EXISTENCE AND MULTIPLE SOLUTIONS OF THE MINIMUM-FUEL ORBIT TRANSFER PROBLEM

In this paper, the well-known problem of piloting a rocket with a low thrust propulsion system in an inverse square law field (say from Eart h orbit to Mars orbit or from Earth orbit to Mars) is considered. By d irect methods, it is shown that the existence of a fuel-optimal soluti on of this problem can be guaranteed, if one restricts the admissible transfer times by an arbitrarily prescribed upper bound. Numerical sol utions of the problem with different numbers of thrust subarcs are pre sented which are obtained by multiple shooting techniques. Further, a general principle for the construction of such solutions with increasi ng numbers of thrust subarcs is given. The numerical results indicate that there might not exist an overall optimal solution of the Earth-or bit problem with unbounded free transfer time.