Mercator Projection Superposition: A Computationally Efficient Alternative to Grid-Based Coverage Analysis for LEO Mega-Constellations

Grid point approaches for LEO mega-constellation coverage analysis become computationally prohibitive for constellations exceeding 103 satellites due to exponential complexity growth. This paper presents the Mercator projection superposition (MPS) approach, which transforms coverage evaluation into a two-dimensional image-processing paradigm by projecting the satellite coverage onto Mercator maps. MPS decouples computational complexity from satellite count, enabling analysis of constellations exceeding 104 satellites. Validation against grid point approaches shows ≤1.2% error with 60× speed improvement for 103-scale constellations without parallel computation. The method establishes that instantaneous coverage rates reliably approximate periodic rates within 0.04% precision for early-stage constellation design. Analysis of Starlink-based configurations identifies optimal principles governing mega-constellation coverage, with particular emphasis on configuration and orbital parameter relationships. These findings enable rapid design iteration and optimization for future mega-constellation development.