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Long term SSO simulation inclination anomaly

PostPosted: Fri Apr 08, 2016 3:16 pm
by niki

I am trying to simulate the perturbations experienced by a LEO satellite in SSO orbit over a period of 7-10 years. To create a baseline scenario I simulate the mission first without point masses or drag. Looking at the inclination over a period of 7 years, I see an increasing amplitude oscillation in the inclination parameter with a period of one year. The image shows the inclination over 7 years.

Inclination of SSO satellite simulated over 7 years.

I have used the JGM-2 model of order 10 and degree 10. I have tried order 20 and degree 20 and still see the same results. This looks like an instability developing over time.
I have also taken data from an actual satellite (TLE history from and compared it to the GMAT simulated results. This is shown below:

Comparison of Actual and Simulated inclination for LEO SSO satellite over 8 years.

The trend seems close, but there is again an oscillation that builds over time which is not seen in the actual data. I realize TLE data is not very accurate and I have not used the SGP4 propagator - I have only taken the inclination parameter from the 8-year long history of TLE-datasets so I would expect to see such an oscillation there if it actually existed. Where could the oscillation in the simulation be coming from? I would appreciate any insights!


Re: Long term SSO simulation inclination anomaly

PostPosted: Thu Sep 08, 2016 10:44 am
by niki
I have recently spent some more time on this and believe that I am (at least partially) able to answer my own question.
The initial simulation was done in the default EarthMJ200Eq Coordinate System, which is an inertial coordinate system, as indicated in the GMAT help:
An inertial coordinate system. The nominal x-axis points along the line formed by the intersection of the Earth’s mean equatorial plane and the mean ecliptic plane (at the J2000 epoch), in the direction of Aries. The z-axis is normal to the Earth’s mean equator at the J2000 epoch and the y-axis completes the right-handed system. The mean planes of the ecliptic and equator, at the J2000 epoch, are computed using IAU-1976/FK5 theory with 1980 update for nutation.
It is my understanding that, since parameters like Inclination are determined relative to the Earth and since the Earths equatorial plane and orbit axis changes over time due to nutation, expressing these quantities in the inertial EarthMJ2000 coordinate system actually also adds the nutation to the result. The inclination measured would only be correct at the epoch of the coordinate system (J2000). To verify this I did a 10 year simulation (from 1995 to 2005) of a satellite at 98.16 degree inclination (with no third body influence) and the resulting inclination is shown below:
10 Year simulation using EarthMJ2000Eq

This seems to show the variations in inclination reaching 0 at the EarthMJ2000Eq epoch and increasing to either end.

A better coordinate system to use would be the True of Date TODEq coordinate system, which is quasi-inertial and uses the current epoch of the object to determine the true equatorial plane. If I repeat the original simulation where I compare the actual satellite orbit parameters with the simulated parameters I now get:
Comparison of actual and simulated sat in TODEq

The correlation is much better. There is still a small slope mismatch which I cannot account for, but the "oscillations" are gone. I am not an astrodynamics expert and I think this as much as I can fathom! Maybe it is useful to others as well.


Re: Long term SSO simulation inclination anomaly

PostPosted: Tue Feb 27, 2018 9:28 am
by Warren58
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Re: Long term SSO simulation inclination anomaly

PostPosted: Tue Feb 27, 2018 3:28 pm
by JudithRivas
Your Simulation is looking a lot perfect, and don't have any issues with it. You have captured a good pattern as the which was initially posted 2 years ago. Your perturbations experienced by a LEO satellite in SSO orbit over a period of 7-10 years are very proper, and easy to understand. May you get some help from some experienced persons if you need any.