Using the flux of debris to assess the criticality of the environment in low earth orbit

In this paper we introduce a new index for evaluating the propensity of a volume of space in low Earth orbit (LEO) to catastrophic collisions, that is to accidental collisions leading to the complete destruction of intact objects. The proposed index is therefore not intended to assess the criticality of individual objects or missions, but rather to estimate the global impact of space activities on a given region of space. Moreover, the new index was conceived to be objective, as simple as possible, built from easily accessible data, as well as smoothly reproducible by third parties. Named "volumetric collision rate index", it was developed starting from the analytical equations that express the collision rate as a function of the fluxes of intact objects and cataloged debris pieces. The application of reasonable simplifying assumptions and approximations finally allowed to define a dimensionless index that explicitly depends only on the spatial densities of intact objects and cataloged debris pieces. It was therefore applied to the LEO environment, analyzing its evolution from mid-2008 to mid-2020, a crucial period characterized by an impressive change of space activity patterns, with the launch of lots of small satellites and mega-constellations. We also discuss how the index can be further improved, taking into account the maneuverable satellites that do not contribute to the collision rate and the increasing number of cubesats, which in many respects would be more similar to debris, finally presenting a preliminary analysis in this direction.