Poynting–Robertson drag and solar wind in the space debris problem

We analyse the combined effect of Poynting–Robertson and solar-wind drag on space debris. We derive a model within Cartesian, Gaussian and Hamiltonian frameworks. We focus on the geosynchronous resonance, although the results can be easily generalized to any resonance in Medium Earth Orbit and in regions located outside the geostationary ring. By numerical and analytical techniques, we compute the drift in semimajor axis due to Poynting–Robertson and solar-wind drag. After a linear stability analysis of the equilibria, we combine a careful investigation of the regular, resonant, chaotic behaviour of the phase space with a long-term propagation of a sample of initial conditions. The results strongly depend on the value of the area-to-mass ratio of the debris, which might show different dynamical behaviours: temporary capture or escape from the geosynchronous resonance, as well as temporary capture or escape from secondary resonances involving the rate of variation of the longitude of the Sun. Such analysis shows that Poynting–Robertson and solar-wind drag must be taken into account, when looking at the long-term behaviour of space debris. Trapping or escape from the resonance can be used to place the debris in convenient regions of the phase space.