Circulating Eccentric Orbits Around Planetary Moons

Abstract

Eccentric orbits in the third-body perturbed problem are evaluated in the context of planetary-moon missions. All possible motion in the doubly averaged problem is reviewed and concisely summarized via contour plots. Special attention is paid to the well-known class of orbits that cycle between low and high eccentricity while circulating in argument of periapse. Applying the doubly averaged assumptions, the maximum sustainable inclinations and eccentricities for long-term circulating ballistic orbits are found and discussed for the dimensioned systems at Ganymede, Europa, Titan, Enceladus, and several other planetary moons. The full-cycle periods of the circulations and librations are reduced to quadratures that are functions only of the two integrals of motion and the moon and orbiter mean motions. In the specific case of Ganymede, higher-fidelity models are considered to analyze the validity of the doubly averaged assumptions. Families of stable long-repeat-cycle periodic orbits are demonstrated in the unaveraged Hill-plus-nonspherical-potential model. Several point designs are considered in a full ephemeris model, and promising results include long-term ephemeris-stable orbits that enjoy maximum inclinations above 60 deg. These circulating ball-of-yarn orbits cycle between high and low eccentricities while distributing close approaches throughout the moon's surface.