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.     

4D Lattice Flower Constellations

4D Lattice Flower Constellations is a new constellation design framework, based on the previous 2D and 3D Lattice theories of Flower Constellations, that focus on the generation of constellations whose satellites can have different semi-major axis and still present a constellation structure that is maintained during the dynamic of the system. This situation can arise when dealing with satellites with very different instruments, or when it is of interest to coordinate two different constellations. In that sense, 4D Lattice Flower Constellations constitutes the most general representation of the Flower Constellation formulation. In addition, the effects of the $J_2$ perturbation are taken into account in order to generate distributions that maintain their initial design configuration under this perturbation for longer periods of time with a low fuel budget. Finally, examples of application are presented, showing the possibilities in satellite constellation design of this new approach.