Non-Self-Intersecting Trajectories and Their Applications to Satellite Constellation Design and Orbital Capacity

Abstract

This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and space traffic management. To that end, this paper introduces three theorems to determine when two spacecraft share the same relative trajectory, to identify the only conditions that allow the existence of non-self-intersecting relative trajectories, and to compute the minimum distances inside these relative trajectories. These results are then applied first to obtain an estimation of the limits of the orbital capacity at a given altitude and, second, in the design of satellite constellations and slotting architectures that present no conjunctions between any element compliant with these space structures.