Abstract: For crewed lunar missions，circumlunar emergency return trajectory is a vital way to ensure the crew′s safety for the period near the moon of earth-moon transfer.A design method for circumlunar emergency return trajectory was proposed by introducing two parameters，the perilune altitude and the perilune time，considering the characteristics of high nonlinearity and high sensitivity of the circumlunar emergency return trajectory.Based on the pseudo-state theory and Quasi-Lambert problem，a simple and effective model was developed in this method，so that the heavy numerical iteration of the traditional trajectory design process was avoided.And a high-precision design result was realized efficiently.Further，the two parameters were applied to establish an ergodic representation of circumlunar emergency return trajectories under fixed abort point and basic reentry constraints，and the characteristics of the feasible circumlunar emergency return trajectory changing with parameters were studied.These offer a global view of all feasible circumlunar emergency return trajectories and provide a reference for translunar trajectory selection in subsequent crewed lunar missions.

Key words: crewed lunar mission, emergency return trajectory, parametric design, pseudostate theory, Quasi-Lambert problem