Optimal Two- and Three-Dimensional Earth–Moon Orbit Transfers

The determination of minimum-propellant-consumption trajectories represents a crucial issue for the purpose of planning robotic and human missions to the Moon in the near future. This work addresses the problem of identifying minimum-fuel orbit transfers from a specified low Earth orbit (LEO) to a low Moon orbit (LMO), under the assumption of employing high-thrust propulsion. The problem at hand is solved in the dynamical framework of the circular restricted three-body problem. First, the optimal two-dimensional LEO-to-LMO transfer is determined. Second, three-dimensional transfers are considered, in a dynamical model that includes the Cassini’s laws of lunar motion. The propellant consumption associated with three-dimensional transfers turns out to be relatively insensitive to the final orbit inclination and exceeds only marginally the value of the globally optimal two-dimensional orbit transfer.