Route satellite constellations for earth discontinuous coverage and optimal solution peculiarities

The way to solve the problem of satellite constellation design was outlined in the 1960s, recognizing the importance of satellite coverage (continuous or periodic) function and allowing interpretation of the operation of different types of space systems. Due to the fact that Earth periodic coverage optimization is extremely complex, for many years, the solutions of this problem have been searched for among a priori fixed constellation types successfully implemented before for continuous coverage, with continuous coverage seeming to be much easier than periodic coverage. In this study, it is shown that the technological advance in satellite constellation design for periodic coverage could be achieved by considering it as a unique and separate problem. The introduction in the route theory for satellite constellation design for Earth periodic coverage that aims at creating methods for optimization of arbitrary constellations, which is an alternative to the traditional approach that considers narrow classes of constellations to be analyzed, is described. The so-called route constellation is presented as a mathematical abstraction for approximation of arbitrary satellite constellation. The theory elements of the optimization procedure in the infinite domain of route constellations are introduced. Previously unknown regularities in Earth periodic coverage and in localization of optimal low-Earth-orbit satellite constellation parameters are presented and illustrated.