Long-term evolution of space debris under the $$J_2$$ J 2 effect, the solar radiation pressure and the solar and lunar perturbations

Abstract

The aim of this paper is the development of a model to propagate space debris in the geostationary ring considering the \(J_2\) effect due to the Earth oblateness, the Sun and Moon perturbations, and the solar radiation pressure. We justify the importance of considering the \(J_2\) effect when propagating space debris independently of the ratio A / m for short and long-term propagation. We study the role of the Sun and the Moon in the period and amplitude of the inclination for different values of A / m. Thanks to the Hamiltonian formulation of the problem and the use of Poincare’s variables it is possible to express the evolution of the space debris through a simplified dynamical system. We test and validate our obtained analytical solutions with the numerical ones, computed with a powerful integrator named NIMASTEP. We analyse the improvements obtained when we include the \(J_2\) effect and the third body perturbations by a rigorous comparison with a previous model, which only considers the solar radiation pressure. Finally, we study the effect of the area-to-mass ratio on short and long-term propagation.