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]


The shown equation gives 1 km error in comparison with GMAT, where degree 2 and order 0 is chosen for JGM-3 model. Is it due to the change of the term with time, which I didn't consider? 


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