Invariant manifolds and Lagrangian coherent structures in the planar circular restricted three-body problem

For the sake of spacecraft mission design, it is indispensable to develop a low energy transfer of spacecrafts using very little fuel for interplanetary transport network. The Planar Circular Restricted Three-Body Problem (PCR3BP) has been a fundamental tool for the analysis of such a space mission design. In this paper, we explore stable and unstable invariant manifolds associated with the collinear Lagrange points L₁, L₂ of the PCR3BP, in which geometrical structures of the invariant manifolds are clarified on a Poincaré section. Further, we compute the Finite Time Lyapunov Exponent fields (FTLE fields) to obtain Lagrangian Coherent Structures (LCS) as the ridges of the FTLE fields. In particular, we compare the LCS with the invariant manifolds on the Poincare section from the viewpoint of the numerical integration times.