Different from the Apollo flight mode, a safer trans-lunar flight mode for the crews is preferred. The previous-arrived lunar module rendezvous with the crew exploration vehicle on the low lunar destination orbit, and then the crews ride the lunar module for descending the lunar surface destination. The lunar module, which includes the descent and ascent stages, flies from low Earth orbit to the low lunar destination orbit with two tangential impulses. The low lunar destination orbital reachable-set of its practical trans-lunar orbit limits the crew’s lunar surface reachable area. Therefore, the low lunar destination orbital reachable-set of the practical trans-lunar orbit is analyzed in this paper. A retrograde semi-analytic model is proposed for rapidly computing the practical two-impulse trans-lunar orbit firstly, which refers the ephemeris table twice for more precision perilune orbital elements. Then, the envelope of the reachable-set, which is generated using the multiple-level traversal searching approach with the retrograde semi-analytic model, is re-checked by the continuation theory with the high-precision orbital model. Besides, some factors that affect the reachable-set are also measured. The results show that neither the Earth-Moon distance nor the trans-lunar duration affects the reachable-set. However, if the trans-lunar injection inclination is smaller than the inclination of the moon’s path, the reachable-set becomes smaller or even reduces into an empty set. In brief, the proposed retrograde semi-analytic model for computing the reachable-set provides a helpful and fast tool for selecting an applicable lunar surface landing site for the manned lunar mission overall design.
