Abstract
In this article we propose in a general form the formulas of the derivatives on the Cartesian co-ordinates for zonal harmonics of planetary potential. These formulas are necessary for description of motion of the Solar system bodies in the circumplanetary space. Used methods of the numerical integration of the derived equations of motion are the Everhart's methods. Here we present calculated coefficients that are necessary for the method construction. Presented formulas and Everhart’s methods are checked using the problem of the asteroid (144898) 2004 VD17 orbit. It should be noted that our results agree well with the NASA predictions.

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