High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem

摘要

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approximations of the manifolds. Since such approximations are not accurate except very close to the base invari-ant object, this requires large amounts of numerical integration to globalize the manifolds and locate intersections. In this paper, we study hyperbolic resonant periodic orbits in the planar circular restricted 3-body problem, and transfer trajectories between them, by: 1) determining where to search for resonant periodic orbits; 2) developing and implementing a parameterization method for accurate computation of their invariant manifolds as Tay-lor series; and 3) developing a procedure to compute intersections of the computed sta-ble and unstable manifolds. We develop and implement algorithms that accomplish these three goals, and demonstrate their application to the problem of transferring between res-onances in the Jupiter-Europa system.(c) 2021 Elsevier B.V. All rights reserved.