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This paper considers the problem of interplanetary guidance in the presence of random injection and measurement errors from the point of view of minimizing the expected value of the square of the control effort to meet a prescribed terminal accuracy. It is shown that the optimal control signal is a linear function of only those components of the predicted miss whose terminal covariance is specified. A one dimensional model which approximates the terminal phase of an interplanetary trip is considered in detail. Computer results are given showing the comparison of this solution with the minimum effort theory developed recently by Breakwell and Striebel  on the requirement for the expected amount of velocity corrections. An analytical expression is given which shows that the present design is about 13 per cent more costly in so far as the terminal portion of the expected velocity requirement is concerned.