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

Abstract

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.

Correction of cosine oscillation to the improved correlation method of estimating the amplitude of gravitational background signal

“…In the measurement of the gravitational constant G with the angular acceleration method, the angular acceleration of the torsion balance turntable can be expressed as [17,18]…”

“…[12] The coupling effect of the spurious gravitational background signal and the linear slow drift of torsion balance's equilibrium position [13][14][15][16] leads to the fact that the angular frequency of the spurious gravitational background signal undergoes a quadratic slow drift. [17] Then, the accurate amplitude determination of the useful angular acceleration signal depends on the effective subtraction of the spurious gravitational background signal. [18] In order to subtract the gravitational background signal from the angular acceleration signal of the torsion balance turntable effectively, we need to determine the amplitudes of the fundamental frequency and second harmonic components of the gravitational background signal accurately.…”

“…Since the angular velocity of the torsion balance turntable, which is also the angular frequency of the gravitational background signal, is the integral of its angular acceleration over time, besides the quadratic slow drift, the time-varying frequency of the gravitational background signal also contains a cosine oscillation coming from the useful angular acceleration signal. [17] The improved correlation method [18] with stretch processing of time is used to accurately determine the amplitudes of the prominent fundamental frequency and second harmonic components of the gravitational background signal with time-varying frequency in the meantime, and the cosine oscillation term is considered to be negligible with respect to the quadratic slow drift term. To judge whether the influence of the cosine oscillation is negligible compared with the error of the estimated amplitude, one needs to calculate the correction caused by the cosine oscillation.…”