### Degree and Order in gravity models

Posted:

**Wed May 17, 2017 3:38 pm**Hello All,

I'm not sure that I understand how Degree and Order are being interpreted in the gravity model of the propagator. Can anyone help?

If I begin by modelling a satellite with inclination and semimajor axis corresponding to a Sun-synchronous orbit, but set degree=order=0 in the gravity model (I'm using JGM-2), I see what I expect - no nodal precession. If I run the same simulation but set degree to 2, we introduce zonal terms in the gravity model, and so J2 is represented, and the spacecraft motion exhibits the nodal precession which gives Sun-synchronous behaviour - exactly as expected.

Now, I wanted to simulate some aspects of orbital motion that depend primarily on sectoral terms. I expected that if I set order equal to degree, I would only represent those sectoral terms - based on e.g. slide 3 of:

http://www.gps.alaska.edu/jeff/Classes/ ... vity05.pdf

However, I find that when I set Degree=Order=2 in my earlier Sun-synchronous example, I still see Sun-synchronous behaviour, which shouldn't be possible if there are no zonal terms in the model. Evidently the interpretation of degree and order is not what I expected.

In an early draft version of the GMAT manual (dating back to 2007: https://ntrs.nasa.gov/archive/nasa/casi ... 047410.pdf ), degree is defined as "This field allows the user to select the the degree, or number of zonal terms" while order "allows the user to select the the order, or number of tesseral terms". That seems to describe what I'm seeing. But the definition is different in the current documentation: references to zonal / tesseral terms are no longer made, and the current version requires order <= degree, while the 2007 version requires order >= degree.

Is my interpretation of Degree & Order incorrect, and how would one go about modelling only the sectoral terms in GMAT?

Thanks

Nigel

I'm not sure that I understand how Degree and Order are being interpreted in the gravity model of the propagator. Can anyone help?

If I begin by modelling a satellite with inclination and semimajor axis corresponding to a Sun-synchronous orbit, but set degree=order=0 in the gravity model (I'm using JGM-2), I see what I expect - no nodal precession. If I run the same simulation but set degree to 2, we introduce zonal terms in the gravity model, and so J2 is represented, and the spacecraft motion exhibits the nodal precession which gives Sun-synchronous behaviour - exactly as expected.

Now, I wanted to simulate some aspects of orbital motion that depend primarily on sectoral terms. I expected that if I set order equal to degree, I would only represent those sectoral terms - based on e.g. slide 3 of:

http://www.gps.alaska.edu/jeff/Classes/ ... vity05.pdf

However, I find that when I set Degree=Order=2 in my earlier Sun-synchronous example, I still see Sun-synchronous behaviour, which shouldn't be possible if there are no zonal terms in the model. Evidently the interpretation of degree and order is not what I expected.

In an early draft version of the GMAT manual (dating back to 2007: https://ntrs.nasa.gov/archive/nasa/casi ... 047410.pdf ), degree is defined as "This field allows the user to select the the degree, or number of zonal terms" while order "allows the user to select the the order, or number of tesseral terms". That seems to describe what I'm seeing. But the definition is different in the current documentation: references to zonal / tesseral terms are no longer made, and the current version requires order <= degree, while the 2007 version requires order >= degree.

Is my interpretation of Degree & Order incorrect, and how would one go about modelling only the sectoral terms in GMAT?

Thanks

Nigel