Locally Geostationary Orbits: Optimal Geometry of Elliptic Orbit for Earth Coverage

The problem of satellite constellation design for Earth coverage using elliptic orbit is considered. Whereas various researchers in this field have mainly considered optimization of the orbital structures of constellations, this paper deals with a previously insufficiently studied problem of optimizing the orbital geometry by coverage characteristics, that is, selecting the form of an elliptic orbit (semimajor axis and eccentricity) to provide the best performance in terms of coverage. From this point of view the class of the so-called locally geostationary orbits is suggested and substantiated. It is shown that optimization in the class of locally geostationary orbits, while the problem of Earth coverage on elliptic orbits is considered, leads to maximum duration of the satellite visibility zones. It is shown that this class of orbits includes the geostationary orbit, the only circular orbit in the class, and known Molniya-type elliptic orbit, as well as an infinite domain of elliptic orbits corresponding to the maximum visibility zone duration among all possible elliptic orbits. The general mathematical relations and optimal solution peculiarities for locally geostationary orbits design are presented.