Analytical treatment of the relativistic and solar radiation pressure effects on an artificial satellite

A development of an analytical solution for the motion of a spherical Earth artificial satellite subjected to the combined effects of the post-Newtonian (PN) geopotential and direct solar radiation pressure (SRP) is presented. The equations of motion are derived in previous paper [A.A. El-Enna, Appl. Math. Comput. 149 (2004) 359-368]. Two Lie transformations are used to derive explicit results for the secular and periodic perturbations of the satellite orbits, retaining secular and periodic terms up to orders 4 and 3, respectively. The developments focussed on the joint effects of the relativistic and SRP terms. The existence of some resonance cases are discussed using the present long periodic terms. Moreover, these cases are investigated using the conditions of resonance.