Space Occupancy in Low-Earth Orbit
Claudio Bombardelli, Gabriele Falco, Davide Amato, Aaron J. Rosengren

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…
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