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When the planar circular restricted 3-body problem (PCRTBP) is periodicallyperturbed, as occurs in many useful astrodynamics models, most unstableperiodic orbits persist as whiskered tori. Intersections between stable andunstable manifolds of such tori provide natural heteroclinic pathways enablingspacecraft to greatly modify their orbits without using propellant. However,the 2D Poincar\'e sections used in PCRTBP studies no longer work to find theseintersections. Thus, in this study, we develop new fast methods to search forand compute such heteroclinics. First, the dynamics are used to restrict theintersection search to only certain manifold subsets, greatly reducing therequired computational effort. Next, we present a massively parallel procedurefor carrying out this search by representing the manifolds as discrete meshesand adapting methods from computer graphics collision detection algorithms.Implementing the method in Julia and OpenCL, we obtain a 5-7x speedup byleveraging GPUs versus CPU-only execution. Finally, we show how to use manifoldparameterizations to refine the approximate intersections found in the meshsearch to very high accuracy, as well as to numerically continue theconnections through families of tori; the families' Whitney differentiabilityenables interpolation of needed parameterizations. The ability to very rapidlyfind a heteroclinic intersection between tori of fixed frequencies thus allowsthe systematic exploration of intersections for tori of nearby frequencies aswell, yielding a variety of potential zero-fuel spacecraft trajectories. Wedemonstrate the tools on the Jupiter-Europa planar elliptic RTBP.

Rapid GPU-Assisted Search and Parameterization-Based Refinement and  Continuation of Connections between Tori in Periodically Perturbed Planar  Circular Restricted 3-Body Problems