This paper describes a novel method to compute minimum-time solar-sail trajectories starting from a given low-thrust solution. The method is based on the use homotopy and numerical continuation. Homotopy is used to link the low-thrust with the solar-sail optimal control problem. Numerical continuation is used to compute the optimal solar-sail solution, starting from a given low-thrust planar solution, which is normally easy to find. Planar solar sail trajectories are computed by means of the homotopic approach. These solutions are used to compute, in a single shooting approach, three-dimensional solar-sail trajectories, for transfer scenarios involving a small change of the orbital inclination. The proposed homotopic approach is tested against a conventional approach, based on the use of a genetic algorithm. Numerical test cases are performed both on Earth-Mars and Earth-Apophis rendezvous. The results show that the proposed method is advantageous, in terms of accuracy of the solution and computational time.
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