Non-self-intersecting trajectories and their applications to satellite constellation design and orbital capacity

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 two theorems to determine when two spacecrafts share the same relative trajectory, and to identify the only conditions that allow the existence of non-self-intersecting relative trajectories. Then, these results are applied first to the estimation of the limits of the orbital capacity at a given altitude, and second, to the design of satellite constellations and slotting architectures that present no conjunctions between any element compliant with these space structures.