The moon lander optimal control problem revisited

We revisit the control problem for a spacecraft to land on the moon surface at rest with minimal fuel consumption. We show that a detailed analysis in the related 3D phase space uncovers the existence of infinitely many safe landing curves, contrary to several former 2D descriptions that implicitly claim the existence of just one such curve. Our results lead to a deeper understanding of the dynamics and allows for a precise characterization of the optimal control. Such control is known to be bang-bang and our results give a full characterization of the switch position.