Polhode dynamics and gyroscope asymmetry analysis of Gravity Probe B using gyroscope position data.

摘要

Gravity Probe B is a joint NASA/Stanford University satellite-based experiment designed to measure two predictions of Einstein's General Theory of Relativity: the geodetic and frame-dragging effects. The two effects are predicted to cause spin axis drift of a gyroscope with respect to the fixed stars at a rate of 3.203 x10-5 and 1.89x10-7 radians (6606 and 39 milli-arcseconds) per year, respectively. The frame-dragging effect has not previously been observed experimentally. The sensors for this experiment are four round gyroscopes of radius 19 mm, spherical to within 20 nm for largest peak to valley distance on their surface. For the success of the mission, it is essential that the measurement of the spin axis orientation be both precise and accurate to within 5 nrad.; Polhode motion is a well understood motion of a body rotating in a torque-free environment. It was believed that the polhode motion would remain constant over the course of the mission. Early in the data analysis it was revealed that the polhode motion changed its behavior over time. To obtain the accuracy desired for the mission, a detailed understanding of the polhode behavior for each of the four gyroscopes is required.; The main focus of this research is to understand and fully characterize the polhode motion. Analysis of the equations reveals that one parameter characterizes the shape of the polhode path, designated as Q. The exact timing of the polhode behavior is captured in the analysis of the polhode phase. To obtain an estimate of Q and the polhode phase, the gyroscope suspension system data is analyzed to reveal variations of measured gyroscope position at spin frequency. A model of the gyroscopes' surface shape is created and used to find the most likely value of Q by means of a multi parameter search. The value for Q is obtained to an accuracy of 0.05 for two of the gyroscopes. The parameters defining the gyroscopes' surface shape are obtained to within sub nanometer levels for all four gyroscopes.; The results obtained are then applied to the specific problem of mapping the trapped magnetic flux on the surface of the gyroscope. An accurate estimate of the trapped flux distribution would provide an estimate of the gyroscope readout scale factor. By using this estimate in the data analysis of Gravity Probe B, the final results for the Gravity Probe B mission have been improved.