Optimal two- and three-impulse fixed-time rendezvous in the vicinity of a circular orbit

Minimum-fuel, multiple-impulse orbital rendezvous is investigated for the case in which the transfer time is specified (time-fixed case). A method for obtaining optimal solutions is employed which is applicable to rendezvous or orbit transfer between elliptical orbits of low eccentricity. In this method optimal solutions are constructed by satisfying the necessary conditions for the primer vector. It is assumed that the terminal orbits lie close enough to an intermediate circular reference orbit that the linearized equations of motion. can be used to describe the transfer. The linear boundary value problem for the impulse magnitudes for rendezvous is then solved analytically. As an application of the method, optimal two- and three-impulse fixed-time rendezvous transfers between coplanar circular orbits are obtained for a range of transfer times. These linearized solutions combined with previously obtained four-impulse solutions provide a complete solution for fixed-time coplanar circle-to-circle rendezvous between close orbits for transfer times up to nearly two terminal orbit periods.