Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios

Abstract

This paper provides a Hamiltonian formulation of the averaged equations of motion with respect to short periods (1 day) of a space debris subjected to direct solar radiation pressure and orbiting near the geostationary ring. This theory is based on a semi-analytical theory of order 1 regarding the averaging process, formulated using canonical and non-singular elements for eccentricity and inclination. The analysis is based on an expansion in powers of the eccentricity and of the inclination, truncated at an arbitrary high order. First, the dynamical evolution of space debris released near the geostationary ring, with area-to-mass ratios as high as 40 m 2/kg is analyzed within the framework of mid-term evolution (∼1 year) as well as long-term evolution (several decades). This study is carried out, using both simplified analytical models to clarify some properties, as well as our complete semi-analytical theory which leads to an accurate understanding of the mid-term and long-term evolution of the eccentricity and of the inclination. We also analyzed the coupling equations between the eccentricity and the inclination, considering a doubly averaged analytical model. Second, we also focused our attention on the comparison of various direct radiation pressure approximations in order to assess their consequences. Last, this paper claims to be the continuation and the counterpart of previous papers dealing with geosynchronous orbits and radiation pressure, that is Anselmo and Pardini (2005) [Anselmo, L., Pardini, C. Orbital evolution of geosynchronous objects with high area-to-mass ratios. In: Danesy, D. (Ed.), Proceedings of the Fourth European Conference on Space Debris, ESA SP-587. ESA Publications Division, Noordwijk, The Netherlands, pp. 279–284, 2005] and Valk et al. (submitted for publication) [Valk, S., Lemaître, A., Deleflie, F. Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence, Advances in Space Research, submitted for publication].