Approximate non-coplanar orbital transfers with minimum expenditure of fuel

Abstract

An approximate method is given for determining the optimal trajectory of a thrust-limited rocket transferring from one known elliptic orbit to another in a vacuum. The trajectory consists of thrust-coast-thrust arcs, and the deviation from the initial orbital plane is of first-order smallness compared to the path projected onto the plane.

In its application, no more than two degrees are iterated concurrently, the first pair to meet the in-plane requirements and the second to satisfy the out-of-plane conditions. It is also shown that since second-order terms were neglected, the approximation in fuel expenditure is of fourth order.

We include an example in order to demonstrate the feasibility of the method.