Near Ballistic Halo-to-Halo Transfers between Planetary Moons

Intermoon transfers are important components of planetary tour missions. However, these transfers are challenging to design due in part to the chaotic environment created by the multi-body dynamics. The specific objective of this work is to develop a systematic methodology to find fuel optimal, near ballistic Halo-to-Halo trajectories between planetary moons, and we achieve this goal by combining dynamical systems theory with a variety of nonlinear programming techniques. The spacecraft is constrained to start at a Halo orbit of a moon and end at another Halo orbit of a second moon. Our approach overcomes the obstacles of the chaotic dynamics by combining multiple “resonant-hopping” gravity assists with manifolds that control the low-energy transport near the Halo orbits of the moons. To help construct good initial guesses, contours of semimajor axes that can be reached by falling off a Halo orbit are presented. An empirical relationship is then derived to find quickly the boundary conditions on the Halo orbits that lead to ballistic capture and escape trajectories, and connect to desired resonances. The overall optimization procedure is broken into four parts of increasing fidelity: creation of the initial guess from unstable resonant orbits and manifolds, decomposition and optimization of the trajectory into two independent ideal three-body portions, end-to-end refinement in a patched three-body model, and transition to an ephemeris model using a continuation method. Each step is based on a robust multiple shooting approach to reduce the sensitivities associated with the close approach trajectories. Numerical results of an intermoon transfer in the Jovian system are presented. In an ephemeris model, using only 55 m/s and 205 days, a spacecraft can transfer between a Halo orbit of Ganymede and a Halo orbit of Europa.