Transfer from the Earth to a Lissajous orbit around the collinear libration point by Lunar swing-by

Abstract

Collinear libration points of the restricted three body problem (RTBP) play a key role in deep space exploration, due to the fact that they are ideal locations for the spacecraft (such as SOHO) with special purposes. The nominal orbit of the spacecraft is conditionally stable but virtually unstable, and will exponentially diverge from the nominal orbit under small perturbations. If the spacecraft is inserted to the stable manifold associated with the collinear libration points, it will approach the nominal orbit without any more maneuvers, and the total fuel consumption will be reduced. For the nominal orbit of small amplitude, the manifold can not approach the Earth. In this case a direct transfer from the parking orbit, such as low earth orbit (LEO) around the vicinity of the Earth to the manifold will be impossible. Nevertheless, in the real solar system, the Moon bends some of the manifolds to approach the Earth. Based on this consideration, this paper takes the transfer of a spacecraft around L2 of the Sun–Earth system as an example and study the Lunar effect in the transfer of the spacecraft. With the help of the Moon, in the case the transfer could be still not achieved with only one maneuver, but the total fuel consumption is saved by around 100 m/s.