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The problem of minimal fuel thrust programming for the terminal phase of a lunar soft landing mission is shown to be equivalent to the minimal time problem for the mission. The existence of an optimal (minimal fuel) thrust program for the problem is then assured by appealing to existence theorems for time optimal controls, and the optimal thrust program is developed by application of the Pontryagin maximum principle. It is shown that the optimal thrust program consists of either full thrust from the initiation of the mission until touchdown, or a period of zero thrust (free-fall) followed by full thrust until touchdown. An approximate switching function which is adequate for a large number of cases is derived, and a preliminary system design is presented.