Space Occupancy in Low-Earth Orbit

TL;DR

This paper introduces the concept of space occupancy for satellites in low-Earth orbit, providing analytical tools and initial conditions for minimizing space occupation to optimize mega-constellation design.

Contribution

It defines space occupancy, links it to frozen orbits, derives analytical expressions, and proposes MiSO orbits to reduce satellite space usage in LEO.

Findings

Analytical expression for space occupancy region in frozen orbits

Initial conditions for minimum space occupancy (MiSO) orbits

Potential for optimizing mega-constellation design

Abstract

With the upcoming launch of large constellations of satellites in the low-Earth orbit (LEO) region it will become important to organize the physical space occupied by the different operating satellites in order to minimize critical conjunctions and avoid collisions. Here, we introduce the definition of space occupancy as the domain occupied by an individual satellite as it moves along its nominal orbit under the effects of environmental perturbations throughout a given interval of time. After showing that space occupancy for the zonal problem is intimately linked to the concept of frozen orbits and proper eccentricity, we provide frozen-orbit initial conditions in osculating element space and obtain the frozen-orbit polar equation to describe the space occupancy region in closed analytical form. We then analyze the problem of minimizing space occupancy in a realistic model including tesseral harmonics, third-body perturbations, solar radiation pressure, and drag. The corresponding initial conditions, leading to what we call minimum space occupancy (MiSO) orbits, are obtained numerically for a set of representative configurations in LEO. The implications for the use of MiSO orbits to optimize the design of mega-constellations are discussed.