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Circulating, eccentric periodic orbits at the Moon

Loosely captured orbits with circulating and pulsating eccentricity vectors have a variety of attractive mission design properties, including low insertion costs, near-circular and highly eccentric phases, mid- to high inclinations, long-term stability, and spatially distributed close approaches. Such orbits are the known result of averaging third-body perturbations over the spacecraft and system motions. Unfortunately, the doubly averaged model does not match long-term unaveraged motion well at high altitudes. Singly averaged dynamics are accurate for orbits with much higher semimajor axis values, providing a mechanism to predict and characterize high-altitude motion in the unaveraged model. In this work, singly averaged circulating, eccentric orbits are surveyed in the specific context of the dimensioned Earth–Moon system, where high-altitude orbits are expected to have the most useful applications. A global search is performed over non-impacting system resonances, and families of periodic orbits are used as a framework to map the feasible space. The resulting database of periodic orbits is provided as an online supplement. The singly averaged families are shown to provide a reliable bridge between the analytic results of the doubly averaged system and initial guesses that converge to periodic orbits in the unaveraged model. Non-impacting circulating, eccentric orbits are demonstrated to maintain their structure for multiple years in a high-fidelity force model. These circulating, eccentric, lunar orbits may be useful for human-crewed space stations, dedicated science orbits, extended missions, loitering orbits, or transfers between the Lagrange points and low-lunar orbits.