  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, compared to similar
gravity tractors in the literature.
