Mission design for close-range lunar mapping by quasi-frozen orbits

The presence of extremely low-altitude, lunar quasi-frozen orbits (QFOs) has given rise to interesting mission opportunities. These QFOs are ideal for close-range, high-resolution mapping of the lunar south pole, and their inherent stability translates into minimal station-keeping efforts. Despite the aforementioned desirable characteristics, designing transfer trajectories to these QFOs poses significant difficulties, specifically, for spacecraft equipped with low-thrust electric engines. A solution strategy is proposed, within the indirect formalism of optimal control, for designing minimum-time trajectories from a geosynchronous orbit to a candidate low-altitude, lunar QFO. The classical restricted three-body dynamical model of the Earth-Moon system is used to achieve more realistic results. The difficulties in using indirect optimization methods are overcome through a systematic methodology, which consists of patching three-dimensional minimum-time trajectory segments together such that the spacecraft terminates in a prescribed highly stable quasi-frozen orbit. Application of a pseudo-arc-length continuation method is demonstrated for a number of lunar capture phases consisting of up to 38 revolutions around the Moon.