A method for asteroid deflection that makes use of a spacecraft moving back and forth on a segment of a Keplerian orbit about the asteroid is studied with the aim of optimizing the initial gross mass of the spacecraft. The corresponding optimization problem is formulated as a discrete nonlinear optimal control problem where the parameters of the orbit segment are the control variables. A hypothetical asteroid deflection problem is solved numerically using the method of dynamic programming, and it is shown that a gravity tractor can be obtained that is significantly more efficient in terms of deflection attained per unit mass of the spacecraft, as compared to similar gravity tractors in the literature. It is further shown using a numerical approach that the results may be applied to a slowly rotating asteroid that is assumed to have an ellipsoidal shape.
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