Assessing and minimizing collisions in satellite mega-constellations

We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first introduce a novel algorithm for conjunction prediction that relies on large-scale numerical simulations and uses a sequence of filters to greatly reduce its computational expense. We then use this brute-force algorithm to establish baselines of endogenous (intra-constellation), or self-induced, conjunction events for the FCC-reported designs of the OneWeb LEO and SpaceX Starlink mega-constellations. We demonstrate how these deterministic results can be used to validate more computationally efficient, stochastic techniques for close-encounter prediction by adopting a new probabilistic approach from Solar-System dynamics as a simple test case. Finally, we show how our methodology can be applied during the design phase of large constellations by investigating Minimum Space Occupancy (MiSO) orbits, a generalization of classical frozen orbits that holistically account for the perturbed-Keplerian dynamics of the Earth-satellite-Moon-Sun system. The results indicate that the adoption of MiSO orbital configurations of the proposed mega-constellations can significantly reduce the risk of endogenous collisions with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.