Calculating two-impulse Earth-Moon transfers in the circular restricted three-body problem

A numerical differential method is developed for calculating the two-impulse trajectories for Earth-Moon transfers in the circular restricted three-body problem (CR3BP). By analyzing the initial and final states of the spacecraft, the Newton-Raphson method is applied to deducing the differential equations of these transfers and the periapsis map is introduced to guess the initial states. With the initial guess, the differential method yields the accurate initial state within a few iterations and then the two-impulse Earth-Moon transfer will be accomplished. Especially for the spatial CR3BP, a simple design procedure is developed to deal with the problem that arises from more unknown parameters. Thus, this method is applied not only to the planar CR3BP but also to the spatial CR3BP, and their analysis indicates preliminarily that that this method can effectively enable a large set of two-impulse Earth-Moon transfers to be computed numerically. Moreover, the two-impulse Earth-Moon trajectories and the Moon-Earth return trajectories are mirror images of one another with aspect to the x-z plane or the x-axis.