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 toolscombining an acceptable accuracy with reasonable computational times. Inparticular, since for problems related to the evaluation of collisionprobabilities for a family of particles or the re-entry times for a given rangeof orbital parameters one need to run a large number of independentrealizations, a good balance between the amount of physical memory allocatedand 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 commonlyused averaged dynamics in orbital elements we directly integrate the Hamiltonequations of motion in Cartesian coordinates. By doing so, we find that thecomputational time for a test orbit is sensibly reduced, for a given timesteplength, with respect to integration made with standard codes based on evolutionof orbital elements. The latter, when needed, are easily recovered byconversion from Cartesian coordinates during the output phase.