An Analysys of Spacecraft Optimal Two-Impulse Flights to Near-Earth Asteroid

Optimal trajectories of a spacecraft (S/C) flight to a near-Earth asteroid (NEA) are analysed for a jet engine with a high thrust. The jet engine is supposed to be used twice. The problem is studied in the impulse approach. A goal of the S/C flight to the NEA is the S/C impact influence on the asteroid to deflect it from the Earth. Maximization of the S/C final mass and asteroid deflection from the Earth is carried out in this paper. The Lawden primer-vector method is used to develop an optimization algorithm and to find the optimal trajectories. It is shown that an additional intermediate velocity impulse on heliocentric part of the S/C flight can essentially increase the efficiency of the S /C influence of the NEA. Numerical analysis is given for the orbit of the asteroid Toutatis.