Long-term stability of trajectories of the space debris population, perturbed by gravitational effects
Résumé
This paper aims at investigating the stability over 200 years of a very large number of orbits in the MEO and GEO regions. The initial conditions of the orbits cover a wide range of semi- major axes and inclinations, regularly sampled, so as to describe as exhaustively as possible the gravitational perturbations acting on the space debris population. In this study, we pay particular attention to the dynamical properties which can make the orbit's eccentricity become very large (up to 0.8 over a few decades), due to coupling effects in the perturbations induced by the non spherical shape of the Earth, and by luni-solar attraction. Hence, the word "stable" stands here for keeping as low as possible the collision risk with operational orbits, such as the geostationnary one or orbits devoted to radionavigation. This is ensured if the eccentricity keeps a very low value, so as to avoid a high difference between the perigee and apogee altitudes. The main goal of this paper consists in identifying the role of resonances inducing an eccentricity's growth, and in finding where the corresponding resonance areas are located in space. We take advantage of numerical as well as analytical integrations of the equations of motion over a long period of time (200 years). The main steps of the work are: 1. Numerical integration of osculating equations of motion of thousands of orbits. Characterization of the kind of chaos and of the variations of the eccentricity. 2. Search for periods within time series of orbital elements linked with resonance effects in the 4-body problem (Earth, Moon, Sun, satellite). 3. Search for combinations of angles involved in the resonance effects, following an analytical approach ("Kaula"-like derivated method). 4. Comparisons of these results with the ones obtained with the theory of mean orbital motion. To study to what extent averaging approaches are efficient or not to propagate chaotic orbits of the space debris population. As a conclusion, we analyse the long-term evolution of the orbital elements of the space debris population, in view of studying the stability of disposal orbits. Some of them are affected by chaotic effects (mathematical sense). One of the results is the defintion of areas where disposal orbits should NOT be located. Our simulations are based on a parallelized code which works on the "Grid", ensuring reasonable integration times.