The role of service areas in the optimization of FSS orbital and frequency assignments

An implicit relationship is derived which relates the topocentric separation of two satellites required for a given level of single-entry protection to the separation and orientation of their service areas. The results are presented explicitly for circular beams and topocentric angles. A computational approach is given for elliptical beams and for use with longitude and latitude variables. It is found that the geocentric separation depends primarily on the service area separation, secondarily on a parameter which characterizes the electrical design, and only slightly on the mean orbital position of the satellites. Both linear programming and mixed integer programming algorithms are implemented. Possible objective function choices are discussed, and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed 'ideal' location set. A test problem involving six service areas is examined with results that are encouraging with respect to applying the linear programming procedure to larger scenarios.