Time-optimal orbit transfer trajectory for solar sail spacecraft

This paper considers the problem of optimally controlling the sail steering angle of a solar sail spacecraft (a spaceship moving under the influence of solar radiation pressure) so as to execute a minimum-time coplanar orbit transfer from the mean orbital distance of Earth to the mean Martian orbital distance around the sun. This problem has been modeled as a free-terminal time-optimal control problem with an unbounded control variable and with state variable equality constraints at the final time. It has been solved by the penalty function approach using the conjugate gradient algorithm. Detailed computational results regarding the convergence of the optimal control, the state trajectories, and the norm of the gradient trajectory, along with the minimization of the performance functional, are presented. In general, the optimal solution is found to be compatible with that obtained by some of the earlier investigators of this problem. In conclusion, the optimized orbit transfer time of the solar sail spacecraft is compared with that of an ionic propulsion system.