Stable Orbiting Around Small Moons Using J₂-Perturbed Elliptic Restricted Problem

Confirmed small-body missions Martian Moons eXploration (MMX) and Hera are set to explore Martian moons and the binary asteroid Didymos’s moon Dimorphos, respectively. Orbital dynamics around these small moons differ substantially from those around previously visited targets. Simplified models, such as the circular-restricted three-body problem, cannot yield accurate predictions for orbits and their stability in real-world operations. To be specific, the orbit of the small moon and its vicinity are significantly perturbed by the oblateness of the planet and their relative positions. Realistic control constraints and the unstable 3:1 resonance of retrograde orbits further complicate orbit maintenance around a small moon. Therefore, minimizing the dynamical perturbation on baseline orbits resulting from model mismatches is crucial. This paper introduces the J2-ER3BP+GH model dedicated to describing the orbital dynamics around the small moon. It incorporates the J₂ perturbation of the planet on the elliptic-restricted three-body problem and can accommodate a nonspherical gravity field of the moon. Bounded orbits can still be identified without much effort in this sophisticated model. Baseline orbits around Phobos and Dimorphos from the J2-ER3BP +GH model become much easier to maintain, as verified in the high-fidelity dynamic and control environments.