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

**ABSTRACT** 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.

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**ABSTRACT:**To explore the dynamics of a test particle in the near-Mercury’s environment, the orbital motion of an orbiter around Mercury is considered. Different perturbing forces, namely the Mercurian gravity field, the solar radiation pressure, the solar wind and the coronal mass ejections, are taken into account. The order of magnitude of each perturbing term is assessed. The equations of motion in canonical representation are obtained. The Hamiltonian in terms of Hansen coefficients is expressed. A procedure for solution is presented. The short and long periodic terms are removed from the Hamiltonian and the solution is obtained. Long periodic perturbations on the orbital dynamics of an orbiter around Mercury due to the solar events are found as revealed by Eq. (26) in the text. Resonance cases are discussed and the different resonant inclinations are obtained. A procedure for the computation of the position and velocity is presented.New Astronomy 08/2007; 12(6-12):490-496. DOI:10.1016/j.newast.2007.02.002 · 1.24 Impact Factor