Optimal solar-sail trajectories for missions to the outer solar system

Although the solar radiation pressure decreases with the square of solar distance, solar sails enable missions to the outer solar system and even beyond. For such missions, the solar sail can gain a large amount of energy by first making one or more close approaches to the sun. Within this paper, optimal trajectories for solar-sail missions to the outer planets and into near interstellar space are presented, both for ideal and for nonideal sails. Therefore, also, near-/medium-term solar sails with a relatively moderate performance are considered. The minimum flight time to the outer solar system depends not only on the lightness of the solar sail, but also on the allowed minimum solar distance. The minimum solar distance, however, is constrained by the temperature limit of the sail film. Within this paper, it is demonstrated that faster trajectories can be obtained for a given sail temperature limit, if not, as usual, the allowed minimum solar distance, but the allowed maximum sail temperature is directly used as a path constraint for optimization. Although, especially for moderate-performance solar sails, the geometry of,optimal trajectories becomes quite sophisticated, the required flight times and the achieved solar system escape velocities obey very simple laws.