Route theory for optimal design of satellite constellations to minimize revisit time in low earth orbits

Design of satellite constellations is associated with continuous or periodical coverage of an Earth region of interest depending on the concrete task of the space mission. Satellite constellations for continuous and periodical coverage are principally differed by orbit parameters as well as by methods of constellation design. In this study route theory for design of constellations for circular low Earth orbits providing periodical coverage with minimum revisit time criteria is described. The route theory includes: 1) consideration of so called route orbital pattern as mathematical abstraction of arbitrary constellation; 2) analytical solution for calculation problem of distribution of revisit time values on Earth surface for one satellite and multi-satellite route pattern; 3) formulating several regularities for revisit time as a function of satellites positions in constellation; 4) development of method for optimal design of constellation under given requirements. It is made clear that using of route orbital patterns is practically not connected with restriction for type of constellation. It is also shown that optimal constellations calculated using the route theory are in general not worse and in many cases much better (in respect of minimum revisit time criteria) comparing with the analogs found using other well-known methods for periodical coverage. One of the results of the route theory implementation is the fact that using of the symmetric constellations (widely used for continuous coverage) is not perspective way for founding optimal constellations for periodical coverage.