Find the cause for strange results in polar orbit constellations

[MatthewGrim]

Following #32 some issues have been found in the data. This issue aims to resolve the problems, or at least uncover the cause of the bug.

[MatthewGrim]

Hypothesis

Below are the results for active times for 1-3 satellites using j4 perturbation.

In the polar case, it can be seen that there is a strange dip in performance for 3 satellites. My prediction is that this is because of the perturbation in argument of perigee. For the lower altitude orbits, the 45 degree North target is blocked by the Moon at a smaller drift angle from the polar axis. My feeling is at this set of orbits where performance dips, this is what is happening. The total drift is large enough to make the target not visible.

How am I going to test this?

[MatthewGrim]

Getting the total active times as raw values from simulations, the discrepancy over a two year period is small - the most elliptical orbit fairs best. This does not do much to explain the discrepancy:

The deviation is only 3% of the overall result. This is a relatively minor deviation...

[MatthewGrim]

Access Durations

The duration of access periods is plotted for 5000km apogee orbits. The results show mid-range apogees fluctuate in continuous access more than the extreme circular and elliptical orbits.

The satellite constellations all pretty much achieve continuous coverage. So what's the cause for the discrepancy? It's still unclear.

[MatthewGrim]

Plotting variation of orbital elements, the only thing that is varying is the argument of perigee:

Though the 800 by 5000 one varies the most, it still performs best for the three constellation case, as well as for a single satellite. Why is that?

Qualitatively, for a single orbit, the satellite should spend more time in range of the target the more elliptical the orbit. So being more elliptical increases the access time. The drift must reduce performance, but not enough to compensate for this benefit. The circular orbit doesn't have drift so the overall access for 3 satellites catches up with more elliptical orbits.

[MatthewGrim]

Taking the access times, the high altitude orbits are effectively equivalent in that they all have permanent access to the target (as shown below - there is only one access event lasting for the total sim time). At the same time, this doesn't mean they deliver the same ammount of power.

Including target eclipses:

The orbits are still equivalent. Removing target eclipses, and now including when the satellite is eclipsed by the Moon:

This is the cause of the variation, and the output costs something like 12 days of access potential. Between the best and worst orbits. This is the cause for the valley in results. Highly elliptical orbits spend less time in the region where the Moon blocks the sun, high altitude circular orbits move across the eclipse region from further away, so that though they are slower, the Moon is a smaller obstruction. This compensates enough to create a small valley in the results

[MatthewGrim]

This explains the strange results up to 5000km. The J4 perturbation is not a valid model for the polar orbits as #39 showed. The main trend is still to be as elliptical as possible, while maintaining orbital stability.

I am closing this issue.