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

In this paper we introduce a new index for evaluating the likelihood of accidental collisions leading to the complete destruction of intact objects in a volume of space in low Earth orbit (LEO). 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 has been designed 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 has been developed starting from analytical equations expressing the collision rate as a function of the fluxes of intact objects and cataloged debris pieces. The application of reasonable simplifying assumptions and approximations has finally made it possible to define a dimensionless index that explicitly depends only on the spatial densities of intact objects and cataloged debris pieces. It has therefore been 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, which do not contribute to the collision rate, and the increasing number of cubesats, which in many respects are more similar to debris, finally presenting a preliminary analysis in this direction.