Lunar flyby transfers to L₅ axial orbit

Sun–Earth/Moon L₄ and L₅ axial orbits provide ideal locations to monitor and search for near Earth asteroids. In this paper, an unstable L₅ axial orbit is selected as the target orbit, and then we first investigate transfers from the Earth to the target axial orbit in the ephemeris model. Based on the dynamical structure, we employ stable manifolds associated with the target axial orbit and lunar flyby technique in the preliminary design process. Then, we implement the multiple-shooting differential correction to refine the lunar flyby transfer orbit in the ephemeris model based on the preliminary design. Through a refinement strategy we proposed, a four-impulse lunar flyby transfer orbit from the initial low Earth orbit to the target axial orbit is obtained in the ephemeris model. Finally, we apply the optimal control method to design a low-thrust transfer for a small satellite to the target axial orbit based on the four-impulse transfer orbit. We obtain a low-thrust end-to-end transfer orbit with three thrust arcs via the optimization piece by piece. Numerical results indicate that the lunar flyby plays an important role in the low-thrust transfer orbit, and helps us efficiently decrease the fuel consumption.