Designing Trajectories in a Planet-Moon Environment Using the Controlled Keplerian Map

The design of fuel-efficient trajectories that visit different moons of a planetary system is best handled by breaking the problem up into multiple three-body problems. This approach, called the patched three-body approach, has received considerable attention in recent years and has proved to lead to substantial fuel savings compared with the traditional patched-conic approach. We consider the problem of designing fuel-efficient multimoon orbiter spacecraft trajectories in the Jupiter―Europa―Ganymede spacecraft system with realistic transfer times. First, fuel- optimal (i.e., near-zero-fuel) trajectories without the use of any control are determined, but turn out to be infeasible due to the very long transfer times involved. We then describe a methodology that exploits the underlying structure of the dynamics of the two three-body problems, that is, the Jupiter―Europa spacecraft and Jupiter―Ganymede spacecraft, using the Hamiltonian structure-preserving Keplerian map approximations derived earlier and small control inputs in the form of instantaneous ΔV to get trajectories with times of flight on the order of months rather than several years. A typical trajectory constructed using the control algorithm can complete the mission in about 10% of the time of flight of an uncontrolled trajectory.