Abstract: Lagrangian coherent structure (LCS) is defined by means of ridges of finite-time Lyapunov exponent (FTLE) fields in this paper. Moreover, a relation between LCS and time-dependent invariant manifold is obtained. Taking LCS as a tool, the property of the invariant manifold in elliptic restricted 3-body problem (ER3BP) is achieved numerically: time-dependent invariant manifold is an invariant set of orbits and acts as the separatrix of transit-orbit set and non-transit orbit set.

Key words: elliptic restricted 3body problem, timedependent invariant manifolds, Lagrangian coherent structures, Poincare section