Optimum Trajectories for an Earth–Asteroid–Earth Mission with a High Thrust Flight

Abstract

The trajectories of a mission to an asteroid with the presence of a spacecraft (SC) near the asteroid for some time and including a return to the Earth have been studied. A two-stage method of constructing optimum (with respect to the maximum of the useful SC mass) interplanetary trajectories for an Earth–asteroid–Earth mission with high thrust engines has been developed: in the central Newtonian field of the Sun’s attraction at the first stage and with allowance for perturbations at the second stage. An algorithm of constructing conjugate functions for the case of maximizing the useful mass has been designed. The optimum trajectories for the Earth–Apophis–Earth mission have been constructed and analyzed. The possibility in principle of organizing the Earth–Apophis–Earth space mission based on the Soyuz and Zenit launch vehicles and Fregat upper stage for a flight in 2019–2022 has been demonstrated.