Optimal transfer orbit trajectory using electric propulsion

In a spacecraft launched into an injection orbit about a central body and oriented in a predetermined attitude, where the injection orbit has an apogee and a perigee, a method for translating said spacecraft from said injection orbit to a geosynchronous orbit having a semi-major axis and a predetermined orbital plane, comprising the steps of:

• providing a propulsion thruster oriented on said spacecraft for generating a thrust when fired which exerts a predetermined force on said spacecraft;
• firing the propulsion thruster at apogees of intermediate orbits to successively increase the perigees thereof until the semi-major axis of an intermediate orbit is substantially equal to the semi-major axis of the geosynchronous orbit to define an initial transfer orbit for the spacecraft;
• and
• thereafter continuously firing the propulsion thruster to translate the orbit of the spacecraft from the initial transfer orbit to said geosynchronous orbit while maintaining the substantial equality of the geosynchronous semi-major axis and the transfer orbit semi-major axis.