The possibility of an unlimited flight endurance of solar aircraft is treated with the objective to maximize their performance. This is a periodic optimal control problem because the trajectory is continued after a one-day flight in the same manner as before. Focus of the performance goal is the minimization of the required battery capacity so that the related weight penalty can be kept as small as possible. Realistic mathematical models of the dynamics of the aircraft and the energy management system for an optimal utilization of the solar energy are applied. With the use of an efficient optimization method, results on periodic optimal solar aircraft trajectories yielding the performance enhancement aimed at are presented.