Energy analysis of Sun-Earth stable manifolds with a lunar flyby and with application to capture asteroids

Abstract

The strategy of capturing near-Earth asteroids to Sun-Earth L1/L2 Lyapunov orbit using a lunar flyby is investigated in this paper. Families of Lyapunov orbits are calculated in the Sun-Earth circular restricted three-body problem (CR3BP), and Lyapunov orbits with small amplitudes serve as the final parking orbits for the captured asteroids. Then the Sun-Earth-Moon bicircular model (BCM) is used to describe the dynamical behavior of the captured asteroid flying close to the Moon. With the assumption that the lunar flyby is simplified as an orbit in the Moon-centered two-body problem, analytical expressions are derived to describe the energy changes of the stable manifolds of the Lyapunov orbits with a lunar flyby. According to the analytical results of the energy changes, optimizations of capturing asteroids to Sun-Earth L1/L2 Lyapunov orbits using a lunar flyby are then carried out. Numerical results indicate that the asteroid capture method using a lunar flyby can potentially save energy compared to the direct asteroid capture strategy without a lunar flyby. Moreover, the asteroid capture with a lunar flyby also has the potential to reduce the total flight time compared to the direct capture strategy without a lunar flyby.