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I've been trying to compare before & after results for some updated algorithms in an application. Basically, I want to be able to start and run the test at any arbitrary Epoch with the satellite starting in the same position relative to a fixed point on the earth.

For simplicity - assuming Mean Anomaly for the starting TLE is 0 at the start of the day, I could update the Mean Anomaly to ((percentTime * 360 * meanMotion) % 360) where percentTime the decimal part of the Epoch.

For some reason, updating TLEs in this fashion results in a satellite in nearly the same location, but it diverges at several miles per hour difference in the Epoch.

As an example - an initial (and fake) TLE:

1 43226U 18022A 22103.00000000 .00000098 00000+0 00000+0 0 9990
2 43226 0.0434 291.0032 0000358 85.9514 000.0000 1.00274097 15127

Updated to the following should have the same location relative to a fixed point on Earth:

1 43226U 18022A 22103.50000000 .00000098 00000+0 00000+0 0 9990
2 43226 0.0434 291.0032 0000358 85.9514 180.4934 1.00274097 15127

Updated to match same day at 12am

Is my understanding for creating a fake TLE on the exact same orbit correct?

I'm uncertain if the propagator and algorithms being used around it has some kind of bug or if I'm missing something.

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2 Answers 2

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I believe the answer is "No, you won't get a same relative position to a point on the surface of the Earth using that method" for three reasons.

  • Your orbit is non-circular (Eccentricity 0.0000358.), so it varies in both angular and linear speed along its orbit.
  • Your orbit is non-equatorial (Inclination 0.0434°), so it varies in latitude relative to the equator.
  • Epoch is measured in solar days (24 hours), but the orbit is fixed in orientation relative to the stars, so a particular point on the orbit passes overhead every sidereal day (23 hours, 56 minutes 4.09-and-change seconds.)
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  • $\begingroup$ Ooooh. This feels obvious in retrospect.... Which brings the follow up question - can I change the Right Ascension of the Ascending Node proportionally to a sidereal day to reproduce the same relative position? $\endgroup$
    – The Dan Hammer
    Commented Apr 14, 2022 at 19:08
  • $\begingroup$ Well - desired relative position, but completely different orbit if I'm wrapping my brain around it right. What matters to me is the relative positions to a fixed point remain the same from the Epoch of the TLE to Epoch + x when the Epoch is changed. $\endgroup$
    – The Dan Hammer
    Commented Apr 14, 2022 at 19:18
  • $\begingroup$ Thinking about it for a bit - no. :/ There really is no easy way to achieve the desired result. $\endgroup$
    – The Dan Hammer
    Commented Apr 14, 2022 at 19:34
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To anyone who follows, contrary to my earlier comment, adjusting the Right Ascension proportionally to the change in sidereal days does actually work!

To be clear, it's not the same orbit - that wasn't my goal anyhow. It does produce an orbit which maintains a near identical vector relative to a fixed point on the Earth.

Thanks a million notovny who pointed out issues with the initial approach and the issue with the sidereal day. I hadn't thought to compensate for that at all.

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