrate a force model how do you compare with one of the many many many reference frames that exist that your fitted orbit will be subjected to! Any suggestions? My understanding is: when you simulate an orbit you will generate a whole host of positions. Then to compare it to an actual orbit you must select a time epoch which will orient the coordinate system ( is this correct??). If this is correct what follows?

The model I would like to numerically integrate is only Newtonian gravity plus relativistic corrections (assuming point particles) as recommended by the IERS given by Eq. (10.12) in the most current technical document/convention.

  • $\begingroup$ When you say "Newton plus relativitic corrections", I'm guessing you mean Newtonian gravity. Are you speaking of point mass gravity? $\endgroup$ Commented Sep 20, 2017 at 14:31
  • $\begingroup$ @DuffBeerBaron Yes I will update the Q to be more clear :) $\endgroup$ Commented Sep 20, 2017 at 22:23

2 Answers 2


Comparisons between predicted orbits (numerically integrated) and fitted orbits (from tracking data) are usually done in an inertial reference frame, such as ICRF or Mean of J2000. Within these frames, the orbit comparison can take several forms, such as point by point comparisons, or comparisons of the orbital elements


First, you need to make sure both results (simulation results and laser ranging data) are converted into the same coordinate system. This is usually chosen as an inertial frame, like ECI.

You can compare two orbits in ECI frame but you will only have one meaningful information from that: the magnitude of the error. However, in most papers, you will see another coordinate transformation to a satellite-based coordinate system is done to get more meaningful results. RSW and NTW systems are most common for this practice since most modeling differences create visible biases in those coordinate elements.

Do not forget to take into account of the differences that are caused by coordinate transformations.

  • $\begingroup$ I think that the OP is asking how to do this. $\endgroup$
    – uhoh
    Commented Sep 21, 2017 at 17:05
  • $\begingroup$ I thought about it but in that case, I believe he should ask again or detail the parts he is stuck at. He could be stuck at determining base coordinate systems, integrating the orbit, transformations to ECI, transformations from ECI etc. $\endgroup$ Commented Sep 21, 2017 at 17:07

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