Optimal control of a spacecraft with a solar sail

Analysis of the results indicates that: a) all the optimal trajectories may be divided into two sections: the phased section, corresponding to motion over a trajectory close to the initial one with a small change in initial energy (amounting to around two-thirds of the total journey time); and the orbital transfer, with considerable change in orbital energy, as a result of active control of the solar-sail orientation (around one-third of the total journey time). In the second section, the spacecraft first moves closer to the Sun and then makes the transfer to Mars orbit; b) the duration of orbital transfer is 581 dyas according to the optimal plan, which includes sections of deceleration and movement from the initial orbit over a distance of 0.2 dimensional length units toward the Sun; with the constraint ϑ<π/2, the deceleration is eliminated, and the distance toward the Sun is reduced (to 0.1 dimensionless units), with a corresponding increase in journey time; c) taking account of the nonideal reflecting surface (e=0.85 rather than e=1) increases the journey time to 615 days without change in the other characteristics of the orbital transfer.