# Equation of motion for Geocentric orbit

I'm simulating the motion of a body in a Geocentric orbit by integrating the equation of motion.

I'm using the following equations for the acceleration of an object in a gravitational field defined by the central mass given by $\mu$ and an axisymmetric oblateness described by $J_2$:

Motion will be a Keplerian orbit, perturbed by the effects of $J_2$.

For increased accuracy, I should also consider other effects of Earth geometry, i.e J22, J3, J4. How could I modify the equation?

I would appreciate if you give links to papers.

• +1 While I've touched on the spherical harmonics of the Geopotential in this answer this new question needs a more thorough and mathematical answer than I can easily provide. Hopefully a "gravity person" will be able to address this better. – uhoh Feb 12 '18 at 8:23
• @uhoh Do you know someone to help with this? – Tarlan Mammadzada Feb 14 '18 at 12:35
• @uhoh I mean, how to use J22, J3, J4 in equation? Edited the question – Tarlan Mammadzada Feb 14 '18 at 18:13
• @uhoh Yes, I'm learning, but checking results on real tests. Thanks, I'll look on SGP4. – Tarlan Mammadzada Feb 15 '18 at 5:03
• I just ran across this answer. You may find it very interesting and possibly helpful. The links/references are great! – uhoh Mar 8 '18 at 9:04