Analysis and testing of gyroscope performance for the Gravity Probe B relativity mission

This dissertation describes the analysis and experimental testing of the performance of electrostatically suspended vacuum gyroscopes (ESVG) designed for the Gravity Probe B Relativity Experiment (GP-B).; The GP-B mission is a satellite-based gyroscope experiment currently under joint development by NASA and Stanford University. It is designed to test two predictions of Einstein's General Theory of Relativity: the geodetic effect and the frame-dragging effect. They are predicted to be 6.6 and 0.042 arc-sec/year, respectively, for a planned circular polar orbit. The primary goal of the GP-B mission is to measure the geodetic effect to better than 0.01%, and the frame-dragging effect to better than 1%. In order to achieve this goal, the non-relativistic drift rate of the gyroscope must be less than 0.3 milli-arc-sec/year.; Presented is the analysis of the part of the Newtonian torque on the gyroscope rotor that is due to the electrostatic support, estimation of the science-mission drift rate, and experimental validation of the theoretical torque modeling. The analysis of the electrostatic torque indicates that the torque depends on both the close-to-perfect rotor shape with very minor manufacturing asphericity, and the voltage applied to the electrodes. To estimate the science-mission drift rate, we used the measured asphericity of an existing rotor that was below flight quality. Throughout the analysis, the estimated drift rate of the gyroscope induced by the non-relativistic effect was less than the maximum allowed drift rate of 0.3 milli-arc-sec/year for this effect. This result is gratifying because the actual flight rotors will exhibit a much lower non-relativistic drift rate. In the laboratory, parameters that characterize the electrostatic torque were measured by changing the voltages applied to the electrodes and the position of the gyroscope rotor in its housing cavity. The results match well with the theoretical expectations, confirming the validity of the theoretical approach regarding the electrostatic torque on the rotor.; As a conclusion, the gyroscopes developed for the GP-B science mission can be trusted to satisfy the mission requirement.