Stability and control problems in Earth-Moon Lagrangian point L2

The use of periodic trajectories around L2 Lagrangian point for lunar operations has been proposed by many authors. A single telecommunication relay, place around L2, could guarantee the permanent connection between the Earth and a lunar base on the far side of the moon, with a 440,000 km link from the Earth and a 64,000 km link from the lunar surface. However, the control of a satellite in L2 Lagrangian point is quite difficult, due to the intrinsic dynamic unstability. To do it, it is necessary to observe continuously the orbital state of the satellite, and control the dynamics of the vehicle with a suitable on-board propulsion system. The analysis of these problems was performed by Farquhar, starting from 1970, and others (Sim, et al 1987). The same concepts were developed, by the author, in a study for European Space Agency (ESA) on a space communication network, for lunar and deep space missions. The present communication describes the dynamics in L2 and in the periodic orbits around L2 (halo orbits). It discusses the possibility of the orbit control, with a particular reference to the control laws based on the observation of the position and velocity of the spacecraft in the Earth-Moon direction. Some numerical simulations are presented, performed with a numerical propagator, to verify the dynamics of the satellite in presence of the perturbations, not accounted for in a simplified analytical approach. The possibility of controlling the satellite with a station-keeping procedure, similar to that used for geostationary satellites, is verified.