Abstract
Gravity probe B (GP-B) was designed to measure the geodetic and frame dragging precessions of gyroscopes in the near field of the Earth using a drag-free satellite in a 642 km polar orbit. Four electrostatically suspended cryogenic gyroscopes were designed to measure the precession of the local inertial frame of reference with a disturbance drift of about 0.1 marc sec/yr-0.2 marc sec/yr. A number of unexpected gyro disturbance effects were observed during the mission: spin-speed and polhode damping, misalignment and roll-polhode resonance torques, forces acting on the gyroscopes, and anomalies in the measurement of the gyro potentials. We show that all these effects except possibly polhode damping can be accounted for by electrostatic patch potentials on both the gyro rotors and the gyro housing suspension and ground-plane electrodes. We express the rotor and housing patch potentials as expansions in spherical harmonics Y(l,m)(θ,φ). Our analysis demonstrates that these disturbance effects are approximated by a power spectrum for the coefficients of the spherical harmonics of the form V(0)(2)/l(r) with V(0) ≈ 100 mV and r ≈ 1.7.
Highlights
Gravity probe B (GP-B) was designed to measure two general relativistic effects calculated in 1960 by Schiff:[1] the geodetic (GE) precession and the frame-dragging (FD) precession
Its proper motion with respect to distant quasars has been determined by very long baseline interferometry (VLBI) measurements[4] to about 10−4 arc sec/yr
The purpose of this paper is to show that a patch effect model applies to the misalignment and the rollpolhode resonance torques, but it explains in a unified patch effect model the other unexpected gyro phenomena observed during the GP-B mission
Summary
Gravity probe B (GP-B) was designed to measure two general relativistic effects calculated in 1960 by Schiff:[1] the geodetic (GE) precession and the frame-dragging (FD) precession. Earth, measured by the gyroscopes, was compared to the reference frame of distant stars determined by a telescope locked onto a guide star.[3] The guide star was HR8703 (IM Pegasi), a binary with optical and radio frequency emissions. Its proper motion with respect to distant quasars has been determined by very long baseline interferometry (VLBI) measurements[4] to about 10−4 arc sec/yr. Equation (1) gives the two precessions, averaged over a polar orbit, predicted by general relativity; the first term is the geodetic precession which is about the perpendicular to the orbital plane, and the second term is the frame-dragging precession which is about the Earth’s rotation axis. The two terms are proportional, respectively, to Me3/2 (Me is the Earth’s mass) and to the Earth’s angular momentum Ieωe:
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