The perching maneuver is considered to be a feasible way to solve the problem of ultra-short landing of shipboard fixed-wing aircraft. Present research focuses on the aerodynamics modeling at high angle of attack, nominal perching trajectory optimization and perching trajectory tracking control, and lacks the overall analysis of landing mission. In this paper, based on the longitudinal perching dynamic model of aircraft, the concept of reachable set is introduced, and the mathematical description of reachable set is given. Then, the reachable set problem is divided into three trajectory optimization problems, which are the upper boundary of terminal altitude problem, the shortest trajectory problem at the certain terminal altitude, and the longest trajectory problem at the certain terminal altitude, and the corresponding mathematical models of trajectory optimization are given. At last, the trajectory optimization problems are solved by Gauss pseudo-spectral method, which has both high accuracy and efficiency. The simulation results indicate that the proposed optimization method is efficient, and the reachable set of perching trajectory for a glider is an asymmetric region with upper narrow and lower width, and the curve on the left and right boundary has good linearity. The relevant analysis conclusions can provide support and reference for the overall design of the perching task in the demonstration stage.