SYMPLECTIC INTEGRATORS FOR THE SIMULATION OF SPACE DEBRIS EVOLUTION

The medium term (i.e. ~ 10 Yrs) to the long term (i.e. ~ 100 Yrs) dynamical study of a population of space debris needs to be tackled with numerical tools combining an acceptable accuracy with reasonable computational times. In particular, since for problems related to the evaluation of collision probabilities for a family of particles or the re-entry times for a given range of orbital parameters one need to run a large number of independent realizations, a good balance between the amount of physical memory allocated and the length of single run must be achieved. In this preparatory work we apply symplectic integrators to model the dynamics of debris particles in low and medium Earth orbit. Instead of the commonly used averaged dynamics in orbital elements we directly integrate the Hamilton equations of motion in Cartesian coordinates. By doing so, we find that the computational time for a test orbit is sensibly reduced, for a given timestep length, with respect to integration made with standard codes based on evolution of orbital elements. The latter, when needed, are easily recovered by conversion from Cartesian coordinates during the output phase.