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The landing maneuver of aircraft is considered to be a feasible way to solve the problem of ultra short distance,precise landing of carrier based fixed wing aircraft. The existing researches mainly focus on aerodynamic modeling,nominal landing trajectory optimization and trajectory tracking control in the process of landing,but few on the overall analysis of the landing mission. Based on the dynamic model of aircraft longitudinal landing maneuver,the concept of landing trajectory reachable region is introduced,and the mathematical description of reachable region is given;On this basis,the Gauss pseudo-spectral method with both computational speed and accuracy is used to solve the reachable region problem,which is divided into three trajectory optimization problems. Firstly,the upper boundary of the terminal height of the perching trajectory is solved. Secondly,the nearest trajectory is solved when the terminal height is fixed. Finally,the farthest trajectory is solved when the terminal height is fixed.The simulation results show that:the model and solution method can quickly get the calculation results,the vertical landing trajectory of unpowered aircraft can reach the asymmetric region of narrow upper and wide lower,and the left and right boundary curves have good linearity.