Back-tracing space debris using proper elements

Abstract Normal form methods allow one to compute quasi-invariants of a Hamiltonian system, which are referred to as proper elements. The computation of the proper elements turns out to be useful to associate dynamical properties that lead to identify families of space debris, as it was done in the past for families of asteroids. In particular, through proper elements we are able to group fragments generated by the same break-up event and we possibly associate them to a parent body. A qualitative analysis of the results is given by the computation of the Pearson correlation coefficient and the probability of the Kolmogorov-Smirnov statistical test.