Analysing a phasing maneuver using GMAT- how do I reliably quantify their "phase difference"

Question

I am trying to recreate a phasing problem that was solved on paper the previous semester, and verify my solutions using GMAT.

Two identical satellites are released on a 550km sun-synchronous orbit by the launch vehicle. Determine the phasing manoeuvres required to put them 180 degrees apart in their (initial, 550km )orbit, conducting the whole process within 30 days of launch.

I understand the basics of phasing and the maneuvers that need to happen, in theory, and have calculated the approximate DV required for the process. I can verify that the two satellites eventually reach the required phase difference in their respective orbits by looking at the 3D view, however I don't know how this can be quantified within the simulator and later on used as a solver target or in an optimisation process. Furthermore, I'd like to be able to evaluate the phase error that developed as time goes by and eventually be able to make some station keeping simulation for both vessels.

Looking through the tutorials and manual I don't see any examples demonstrating this capability. Is there any resource or advice you can share for this sort of problem?

Answer 1

...I don't know how this can be quantified within the simulator...
... I'd like to be able to evaluate the phase error...

If I correctly understand your question, in your case you need to create a variable in GMAT, in that variable you will write a difference between longitudes of satellites after finishing of phasing (at any time endeed). Something like this:

GMAT dLong = DefaultSC2.Earth.Longitude - DefaultSC.Earth.Longitude;

(GMAT don't allow to use statements like DefaultSC2.Earth.Longitude - DefaultSC.Earth.Longitude directly in many cases, so we need a variable.) And then you will write this variable to the GMAT console (for monitoring):

Write  dLong { Style = Concise, LogFile = false, MessageWindow = true }

And the phase error will be 180 - dlong.

UPD:
A small addition to the excellent and clear answer of ChrisR: the "true longitude" as a sum of AoP, RAAN and TA exists in GMAT and denoted as TLONG. Its using in calculations is slightly differs from the geodesic longitude:

GMAT dTLONG = DefaultSC2.EarthMJ2000Eq.TLONG - DefaultSC.EarthMJ2000Eq.TLONG;

And there is MLONG parameter besides TLONG, which is a sum of AoP, RAAN and Mean Anomaly.

Answer 2

From what I understand, you need to ensure that both spacecraft are phased by 180 degrees. There are different orbital elements used to assess the phasing of spacecraft. The main one is the true anomaly, but it's ill-defined for circular orbits (in which case I would recommend using the "true longitude," defined as AoP + RAAN + TA, it is unrelated to the geodesic longitude).

As you know, the altitude of a spacecraft defines its speed of travel. Hence, if two spacecraft are on the same orbit, they will travel at the same speed. Similarly, if they're on different orbits (specifically at different altitudes), they will travel at different speeds.

A very common maneuver in spacecraft operation is a "drift maneuvers." It allows one to have one spacecraft drift with respect to another. This is done simply by changing the altitude of one of the spacecraft (with a single maneuver), then letting the orbital dynamics work in favor, and finally, once you have achieved the desired phasing drift, perform another burn to return to the altitude you wish to have.

From the problem statement, it seems like you have up to thirty days to perform this maneuver. As such, I would recommend the smallest burn possible such that you achieve a 180 degree phase in exactly 30 days.

Off the cuff, I think the simplest is to "guess" the correct maneuvers.

In GMAT, define both spacecraft, and setup a "propagate synchronized" segment for both spacecraft (this ensures that they have the same time step). Then, create a new plot and plot the true longitude over time (or the true anomaly if the spacecraft are not in a circular orbit).

Then, for one of the spacecraft, add an instantaneous burn to lower (or raise, as you wish) its apoapse (this is a burn against the velocity direction, so the norm of the burn is [-1 ,0 ,0] in the VNC frame). Propagate both spacecraft for 30 days, and see how much they have drifted by. If their phasing is greater than 180 degree, you know you can use a small burn, i.e. the apoase of the drifting spacecraft can be closer to the 550km target altitude. If the phasing is less than 180 degree, then you need a bigger burn.

Finally, add another maneuver just when the 180 degree phase is reached to circularize the orbit (your initial burn will make it elliptical) and return to 550km. By doing the burn, you'll be introducing some error, so you will need to play around a bit with the timing of the maneuvers.