Solar sail transfer trajectory from L1 point to sub-L1 point

Solar sail working at a sub-L1 point can increase the warning time for geomagnetic storms. The transfer trajectory consists of launch of the spacecraft from Earth to a halo orbit and transfer phase from the halo orbit to the vicinity of the targeted sub-L1 point. This paper proposes a new transfer profile from the L1 periodic orbits to the sub-L1 point or periodic orbits around it. Both the invariant manifolds of the periodic orbits around L1 point and sub-L1 points are used to design the transfer trajectory. The spacecraft evolves along the unstable manifold of the L1 periodic orbit during pre-sail-deployment phase and flies to the target sub-L1 periodic orbit along its stable manifold after sail deployment. Previous to the transfer trajectory design, the existence of this kind of transfer trajectory is checked from the point of view of energy. Then, the transfer trajectory design problem is parameterized and the design parameters are optimized to achieve the transfer trajectory, both 2-dimensional and 3-dimensional cases. The influences of different design parameters on the transfer trajectory are investigated for 2-dimensional cases. Several 3-dimensional transfer trajectories are used to illustrate the differences from 2-dimensional cases.