Abstract:Asteroid impacts pose a major threat to all life on Earth. The kinetic impactor remains a promising strategy for asteroid deflection. One objective function of a kinetic impactor mission is to maximize the deflection distance (the change of the closest-approach distance before and after the asteroid is deflected). If the deflection distance is accurately calculated by a numerical integration, the efficiency of the optimization problem will be reduced. The dynamical model and the deflection distance calculation method can be simplified in the preliminary design of a kinetic impactor mission. This paper first simplifies the high-precision N-body dynamic model to the two-body dynamic model. Two classic deflection distance analytical models are introduced, at the same time, an approximate model of deflection distance based on closest-approach epoch estimation. Considering the launch performance and simplifying the chemical propulsion to the impulsive maneuver, the direct transfer trajectory optimization model and the planetary gravity assist trajectory optimization model are established. The Genetic Algorithm is used to solve the optimization problem. Taking deflecting Apophis as an example, compared with the analytical model, it is verified that the approximate model proposed in this paper can simultaneously improve the optimality and reduce the complexity of the solution. The simulation results show that the optimal deflection effect of the three-impulse direct transfer trajectory and the two-impulse direct transfer trajectory is almost the same, and the improvement of the planetary gravity assist transfer trajectory on the deflection distance is not obvious compared with the direct transfer trajectory. During the preliminary design stage of a kinetic impactor mission, the deflection distance can be quickly evaluated based on the two-body model. Although there is a certain error in the deflection distance, it does not affect the deflection window. The main gravitational perturbation terms (Venus, Earth, Jupiter) can be introduced to further modify the two-body dynamic model, so that the deflection distance error between modified two-body and the high-precision dynamic model is below 1%.