High precision mapping of the geoid and the Earth's gravity field are of importance to a wide range of ongoing studies in areas like ocean circulation, solid Earth physics and ice sheet dynamics. Using a satellite in orbit around the Earth gives the opportunity to map the Earth's gravity field in 3 dimensions with much better accuracy and spatial resolution than ever accomplished. To reach the desired quality of measurements, the satellite must fly in a low Earth orbit where disturbances from atmospheric drag and the Earth's magnetic field will perturb the satellite's motion. These effects will compromise measurement accuracy, unless they axe accurately compensated by onboard thrusters. The paper concerns the design of a control system to performing such delicate drag compensation. A six degrees-of-freedom model for the satellite is developed with the model including dynamics of the satellite, sensors, actuators and environmental disturbances to the required micro-Newton accuracy. A control system is designed to compensate the nongravitational disturbances on the satellite, in three axes using an H_∞ design. Performance is validated against mission requirements.