Method of and system for on-board substantially autonomous control for transferring a spacecraft from an initial orbit to a final geosynchronous orbit, by a trajectory that minimizes remaining transfer time and orbit transfer fuel. The spacecraft determines its orbit using a GPS-based system to determine the spacecraft orbital elements. Based on the measured orbit error, corrected co-state parameters are calculated and used to generate an updated thrust trajectory. The corrections are calculated using an innovative numerical procedure, carried out repetitively at a fixed interval until the target geosynchronous orbit is achieved.