Analysis of Capture Trajectories into Periodic Orbits About Libration Points

Abstract

Spacecraft capture trajectories to Lyapunov/Halo periodic orbits of the L1 and L2 points in the restricted Hill three-body problem are analyzed. The specific focus is on transfer to these orbits from interplanetary trajectories. This application is motivated by future proposals to place “deep space ports ” at the Earth andMars L1 or L2 points. We use stable manifolds for capture trajectories to periodic orbits around the libration points. Numerical results show that the stable and unstablemanifolds fromperiodic orbits around the libration points can intersect the surface of anyof the planets of the solar systemby changing the size of periodic orbits.Applying this toEarth–Mars transfers, the cost of capture into a periodic orbit is reduced comparedwith direct capture into a parabolic orbit.Moreover, if a spaceport is built on a periodic orbit in the vicinity of a sun–Mars libration point andpropellant can be supplied there to the spacecraft, the requiredV for entry into a circular orbit aboutMars froman interplanetary trajectory canbe considerably reduced compared with a direct entry into a circular orbit. I.