Gravity Probe B Data Analysis

Abstract

This is the first of five connected papers detailing progress on the Gravity Probe B (GP-B) Relativity Mission. GP-B, launched 20 April 2004, is a landmark physics experiment in space to test two fundamental predictions of Einstein's general relativity theory, the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection began 28 August 2004 and science operations were completed 29 September 2005. The data analysis has proven deeper than expected as a result of two mutually reinforcing complications in gyroscope performance: (1) a changing polhode path affecting the calibration of the gyroscope scale factor C g against the aberration of starlight and (2) two larger than expected manifestations of a Newtonian gyro torque due to patch potentials on the rotor and housing. In earlier papers, we reported two methods, 'geometric' and 'algebraic', for identifying and removing the first Newtonian effect ('misalignment torque'), and also a preliminary method of treating the second ('roll-polhode resonance torque'). Central to the progress in both torque modeling and C g determination has been an extended effort on "Trapped Flux Mapping" commenced in November 2006. A turning point came in August 2008 when it became possible to include a detailed history of the resonance torques into the computation. The East-West (frame-dragging) effect is now plainly visible in the processed data. The current statistical uncertainty from an analysis of 155 days of data is 5.4 marc-s/yr (∼ 14% of the predicted effect), though it must be emphasized that this is a preliminary result requiring rigorous investigation of systematics by methods discussed in the accompanying paper by Muhlfelder et al. A covariance analysis incorporating models of the patch effect torques indicates that a 3-5% determination of frame-dragging is possible with more complete, computationally intensive data analysis.

Analytical solution of the geodesic equation in Kerr-(anti-) de Sitter space-times

“…In the case of the ISCO in the equatorial plane we are now done. For the LSSO, we have to check in addition whether the corresponding values of E 2 (r) andL z (r) (given by (36)) are located in an allowed region of the θ motion. If this is the case, we found the LSSO.…”

The Gravity Probe B Data Analysis Filtering Approach

“…There is a clear way to improve the accuracy of GP-B results (Everitt et al 2009). Existence of a roll component in the patch effect torque suggests the development of a one-level estimator ("2-second filter"), with a sampling data rate much higher than the roll period.…”

“…Data analysis in the GP-B experiment (Everitt et al 2009)-estimation of the relativistic drift rate for each of the four unique GP-B gyroscopes-was supposed to be rather straightforward (Haupt 1996;Heifetz et al 2003). One should take the low frequency (LF) SQUID readout signal for the duration of the mission, calibrate the scale factor based on orbital and annual aberration known from the GPS orbit data and earth ephemeris; obtain the timehistory of the gyroscope inertial orientation in the projections on the directions in the orbital plane and perpendicular to it, and then estimate the slopes of those projections, which were supposed to be almost straight lines.…”

Polhode Motion, Trapped Flux, and the GP-B Science Data Analysis

“…The LM scale factor C LM g , proportional to the spin speed, is constant, up to a very small spin-down rate of GP-B gyros (spin-down time ∼ 10 4 years, see Everitt et al 2009). The angle β(t) carries the relativity signal at the low roll frequency f r ≈ 0.01 Hz.…”

“…The GP-B relativity science mission to measure the geodetic and frame-dragging effects on the four spinning superconducting gyroscopes (see Adler and Silbergleit 2000 and the references therein) is described in Everitt et al (1980Everitt et al ( , 2009; Turneaure et al (2003). It uses the low frequency (LF) London Moment magnetic readout provided by a high-precision low-noise SQUID.…”