I'm trying to take into account the Earth geopotential effect on the orbit. The only term I could consider, is `J2`.

 1. Are the terms (J2, etc.) change with time?
 2. I found other terms coefficients [here][1]. How to add them also to differential equation?

  [![enter image description here][2]][2]

 3.Why does the shown equation give 1 km error in 1 day in comparison with GMAT (configuration is below)? The coefficients for `Eq radius` and `J2` are the same. The integrator is 9th order Runge-Kutta with `tol=10e-13`.


[![enter image description here][3]][3]

[![enter image description here][4]][4]


  [1]: http://www.csr.utexas.edu/publications/statod/TabD.3.new.txt
  [2]: https://i.stack.imgur.com/MKbbw.png
  [3]: https://i.stack.imgur.com/Jdkgr.png
  [4]: https://i.stack.imgur.com/lXdE7.png