A Copula based approach to on-orbit satellite breakup simulation

The fragmentation processes (explosions and collisions) of on-orbitsatellite were identified as dominating contributions to the evolution and stability of the future space debris environment. Based on statistical measurement of the distribution and dependence of the fragments characteristic parameters generated in a breakup event, a new way of simulating on-orbit satellite breakup fragments is proposed using Copula. Firstly, collect the breakup event data including breakup time, position and TLE sets of the cataloged fragments. By choosing the best copula, the multivariate distributions of the fragments orbital parameters are acquired then. Secondly, the appropriate empirical relationships for the fragments physical parameters including size, area-to-mass and imparted velocity are chosen. After that, random orbital and physical parameters sets could be generated using Monte-Carlo methods and the imparted velocity of each fragment could be calculated. Finally, associate the orbital and physical parameters together, the assembled characteristic simulation sets of the breakup fragments could be obtained. Illustrated by the simulated Gabbard diagrams and the physical parameters of the fragments with respect to four well-known breakup events (1) STEP II rocket body, (2) CZ-4 upper stage, (3) COSMOS 1813 and (4) PSLV final stage, it can be seen that this method is an appropriate alternative to the conventional simulation process, and will facilitate the research on modeling of space debris environment.