A web of secondary resonances for large A/m geostationary debris

The dynamics of space debris with very high A/m near the geostationary orbit is dominated by the gravitational coefficient C ₂₂ and the solar radiation pressure. An analysis of the stability of the orbits by the chaos indicator MEGNO and frequency analysis map FAM shows chaotic layers around the separatrix and reveals a web of sub-structures associated to resonances with the annual period of the Sun. This succession of stable thin islands and chaotic layers can be reproduced and explained by a quite simple toy model, based on a pendulum approach, perturbed, through the eccentricity, by the external (Sun) frequency. The use of suitable action-angle variables in the circulation and libration regions of the pendulum allows to point out new resonances between the geostationary libration angle and the Sun’s longitude. They correspond very well (positions, shape, width) to the structures visible on the FAM representations.