Abstract: One of the key distinctions between a crewed lunar mission and traditional lunar exploration missions lies in the requirement to ensure astronaut safety throughout the mission. In the event of an emergency during lunar orbitoperations, it is essential to possess a return capability that satisfies both reentry and landing constraints, which constitutes a complex Earth-Moon transfer trajectory design problem. This study employs a trajectory design method that combines a parametric approach with the solution of the Quasi-Lambert problem to systematically investigate the family characteristics and reentry regions of Earth-Moon return trajectories under such constraints. The proposed method enables the parametric generation of impulsive escape trajectories from lunar orbit at any epoch, targeting designated landing sites on Earth. On this basis, the velocity increment requirements and reachable landing regions associated with trajectory families of different transfer times are computed and analyzed. Furthermore, the feasibility and distribution characteristics of the landing sites are assessed by incorporating the declination variation patterns under different lunar phase conditions. Results demonstrate that for trajectory families with transfer times of 2, 3, and 5 days, the required velocity increments exhibit pronounced short-period and long-period coupled oscillations influenced by Earth's rotation and lunar phase evolution. Moreover, under different lunar phase declination conditions, the distribution of feasible Earth landing sites shows significant variation. To ensure emergency return capability at any epoch, the target landing site latitude should be restricted to below 20° N. If higher-latitude landing sites are desired, the lunar phase declination at the emergency epoch must fall within specific ranges.

Key words: Earth-Moon transfer trajectory, emergency return trajectory, crewed lunar mission, reentry landing analysis, Quasi-Lambert problem