ИСТИНА

The problem of optimization of the interplanetary spacecraft expedition from the Earth to Mars with a returning to the Earth is considered. Two trajectories of interplanetary flights of this mission are approximated by Keplerian orbits and obtained as a solution of Lambert's problems with the use of universal variable, Shtump’s functions and Newton's method. Position and velocity of the Earth and Mars are calculated with the use of ephemerides. The 29 local minima of this multiextremal problem are found numerically with the use of the gradient method and examined with the second-order optimality conditions with the use of Sylvester’s criterion.