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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.

The Dan Hammer
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2 Answers2

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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.)
notovny
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  • 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?

     – The Dan Hammer Apr 14 '22 at 19:08
  • 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.

     – The Dan Hammer Apr 14 '22 at 19:18
  • Thinking about it for a bit - no. :/ There really is no easy way to achieve the desired result. – The Dan Hammer Apr 14 '22 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.

The Dan Hammer
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