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 longterm 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 Poincaré'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.

Phase space description of the dynamics due to the coupled effect of the planetary oblateness and the solar radiation pressure perturbations

“…Finally, as mentioned at the beginning, it will be our priority to see how the phase space may change when an additional perturbation comes into play. In the case of the Earth, lunisolar gravitational perturbations and the ellipticity of the Earth will be considered for high-altitude orbits (see, e.g., [26,27,36]) and the role of the atmospheric drag in the final deorbiting phase (see, e.g., [37]).…”

“…Moreover, the concept proposed will hold certainly in the cases described above, where the two perturbations -oblateness and solar radiation pressure -play a major role, but it will be of high interest to see how the solutions presented may persist under the effect of an additional effect and under which conditions they remain the skeleton of the long-term dynamics. For orbits at the Earth, the key case will be the dynamics due to lunisolar gravitational perturbations for Highly Elliptical Orbits [25] and in the geosynchronous region (e.g., [26,27]).…”

Secular dynamics around small bodies with solar radiation pressure

“…[5,7,27,29,34]; (3) the space debris have become an emergent research topic because of its exponential rate of increase and potential hazards to spacecraft. For the high area-to-mass ratio and high-altitude debris, their orbital motion is strongly affected by the SRP [4,6,31,32,35].…”

Orbital flips due to solar radiation pressure for space debris in near-circular orbits

“…We can mention works focused on the orbital evolution of Geostationary Earth Orbits (GEO) (e.g. [5][6][7][8][9]) and Medium Earth Orbits (MEO) (e.g. [10][11][12][13][14][15]).…”