Design of energy-efficient satellite transfer trajectories to asteroids using FTLE fields in the HR3BP

Asteroid flybys near Earth pose significant risks of potential impacts on Earth while simultaneously offering valuable opportunities for exploration missions. This study investigates the dynamics of a satellite transferring from Earth to an asteroid during a flyby, modeled by the Hyperbolic Restricted Three-Body Problem (HR3BP). Previous research has mainly focused on the dynamical behaviors of boundary manifolds in the HR3BP. However, boundary manifolds only exist in theoretical and radical situations and cannot be applied to the satellite trajectory design. To address this limitation, this work proposes a novel approach for satellite transfer trajectories to an asteroid by developing the applications of Finite-Time Lyapunov Exponent (FTLE) fields. By applying the method of FTLE fields, one of the libration points, the (Formula presented) point, is proven to hold the property of an energy-efficient transfer window in the HR3BP. Then, transfer trajectories to an asteroid are generated and patched with multiple trajectories to achieve lower energy cost transfer from Earth to the asteroid than before. Numerical simulations indicate that the proposed approach reduces the energy cost of transfer trajectories by 23(Formula presented) compared to the conventional Hohmann transfer approach. Additionally, to expedite the generation of FTLE fields, this study integrates the differential algebra (DA) method to reduce the generation time for FTLE fields to approximately 11(Formula presented) of the time required without the DA.