Solar sailing is a propulsion technology that uses the solar radiation pressure of the sun as a source for thrust. By transferring the momentum of photons to the sail, it gains large changes in its velocity, making solar sails viable for propellant less space exploration. Due to the continuous applied thrust, solar sailing has potential applications in deep space, solar, planetary, and asteroid missions. One problem that arises in solar sailing research is the design and optimization of trajectories, which seeks to obtain the best path to be taken by the sail, given the needs, limitations, and objectives of the mission. This paper addresses this problem by proposing the surface constraint approach, which is useful for the special case of sails that are constrained to move on surfaces. While many trajectory design approaches focus on purely numerical optimization, our approach is semi-analytic, for which the results are vital as initial guesses in more robust numerical optimization. By utilizing a generalized conserved quantity that is related to the sail’s orbital angular momentum, we were able to obtain a family of possible trajectories that satisfy the sail’s equation of motion. We then optimize the trajectory by choosing the one that minimize the flight time for the same initial and terminal conditions. Finally, we applied the surface constraint approach in a mission towards the highly inclined orbit of an asteroid.

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