Optimal trajectories of a spacecraft flight to a near-Earth asteroid with using electric-jet thrust are determined and analysed. A goal of the spacecraft flight to the asteroid is the spacecraft impact influence on the asteroid to change the asteroid orbit and deflect it from the Earth. The electric thrust is suggested to be stepped. Maximization of asteroid deflection from the Earth is carried out in this paper. Effective method based on the Pontrjagin maximum principle for the optimal trajectories determination is used. Numerical analysis is given for the asteroid Toutatis orbit.

asteroid hazard, near-Earth asteroid, flight to asteroid, electric jet thrust.

Theoretical and applied problems of mechanics