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 may 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 (200AU) are presented, both for ideal and for non-ideal sails. Thereby, also near/medium-term solar sails with a relatively moderate performance are considered. The minimal flight time to the outer solar system depends not only on the lightness of the solar sail, but also on the allowed minimal solar distance. The solar distance, however, is limited 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 minimal solar distance but the allowed maximal sail temperature is directly used as an optimization constraint. Although, especially for moderate-performance solar sails, the topology of optimal trajectories becomes quite sophisticated, the required flight times and and the achieved solar system escape velocities obey very simple laws.