WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 11, 2012
Low Thrust Sub-Optimal Transfer Trajectories to the Moon
Author:
Abstract: In the present research the problem of transferring a spacecraft from the Earth to the Moon with minimum fuel consumption is considered. The Two-Body model is assumed to be a valid mathematical representation for the dynamics during the transfer. The spacecraft starts in a Low Earth Orbit and then goes to a Polar Orbit around the Moon. In previous publications, impulsive and optimal low thrust maneuvers were used to perform this transfer. In the present paper this research is extended to consider two types of sub-optimal maneuvers: the first one using a linear and the second one using a quadratic form for the direction of the thrust. To obtain those low thrust sub-optimal maneuvers, the Euler-Lagrange equations are also used here, as done before in the optimal approach. They give a set of differential equations that can be used to solve numerically the problem. The results obtained here show that the extra fuel expenditure caused by using both sub-optimal approaches for the control are small, so this is an interesting approach if a simple implementation for the hardware is desired. Two types of missions are studied, one with a single spacecraft and another one with a set of two spacecrafts.