Support-electrode torque on a spherical superconducting gyroscope

In 1960, L.I. Schiff observed that precise measurement of the precession of a spherical gyroscope orbiting the earth could provide a test of general relativity. The current effort to implement this experiment was initiated shortly thereafter by W.M. Fairbank. The gyroscope will be a fused-quartz sphere coated with superconductive niobium. The spinning superconducting coating generates a small magnetic field (the London field) which outside the rotor is that of a magnetic dipole and inside is uniform and parallel to the spin axis. The magnetic flux that this field produces in superconducting loops encompassing the rotor will change as the gyroscope precesses; the precession of the gyroscope will be measured by measuring the change in flux. Because the anticipated relativistic precession is extremely small, it is essential that no significant torques be coupled to the gyroscope through its London field. The torque on a superconducting sphere rotating in an arbitrary magnetic field can be expressed in terms of the l = 1 coefficients of the expansion of the field in spherical harmonic functions. In general, a boundary-value problem must be solved in order to obtain these coefficients. The diamagnetic torque produced by superconducting support electrodes is calculated. (WHK