The present system and methods enable simultaneous momentum dumping and orbit control of a spacecraft, such as a geostationary satellite. Control equations according to the present system and methods generate accurate station-keeping commands quickly and efficiently, reducing the number of maneuvers needed to maintain station and allowing station-keeping maneuvers to be performed with a single burn. Additional benefits include increased efficiency in propellant usage, and extension of the satellite's lifespan. The present system and methods also enable tighter orbit control, reduction in transients and number of station-keeping thrusters aboard the satellite. The present methods also eliminate the need for the thrusters to point through the center of mass of the satellite, which in turn reduces the need for dedicated station-keeping thrusters. The present methods also facilitate completely autonomous orbit control and angular momentum control using.