Transfer to distant retrograde orbit using finite time Lyapunov exponent field

Distant Retrograde Orbits (DROs) are a group of stable periodic orbits under the restricted three-body problem and have great utilization in the future cislunar exploration. However, traditional methods relying on stable or unstable manifolds for constructing low-energy transfers to DRO are limited due to their inherent stability. Instead of constructing trajectories utilizing invariant methods, an innovative approach is proposed in this paper utilizing Finite Time Lyapunov Exponent (FTLE) field to guide low-energy transfers to DRO. The separatrix characterized by the FTLE field is used to identify different transfer trajectories to DRO and the ones with minimum insertion cost are derived. With the assistance of Poincaré section technique, the trajectories with less fuel consumption are obtained by patching arcs derived from the FTLE field and the manifold of Lyapunov orbit around (Formula presented) point. Through the proposed correction algorithm, practical orbits are successfully attained within engineering constraints in the ephemeris model.