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

TL;DR

This paper introduces new theorems for generating non-self-intersecting satellite trajectories, enabling improved constellation design, orbital capacity estimation, and space traffic management by ensuring collision-free satellite configurations.

Contribution

It presents two theorems that characterize when two spacecraft share the same trajectory and conditions for non-self-intersecting trajectories, applied to satellite constellation design and orbital capacity.

Findings

Derived limits of orbital capacity at specific altitudes.

Developed methods for collision-free satellite constellation design.

Provided theoretical foundations for space traffic management.

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 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.