Abstract
Coupling effects of Earth oblateness and direct solar radiation pressure on the motion of an artificial satellite are evaluated. Secular and periodic terms are retained up to order three and two respectively, where the coefficient of the second zonal harmonic of the geopotential is considered of first order. The solution revealed the existence of secular terms at order three that arises from the couplings between terms, of lower orders, resulting from the solar radiation pressure.
Highlights
Analytical theories of celestial mechanics are usually more tractable when tackled within the domain of Hamiltonian mechanics, and most non-Hamiltonian systems of differential equations can be Hamiltonized by a simple technique [1] [2]
Many works deal with the effects of solar radiation pressure, Musen (1960) [3] derived first order expansion for the rate of change in the osculating elements using the method of variation of vector elements
De Moraes (1981) [7] developed semi-analytical theory including the joint effects of direct solar radiation pressure and atmospheric drag for satellites of perigee heights between 500 and 900 Kms
Summary
Analytical theories of celestial mechanics are usually more tractable when tackled within the domain of Hamiltonian mechanics, and most non-Hamiltonian systems of differential equations can be Hamiltonized by a simple technique [1] [2]. (2014) Analytical Third Order Solution for Coupling Effects of Earth Oblateness and Direct Solar Radiation Pressure on the Motion of Artificial Satellites. Many works deal with the effects of solar radiation pressure, Musen (1960) [3] derived first order expansion for the rate of change in the osculating elements using the method of variation of vector elements. De Moraes (1981) [7] developed semi-analytical theory including the joint effects of direct solar radiation pressure and atmospheric drag for satellites of perigee heights between 500 and 900 Kms. The difficulties arising from solar radiation pressure are analyzed in three very useful and interesting expositions given by Kampos (1968) and Sehnal (1970 and 1975) [8]-[10]. The present work is concerned with the effects of solar radiation pressure at higher orders to emphasize the effects of the couplings between them and with those resulting from the oblate gravity field of the Earth. H1∗;W1∗r ; w1∗r where the suffix r refers to terms arising from solar radiation pressure
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