| In this thesis we examine various aspects of the error analysis in the Relativity Gyroscope Experiment. This experiment is designed to measure the relativistic precessions of a gyroscope in orbit around the Earth. For a polar orbit at altitude 500 km, there are two precessions: a "geodetic" precession in the north-south direction, of magnitude 6.9 arcsec/year, due to the motion of the gyroscope around the Earth and a "motional" precession in the east-west direction, of magnitude 44 milliarcsec/year, due to frame-dragging by the rotating Earth. The design goal of the experiment is to measure the relativistic precessions with a precision of 1 milliarcsec/year.; Four electrostatically suspended superconducting spherical gyroscopes are onboard a cryogenic satellite. The direction of their spin axis is measured with SQUID magnetometers and compared to an inertial reference direction which is provided by a telescope pointed at the star Rigel.; We use a Kalman filter in its square root form to estimate the precision on the relativistic precessions at the end of one year. In order to reduce the computer time we used an analytical averaging technique.; We give a detailed examination of the aberration of starlight. We study the possibility of determination of the bending of starlight by the Sun by means of the Gyroscope experiment and show that it compares in precision with VLBI techniques.; We examine the dynamics of the gyroscope taking into account the effects of elastic distortion due to centrifugal force.; When the gyroscope rotors are cooled through their superconducting transition temperature, the ambient magnetic field is trapped in the rotor. We show how the trapped flux signal at spin frequency can be used to calibrate the scale factor of the SQUID magnetometers. |
