Low energy missions to the moon and lagrangian points

Abstract

Linear astrodynamics theory is used today for the design of transfer trajectories to the Moon or planets. This theory is based on the previous calculation of the ideal path (Hohmann or patched conics with Lambert problem solver) and the assumption of small disturbances. An easy numerical refinement (Newton methods, single or parallel shooting) is enough to precisely compute the transfer trajectory. This method has been used with great success fkom the beginning of interplanetary missions. Since 1987, with the first publication of Dr. Belbruno (1,2) on lunar transfers trajectories, a new class of transfer trajectories has emerged. This new theory is founded on the use of very large disturbances (non-linear astrodynamics theory). The dynamics of three and four body motions present unexpected effects for some very specific initial conditions. The typical case of this trajectory is the motion of a spacecrafi in Earth - Sun - Moon system close to the boundaries of the spheres of influence, which deviates fiom the two - body and also three - body problem behaviour. This fact has been observed by Belbruno and was already tested in a space mission, namely the Japanese Hiten spacecraft in 1991. Hiten was in a looping Earth orbit and it had too small amount of propellant to reach the Moon using conventional techniques. It entered into an orbit around the Moon after passing through the boundary region in the Earth - Sun system. The lunar transfer of Hiten was the spectacular validation of W.S.B. (weak stability boundary) trajectories. In recent years the WSB transfer trajectories have gained interest due to significantly reduced propulsion requirements. Such transfers are of particular interest for lunar missions or orbits near the lagrangian equilibrium points in the Earth - Moon or Earth - Moon - Sun systems. In this paper a mission through all five lagrangian points of the Earth - Moon system is presented. A new WSB algorithm, with only forward integration, is implemented for the first part of the mission. This type of trajectories allows the satellite capture, by the Moon, passing close to the first lagrangian point of Sun-Earth system and the second lagrangian point of the Earth-Moon system. After a few revolutions around the Moon, the satellite escapes fiom the lunar gravitational field. During the orbits around the Moon, with only a little maneuver, it is possible to design a new trajectory through all others lagrangian points of the Earth - Moon system. On this subject it is interesting to know if there are bodies or particles around the equilateral lagrangian point, as in the Sun - Jupiter system.