PREFERRED SCHEMES FOR MULTIPLE ORBIT TRANSFER

Abstract

A mathematical structure is formulated and used to obtain the preferred sequence of orbits visited for a multiple orbit maneuver between m given coplanar circular orbits. Various constraints are placed on the initial and final orbits visited, and it is assumed that each transfer mode is accomplished via a Hohmann maneuver. The criterion used to extract the class of preferred schemes from the totality of transfer schemes is that the velocity required to perform the maneuver be minimized; phasing considerations are neglected. Although under certain conditions a unique optimal procedure is obtained, in general, the class of possible transfer schemes between m orbits with typical constraints is reduced from m — 1! to 2~, preferred schemes. An example of the former arises when the initial orbit visited is the innermost; then all other orbits must be visited, and the final orbit is unconstrained. An example of the latter occurs when it is required to start at the innermost orbit, visit all the other orbits, and then return to the innermost orbit. The mathematical results obtained are developed as a series of theorems, lemmas, and corollaries in order to facilitate application to other problem areas.