Titan Trajectory Design Using Invariant Manifolds and Resonant Gravity Assists

Following the spectacular results of the Cassini mission, NASA and ESA plan to return to Titan. For missions such as this to the giant planets and their moons, the primary challenge for trajectory designers is to minimize ΔV requirements while simultaneously ensuring a reasonable time of flight. Employing a combination of invariant manifolds in the planar circular restricted three-body problem and multiple resonant gravity assists allows for the design of trajectories with a very low ΔV. However, these trajectories typically exhibit long flight times. In this study, desired resonances are targeted that, at any single node, minimize the time of flight. The resulting time of flight for a trajectory created using this methodology is compared to that of a trajectory utilizing the maximum single point decrease in semi-major axis. Then, using this framework, the effect of the Jacobi constant on the trajectory's total ΔV and time of flight is explored. The total trajectory ΔV is shown to vary over the range of Jacobi constants tested due to the interaction between the ΔV required for capture at Titan and the resonances encompassed by the targeted invariant manifold exit region. Over the range of Jacobi constants tested, the total ΔV varies by 28 m/s while the time of flight varies by 3.2 months between the minimum and maximum cases. The lowest Jacobi constant tested results in a 23-month trajectory and a total ΔV of 626 m/s, including a controlled insertion into a 1000 km circular orbit about Titan.