Analytic solutions for earth discontinuous coverage and methods for analysis and synthesis of satellite orbits and constellations

The analytical model for Earth coverage by the satellites' swath conforming to essential of discontinuous coverage, in contrast to continuous coverage, is presented. The analytic relations are consecutively derived for calculation of single- and multi-satellite Earth surface latitude coverage as well as for generating full set of typical satellite visibility zone time streams realized on the latitude points for given arbitrary satellite constellation. The analytic relations mentioned are used for developing the method for analysis of discontinuous coverage of fixed arbitrary Earth region for given satellite constellation using both deterministic and stochastic approaches. The method provides analysis of the revisit time for given satellite constellation, as a result of high speed (fractions of a seconds or seconds) computer calculations with high accuracy and in wide range of possible variations of this parameter. The method for synthesis of satellite orbits and constellations, optimized by given criterion (minimum of number of satellites in the constellation, or minimum revisit time, or minimum of the required width of the satellite swath) for fixed parameters of on-board satellite equipment and constraints for unused criterion parameters of a list of mentioned above is presented. The numerical results demonstrate the possibilities of the methods developed for analyzing the given satellite constellation revisit time values distributed on the fixed Earth coverage area, and for synthesizing the satellite constellations in comparison with the traditional approaches based on constellation design in a priori fixed classes used for continuous coverage. Particularly, it is shown that the suggested method for synthesis of Secure Route Constellations, using determenistic and stochastic basis, leads to the optimized satellite constellations which provide consistently high performance and are at least on the same level, or better, in comparison with the best Walker constellations for discontinuous coverage.