A study of Earth-Moon Trajectories based on Analytical Expressions for the Velocities Increments

Abstract

A study of Earth-Moon bi-impulsive trajectories is presented in this paper. The dynamic model utilized to describe the motion of the space vehicle is the classic planar circular restricted three-body problem (PCR3BP). The velocities increments are obtained through analytical expressions, which are derived from the development of the complete Jacobi Integral expression. In order to determine the trajectories, a two-point boundary value problem (TPBVP) with prescribed Jacobi Integral is formulated. In this way, internal and external trajectories are determined with several times of flight. The results show that this method facilitates the determination of Earth-Moon trajectories with large time of flight; it offers a better intuition of the problem since the Jacobi Integral is specified; it allows several kind of studies since all Earth-Moon trajectories can be obtained; and, it provides a good estimate for optimization algorithms which can be, eventually, applied in order to minimize the total fuel consumption.