Abstract
Satellite collisions or fragmentations generate a huge number of space debris; over time, the fragments might get dispersed, making it difficult to associate them to the configuration at break-up. In this work, we present a procedure to back-trace the debris, reconnecting them to their original configuration. To this end, we compute the proper elements, namely dynamical quantities which stay nearly constant over time. While the osculating elements might spread and lose connection with the values at break-up, the proper elements, which have been already successfully used to identify asteroid families, retain the dynamical features of the original configuration. We show the efficacy of the procedure, based on a hierarchical implementation of perturbation theory, by analyzing the following four different case studies associated to satellites that underwent a catastrophic event: Ariane 44lp, Atlas V Centaur, CZ-3, Titan IIIc Transtage. The link between (initial and final) osculating and proper elements is evaluated through tools of statistical data analysis. The results show that proper elements allow one to reconnect the fragments to their parent body.
Highlights
Motivated by the successful results on asteroids, we propose to group and reconnect space debris through the computation of the proper elements associated to fragments generated by a satellite break-up e vent[7,8,9]
Based on a solid mathematical method, our approach provides a reliable and effective way to connect the proper elements of a set of fragments to a specific break-up event
Even not knowing the break-up time, we can propagate backward the elements of the space debris to reconnect the debris to the parent body; we show the effectiveness of this procedure in the specific example of Titan IIIc Transtage
Summary
We investigate the test cases by computing osculating and proper elements, and by analyzing the results through histograms, Kolmogorov-Smirnov test, Variance Equivalence test and Pearson correlation coefficient. Recalling that the space debris model described above depends on fast, semi-fast and slow variables, we compute the normal form, taking advantage of the hierarchical structure of the coordinates associated to the debris, Moon and Sun. We first average the Hamiltonian over the fast (mean anomaly of the debris and sidereal time) and semi-fast (mean anomalies of Moon and Sun) angles.
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