# Comparison of AOP change of the orbits

I'm comparing how the Argument of perigee (AOP) changes for 2 orbits (O1 and O2). The orbits are equal, but the difference in inclination is 0.05deg. I have to choose the orbit, which change in AOP is less.

I made simulation in GMAT in 1 year and 5 years time interval. The problem is, in the first scenario AOP(O1)>AOP(O2), however, in the second AOP(O2)>AOP(O1). Also, different parts of time interval (1st year, 2nd year, etc.) affect the AOP differently.

1. On which time interval simulation should I rely?
2. Which orbit should I choose in terms of stability of AOP (on the basis of plots below)?

This is a plot of AOP change in 5 years:

O1

O2 The GMAT configuration:

• Central body- Earth
• JGM-3 21 degree to 21 order
• Sun and Moon
• Atmosphere model- JacciaRoberts
• I think "on which time interval?" is a question that you should ask directly to the person who is asking you to "choose the orbit, whose change in AOP is less". For any situation where the rate of change varies (i.e. which has nonzero higher derivatives) there's no simple answer. If I ask "What changes faster, sine or cosine?", of course the answer can be "it depends on where you look" as well as can be "on average they are equal". In other words, "it's not clear what you are asking here" yet. – uhoh Jul 12 '18 at 23:11
• On an aside, you'll note that the AoP hardly changes. The RAAN on the other hand drifts considerably, even in just a day depending on the inclination. – ChrisR Jul 13 '18 at 1:49
• @uhoh Does the change in AOP depends on chosen years interval due to the effects of Moon and Sun? – Leeloo Jul 13 '18 at 5:30
• @ChrisR The orbits are equal, but the difference in inclinations in 0.05 deg. Added additional plot – Leeloo Jul 13 '18 at 5:32
• Edited the question, added more details – Leeloo Jul 13 '18 at 5:38

## 1 Answer

From the provided plots, O1 is the orbit which returns to the initial AoP after the five year period. Hence, that is the best answer to the question "which of the two orbits is the most stable after a five year period?"

Moreover, the overall amplitude of the change in AoP (the difference between the minimum value and the maximum value) throughout the five year period shows that for O1, the amplitude is about 2 degrees (from what I can tell from the plots). For O2 that amplitude is about 4.5 degrees.

Therefore, both in terms of greatest amplitude change and in terms of "difference in AoP after 5 years", O1 beats O2.

• Thank you! 1 question: Why is it important to keep the AOP stable? – Leeloo Jul 13 '18 at 10:33
• The AoP can be seen as the orientation of an orbit. It says where the apoapsis and periapsis will be. If your mission must observe a given specific spot over the planet over a long time, then you probably want to make sure that you spend the longest time over that point. As such, you can design your orbit to have its apogee above that point, and make sure that your AoP doesn't drift much (not that at the apogee, your aop is by definition 180 degrees). – ChrisR Jul 13 '18 at 15:39