Nonimpact Lunar Transfer Trajectories Using the Pseudostate Technique

Abstract

An algorithm is developed for the design of one-way direct-transfer trajectories to the moon that achieve a specified approach trajectory periapsis altitude and inclination, at a specified time of arrival. A variant of the pseudostate technique is employed to derive the analytical transfer trajectory design. A novel and simple matching strategy that synchronizes the geocentric two-body transfer trajectory with the selenocentric approach trajectory is devised. This matching strategy avoids computation of the complicated and conventional state transition matrices. Two methodologies are presented for the computation of the nonimpact approach trajectory characteristics from the excess velocity vector. These methods and the matching strategy are incorporated in the algorithm to ensure nonimpact. The use of this nonimpact algorithm for quick mission design analysis of orbiter missions is demonstrated. Further, in order to achieve the approach trajectory characteristics accurately, a biased targeting technique is proposed. This semi-analytical technique uses the nonimpact algorithm and numerical integration and helps obtain fast and near-exact solutions for the three-body problem of generating lunar transfer trajectory design.