Space Occupancy In Low-Earth Orbit

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. This paper introduces 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, frozen orbit initial conditions are provided in osculating element space and a frozen-orbit polar equation is obtained to describe the space occupancy region in closed analytical form. Next, the problem of minimizing space occupancy is analyzed in a realistic model including tesseral harmonics, third-body perturbations, solar radiation pressure, and drag. The corresponding initial conditions, leading to 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.