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This work focuses on the generation of non-self-intersecting relativetrajectories, and their applications to satellite constellation design,slotting architectures, and Space Traffic Management. To that end, this paperintroduces two theorems to determine when two spacecrafts share the samerelative trajectory, and to identify the only conditions that allow theexistence of non-self-intersecting relative trajectories. Then, these resultsare applied first to the estimation of the limits of the orbital capacity at agiven altitude, and second, to the design of satellite constellations andslotting architectures that present no conjunctions between any elementcompliant with these space structures.

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