Elliptical Lunar Frozen Orbit Constellations: Torus-Based Design and Analysis

Abstract

Elliptical Lunar Frozen Orbits (ELFOs) are attractive candidates for lunar satellite constellations supporting lunar south pole exploration. Building on prior frequency-based orbit analysis methods, this investigation develops a torus-based, frequency-domain framework for constellation-level ELFO design and analysis. Within a doubly-averaged dynamical model, each ELFO is characterized by three frequency-angle pairs; a systematic comparison across progressively higher-fidelity models identifies the additional frequency components introduced at each level. The angular parametrization admits multiple symmetries that substantially reduce the design space, enabling a rapid, epoch-free global survey of constellation configurations. A higher-fidelity refinement and analysis layer then combines a (1) Frequency-Domain Differential Corrector (FDDC) that targets desired frequency properties and suppresses undesired long-period oscillations, (2) Fourier surrogate re-optimization for inter-satellite phasing without propagation in the loop, and (3) spectral attribution that separates design-refinable coverage losses from those inherent to the dynamics. Together, these elements supply a fidelity-bridging and diagnostic framework for ELFO constellation design and analysis.