Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence

This paper provides a hamiltonian formulation of the equations of motion of an artificial satellite or space debris orbiting the geostationary ring. This theory of order 1 has been 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. The theory accounts for the influence of the Earth gravity field expanded in spherical harmonics, paying a particular attention to the resonance occurring for geosynchronous objects. The luni-solar perturbations are also taken into account. We present the resonant motion and its main characteristics: equilibria, stability, fundamental frequencies and width of the resonant area by comparison with a basic analytical model. Finally, we show some results concerning the long term dynamics of a typical space debris under the influence of the gravitational field of the Earth and the luni-solar interactions.