Optimal Trajectories Determination for Space Missions to Near-Earth Asteroid Using Low Thrust

The optimal trajectories of the spacecraft flight from the Earth to the Near-Earth asteroid are determined. The aim of the flight is the spacecraft's impact on the asteroid in order to prevent its collision with the Earth. The application of high thrust (for geocentric motion) and low thrust (for heliocentric motion) is investigated. The spacecraft initial mass in the circular orbit near the Earth is supposed to be given. The spacecraft final mass at the moment of the spacecraft-asteroid impact is a criterion of the optimization. Three models of the spacecraft motion are investigated. The approximate models are investigated using transporting coordinate system which is connected with the spacecraft on the basic trajectory. These are the model of the motion in the space without gravitation, the model of the motion in the space with linear gravitation and the model with exact statement of the problem. The numerical results are given for the flight to the asteroid Toutatis.