An improved correlation method for amplitude estimation of gravitational background signal with time-varying frequency.

In the measurement of the gravitational constant G with angular acceleration method, the accurate estimation of the amplitude of the useful angular acceleration generated by source masses depends on the effective subtraction of the spurious gravitational signal caused by room fixed background masses. The gravitational background signal is of time-varying frequency, and mainly consists of the prominent fundamental frequency and second harmonic components. We propose an improved correlation method to estimate the amplitudes of the prominent components of the gravitational background signal with high precision. The improved correlation method converts a sinusoidal signal with time-varying frequency into a standard sinusoidal signal by means of the stretch processing of time. Based on Gaussian white noise model, the theoretical result shows the uncertainty of the estimated amplitude is proportional to σNT, where σ and N are the standard deviation of noise and the number of the useful signal period T, respectively.

Influence of tungsten fiber's slow drift on the measurement of G with angular acceleration method.

In the measurement of the gravitational constant G with angular acceleration method, the equilibrium position of torsion pendulum with tungsten fiber undergoes a linear slow drift, which results in a quadratic slow drift on the angular velocity of the torsion balance turntable under feedback control unit. The accurate amplitude determination of the useful angular acceleration signal with known frequency is biased by the linear slow drift and the coupling effect of the drifting equilibrium position and the room fixed gravitational background signal. We calculate the influences of the linear slow drift and the complex coupling effect on the value of G, respectively. The result shows that the bias of the linear slow drift on G is 7 ppm, and the influence of the coupling effect is less than 1 ppm.

Influence of temperature on period of torsion pendulum with a high-Q fused silica fiber.

Due to the high-Q fused silica fiber's extreme sensitivity to temperature change, the period estimation of torsion pendulum with high precision depends on the effective correction of the thermoelastic effect. In the measurement of G with the time-of-swing method, we analyze the complex relation between temperature and the pendulum's period and propose a developed method to find the shear thermoelasticity coefficient as well as isolate the influence of temperature on period alone. The result shows that the shear thermoelasticity coefficient is 101(2) × 10(-6)/°C, the resultant correction to Δ(ω(2)) is 9.16(0.18) ppm, and the relative uncertainty to G is less than 1 ppm.