Precision Measurement Of The Torsion Fiber's Anelasticity

Precision measurements of the Newtonian gravitational constant have been performed by using torsion balances with the time-of-swing (ToS) method widely, which has a nice feature that the ToS method converts a small change in weak gravitational force into an obvious change in oscillation period. However, the accuracy of the ToS method is dependent on the constancy of the spring constant k of the used torsion fiber severely, which has been assumed since the ToS was proposed. Recent progress in the study of the internal friction of the fiber suggested that there existed the anelasticity, the frequency-dependent property of the spring constant. Under the assumption of a continuum Maxwell model with particular distribution of relaxation strengths, Kuroda proposed that an upward fractional bias of 1/Ï€Q with Q bing the pendulum's qulity factor should be introduced in the measurements of G using the ToS method, which received much concern due to the proposed larger systematic bias about 187 ppm with Q～1700 in general torsion pendulum. Unfortunately, many researchs has failed to measure this effect directly because of the difficulty and complexity of this problem itself, so the anelasticity of the fiber could be a suspensive error in ToS method.We firstly measured the anelastictiy of the tungsten fiber directly with "two additional disk pendulums" method. To solve the problem about the difficulty in directly measuring the inertial moments of the two pendulums accurately, a high-Q (～350000) quartz fiber whose anelasticity was negligible was utilized to determine the ratio of the inertial moments. In order to get a convincingly result, we studied many possible systematic errors in our experiment comprehensively, such as the creep of the fiber, the coupling effect between the local gravitational field and the pendulum, the fiber's thermoelastic and the nonlinearity et. al. The last, we obtained the frequency dependence of the torsion spring constant k of the fiber asΔk/Δ(ω²)=(0.954±0.084)×10^-8kg.m² within several mHz frequency range, and the resulting bias in G measurement with ToS method due to the tungsten fiber's anealticity isΔG/G=(211.80±18.69) ppm, which proved quantitively the existence of fiber's anelasticity. In addition, the Boltzmann's superposition principle was tested in our fiber system by using a modulated light pressure driving a symmetric disk torsion pendulum, which is helpful to describle the anelastictiy in a fiber integratedly. This new method is simpler than the similar one performed by other researchers. Furthermore, by means of this new method, we can also investigate the frequency dependency of the internal friction of the fiber.