Exploration opportunity search for near earth small body

Near-Earth object (NEO) exploration missions attract many scientists because asteroids and comets hold the key clues that could help us to understand the origin of the solar system and the formation of the planets. When selecting the target for a space mission, it requires trying to minimize the total velocity increment. Traditional "pork-chop" plot method exhausts the possible combination of launch time and arriving time to find the optimal exploration opportunity. In this paper, a novel search method based on the theory of transition matrix and calculus of variations is presented. This method firstly derive the analytical gradients of total velocity increment with respect to launch time and arriving time, and then a quasi-Newton method is utilized to search the optimal launch and arriving time under the drive of these analytical gradients. At the end of this paper, exploration opportunities of some NEOs with high scientific value are searched by the novel method. The novel method can find the exploration opportunity with low computational complexity, compared with "pork-chop" plot, and the precision of launch and arriving time could be increased easily.