Optimal placement for gravitational tractor in trajectory deflection mission of small bodies

In order to solve the optimal placement problem for a gravitational tractor in the trajectory deflection mission of small bodies, this paper gives an optimal selection method for the tractor placement based on a hybrid optimization strategy. First, the movement of small bodies is modeled based on the modified equinoctial orbital element, and the position of gravitational tractor related to small bodies is regard as the control angle to small bodies. Then, an optimal control angle is derived based on the maximum principle, and the selection problem for placement is changed into an optimal problem for the initial value of the costate. In order to obtain the global optimal solution, the differential evolution algorithm is used to do a wide range of initial search for the optimal model, furthermore, sequential quadratic programming algorithm is used to obtain the local precise optimization. By taking high-risk small body Apophis as an example, the proposed method is verified. Numerical results demonstrate that the optimal placement for the gravitional tractor oscillates near the direction of small bodies' velocity and gravitional tractor can effectively deflect the small bodies.