Geometric approach for analytical approximations of satellite coverage statistics

The analysis and optimization of satellite coverage statistics have been ongoing for several decades. Designing an orbit or a constellation of orbits to meet specific coverage statistics (such as the mean pass duration, mean passes per day, and maximum gap time) can help maximize coverage time and meet mission goals for ground-based assets. In the past, most coverage optimization research has used numerical orbit propagators to generate the statistics. Although they result in very accurate numerical simulations, they are computationally expensive. Were analytical approximations for these orbit statistics available, the time required for optimization could be greatly reduced. This paper provides a geometrical derivation for approximating the maximum gap time and mean passes per day for nonrepeating, circular orbits. Furthermore, it links this derivation with the station view ratio to derive approximations for mean pass duration. The error in these approximations is analyzed with numerical orbit propagation simulations. The analytical solutions are then used to explore the relationship between the orbit parameters and the resulting coverage statistics for selected cases. The derivations for the coverage statistics presented in this paper have been, and continue to be, used for constellation design and loading analyses for Mars missions.