Semi-analytical investigations of high area-to-mass ratio geosynchronous space debris including Earth’s shadowing effects

Abstract

This paper investigates the long-term perturbations of the orbits of geosynchronous space debris influenced by direct radiation pressure including the Earth’s shadowing effects. For this purpose, we propose an extension of our homemade semi-analytical theory [Valk, S., Lemaître, A., Deleflie, F. Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence. Adv. Space Res., submitted for publication], based on the method developed by Aksnes [Aksnes, K. Short-period and long-period perturbations of a spherical satellite due to direct solar radiation. Celest. Mech. Dyn. Astron. 13, 89–104, 1976] and generalized into a more convenient non-singular formalism. The perturbations accounting for the direct radiation pressure with the Earth’s shadow are computed on a revolution-by-revolution basis, retaining the original osculating Hamiltonian disturbing function. In this framework, we compute the non-singular mean longitude at shadow entry and shadow exit at every orbital revolution in opposition to classical approaches where the singular eccentric anomalies at shadow entry and shadow exit are computed. This new algorithm is developed using non-singular variables. Consequently, it is particularly suitable for both near-circular and near-equatorial orbits as well as orbits which transit periodically around null eccentricities and null inclinations. The algorithm is tested by means of numerical integrations of the equations, averaged over the short periods, including radiation pressure, J 2, the combined Moon and Sun third body attraction as well as the long-term effects of the 1:1 resonance occurring for geosynchronous objects. As an extension of [Valk, S., Lemaître, A., Anselmo, L. Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios influenced by solar radiation pressure. Adv. Space Res., doi:10.1016/j.asr.2007.10.025, 2007b], we especially apply our analysis to space debris with area-to-mass as high as 20 m 2/kg. This paper provides numerical and semi-analytical investigations leading to a deep understanding of the long-term evolution of the semi-major axis. Finally, these semi-analytical investigations are compared with accurate numerical integrations of the osculating equations of motion over time scales as high as 25 years.