Mean-motion resonances (MMRs) are regions of a celestial system’s phase space where the orbital periods of two smaller bodies (e.g. a spacecraft and a moon) revolving around a common large central mass (e.g. a planet) are rationally commensurate. Each resonant region contains both stable and unstable orbits, the latter of which form a cylindrical normally hyperbolic invariant manifold and have attached stable and unstable manifolds. Heteroclinics between unstable orbits contained in different MMRs, also known as mean-motion resonance overlapping, result in natural trajectories between orbits of different sizes. This in turn is useful for low or zero-propellant space mission design.
While most related prior work on finding such spacecraft pathways uses a planar circular restricted 3-body problem model (PCRTBP) that accounts for the gravity of the planet and a single moon, tours of multi-moon systems require using resonant orbits whose motion may be strongly affected by not just one but by two moons. In this case study, we investigate Jupiter-Ganymede unstable 4:3 mean motion resonant orbits in a concentric circular restricted 4-body Jupiter-Europa-Ganymede model. We show that despite their high order, secondary resonances between the 4:3 orbit periods and that of Europa have a large effect on the dynamics inside the 4:3 resonance's normally hyperbolic invariant manifold. Computing separatrices for the secondary resonances definitively confirms their overlap over a wide range of the orbit family, which causes a complete structural change of the higher-energy unstable 4:3 orbits that are most useful for faster orbit transfers.