  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.
