spherical harmonics of earth - J2 squared

[Peter Jackson]

Hey, I am writing a code in matlab to integrate the equations of motion of a low earth orbiting satellite, and I need to use a few spherical harmonic terms. The expressions for the acceleration due to J2, J3, J4, J5, and J6 effect in Cartesian coordinate system is given in the book "Fundamentals of Astrodynamics" by David A. Vallado. However, he does not have the expression for acceleration due to "J2 squared". I didn't even know there was a J2 squared until my prof. asked me to include it and when I asked him more, he asked me to do my own search. So please help me find an expression for this J2 squared.
Thanks

 

[Urwumpe]

J2 squared??? sorry, but that is no coefficient for harmonics. [math]J_{2,2}[/math] would be one.

Also, you get the most accurate J-terms by downloading a gravity model, like the GRACE Gravity Model - at least until the GOCE data is done.

http://www.csr.utexas.edu/grace/gravity/