Optimal phase angle design for the lunar lander

Abstract

To design the optimal lunar landing trajectory, the periapsis of de-orbit burn phase is usually used as a starting point of the powered descent phase. And the optimal problem is constructed based on the initial states at this point. For this optimal problem, some kinds of result trajectories have the increase in their own altitude at the early stage to earn the enough time to reduce their huge horizontal velocity for the low thrust, and this phenomenon increase the consumption of the propellant mass. For this reason, it is possible to exist another phase angle to reduce this phenomenon instead of zero for periapsis of de-orbit burn phase because the vertical velocity is not zero at this point. To find out this optimal phase angle, in this paper, the initial free state optimal problem method is applied without any additional assumption and change of hardware for the traditional optimal lunar landing problem. Using this approach, it shows that the optimal phase angle does not always equal to the periapsis for some cases, and it is possible to reduce the fuel consumption of the lunar lander.