I'm trying to take into account the Earth geopotential effect on the orbit.

 1. Are the terms (J2, etc.) change with time?
 2. Is it worth to take into account `J0` and `J1`? 
 3. In JGM-3 N=M=70 (about 5000 coefficients). I found till degree 8 [here][1]. Where to find others?
 4. I'm solving a differential equation with `J2`. How to add other terms?

  [![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. Probably, it takes into account `J1` and `J0`? 

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