On-orbit performance of Gravity Probe B drag-free translation control and orbit determination

The Gravity Probe B (GP-B) Relativity Mission is a fundamental physics experiment to test Einstein's theory of General Relativity based on observations of spinning gyroscopes onboard a satellite in a near-polar, near-circular orbit at an altitude of about 640 km around the Earth. The GP-B mission was designed to test two predictions of Einstein's theory, the geodetic effect and the frame-dragging effect, to an accuracy better than 5 × 10−4 arcsec/yr. Drag-free control technology is implemented in the GP-B translation control system to minimize support forces and support induced torques on the gyroscopes. A Global Positioning System (GPS) receiver onboard the GP-B satellite provides real-time position, velocity and timing data. The GP-B orbit is determined on the ground based on the 3-axis GPS position data and verified independently with ground-based laser ranging measurements. This paper describes the design and implementation of the drag-free translation control and orbit determination system of the GP-B satellite. The on-orbit performance of the drag-free translation control system satisfies the requirements of the GP-B science experiment. The residual accelerations from the gyroscope control efforts are less than 4 × 10−11 m/s2 (along the satellite roll axis) and less than 2 × 10−10 m/s2 (transverse to the satellite roll axis) between 0.01 mHz and 10 mHz in inertial space. The non-gravitational acceleration along the satellite roll axis, including a nearly constant component (which is kept below 1 × 10−7 m/s2) and a sinusoidal component (whose amplitude varies from about 5 × 10−7 m/s2 to less than 1 × 10−8 m/s2), causes the gyroscope spin axis to drift less than 9 × 10−5 arcsec/yr. The orbit determination system is found to provide overlapping orbit solution segments having RMS (root mean square) position and velocity errors of a few meters and a few mm/s, well within the RMS mission requirements of 25 m and 7.5 cm/s.