Explicit Mathematical Formulation and Coverage Consistency of Satellite Constellation Designs for Repeating Ground Track Orbits

To solve the coverage consistency and launch cost problems of continuous and periodic coverage, this study proposes a regular and symmetric constellation method for repeating ground track orbits and its closed-form solution for constellation design. The equations of motion developed in this study were implemented via a geometric analysis of Ptolemy's deferent and epicycle systems, and the solution was composed of design parameters. Therefore, unlike the existing constellation method, design and analysis can be realized simultaneously and efficiently. The performance of the proposed constellation method was compared with that of a typical Walker constellation in terms of the figure of merit sensitivity and coverage consistency, and its superior performance was verified. In addition, a comparison with Flower constellations using the same repeating ground track orbit was evaluated via launch cost problems and theoretical comparisons with respect to constellation design.