Optimal trajectories for a multiple rendezvous mission to asteroids

Optimal trajectories are designed for an ion-driven spacecraft from Earth to the asteroid 8 Flora with an intermediate stop at 4 Vesta under the constraints imposed by a low-cost mission scenario. For each set of boundary conditions and constraints the problem is transformed into a multipoint boundary value problem which is solved by the multiple shooting method. For the first time, complete flight trajectories are fully optimized including a Moon swing-by manœuvre (with thrusters in operation) and spiraling down to and up from low asteroid orbits. The swing-by manœuvre at the Moon reduces the transfer time to the first rendezvous target, asteroid 4 Vesta, by about 9 months. No simplifications or "splitting up" in the computation of the flight trajectories are made. There is another interesting and new result: the Earth departure window is proven to cover the full reference year of 1987. This year has been chosen in order to allow comparisons with results for the flight to Vesta published by other authors. Fuel consumption of the spacecraft for the first part of its journey (i.e. from Earth to Vesta) is in the range between 17.9 and 23.4% of the initial mass; in comparison to other results known so far the fuel saving is more than 7.6% on an average. In addition, the effect of prescribed transfer time is examined in detail.