Long-Term Fragmentation Reconstruction Techniques Leveraging the Dynamics of Debris Cloud Expansion

The increasing number of space debris is a prominent issue for the sustainability of space use. Indeed, among the several concerns generated by debris, in-orbit fragmentation events stand out as they are becoming more frequent, leading to threats for the safety of space operations and potentially causing a chain reaction of breakup events. In this context, it is fundamental to investigate these events a posteriori, to gain insights on the causes of the fragmentation as well as to estimate the epoch of the event and the objects involved in it. Several techniques for fragmentation reconstruction were devised in the past. Among them, the approach developed at Politecnico di Milano aims at reconstructing fragmentation events from available Two-Line-Elements data exploiting a series of filtering techniques. In this work, the long-term reconstruction of breakups, i.e. after months up to years from the event, is enhanced by leveraging a novel cloud expansion metric based on a Gaussian Mixture Model (GMM) approach. The metric performs a reduction of the multidimensional evolving debris cloud generated from a breakup simulated with the NASA Standard Breakup model to a set of time-varying mono-dimensional GMMs, representing the marginalised distribution. To achieve this, the discretised probability density function is computed through samples binning and the GMM is acquired with a least square fitting technique. The method can be applied to fragmentations in any orbital regime, moreover it allows to identify the typical ranges of variation of the orbital parameters of a debris cloud in each orbital region over a given time interval. This is highly beneficial both to identify new pruning and clustering criteria, to filter out objects unrelated to the breakup exploiting the orbital evolution of the Keplerian elements, and to set realistic thresholds for pre-existing filters to prune from a given set of objects those involved in a fragmentation event. Indeed, an inclination pruning filter is adopted for the long-term reconstruction of breakup events in low Earth orbit (LEO) to identify clusters of objects exploiting the reduced variability of inclination (both after the breakup and during the evolution over time) for obj ects orbiting in the LEO region. Preliminary studies showed that accuracy of this filter can be greatly improved when using an appropriate inclination range for the selection of objects with respect to a cluster to analyse. This work was developed within the ESA-funded project "On-Orbit Break-up Forensics".