Analysis of optimal strategies for soft landing on the Moon from lunar parking orbits

Optimal trajectory design of a probe for soft landing on the Moon from a lunar parking orbit by minimizing the fuel required is obtained. The problem is formulated as an optimal control problem with the thrust direction being the control variable. Using the maximum principle of Pontryagin, the control variable is expressed as a function of co-state variables and the problem is converted into a two-point boundary value problem. The two-point boundary value problem is solved using an optimization technique, i.e., controlled random search. The strategies such as• direct landing from a lunar parking orbit using powered braking• direct landing from an intermediate orbit using powered braking• by executing powered braking in two phases: through horizontal braking and vertical landingare analyzed and an optimal strategy that achieves the goals is suggested. Also, appropriate design parameters are selected using this analysis