Analytical Solution for the Combined Solar Radiation Pressure and Luni- Solar Effects on the Orbits of High Altitude Satellites

ABSTRACT

A new analytical solution is obtained for the motion of high-altitude earth satellites. The basic idea is to study the joint effects of direct solar radiation pressure and the gravitation of the Earth, Moon and the Sun on the orbits of the satellites. The mathematical model includes the zonal harmonics of the geopotential effects up to 4 J . The order of magnitude of each perturbing term is assessed. The formulae for the all perturbations forces are obtained up to the fourth order (where the mean motion of the moon (~ 10-2) is considered a small quantity of first order). The short, intermediate and long-period terms are eliminated from the Hamiltonian using a perturbation technique based on the Lie-Deprit-Kamel transform through three canonical transformations. The solution is intended to be used for ephemeris predictions for orbiters whose orbital semimajor axes are in the range of 15000 to 70000 kms.

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