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, 372 (2026)

Preliminary Determination of Newtonian Gravitational Constant With Angular Acceleration Feedback Method

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Preliminary Determination of Newtonian Gravitational Constant With Angular Acceleration Feedback Method

Chao Xue et al. Philos Trans A Math Phys Eng Sci.

Abstract

This paper describes the preliminary measurement of the Newtonian gravitational constant G with the angular acceleration feedback method at HUST. The apparatus has been built, and preliminary measurement performed, to test all aspects of the experimental design, particularly the feedback function, which was recently discussed in detail by Quan et al. The experimental results show that the residual twist angle of the torsion pendulum at the signal frequency introduces 0.4 ppm to the value of G. The relative uncertainty of the angular acceleration of the turntable is approximately 100 ppm, which is mainly limited by the stability of the apparatus. Therefore, the experiment has been modified with three features: (i) the height of the apparatus is reduced almost by half, (ii) the aluminium shelves were replaced with shelves made from ultra-low expansion material and (iii) a perfect compensation of the laboratory-fixed gravitational background will be carried out. With these improvements, the angular acceleration is expected to be determined with an uncertainty of better than 10 ppm, and a reliable value of G with 20 ppm or below will be obtained in the near future.

Keywords: Newtonian gravitational constant; angular acceleration; torsion balance; turntable.

Figures

Figure 1.
Figure 1.
The principle of the angular acceleration feedback method. (Online version in colour.)
Figure 2.
Figure 2.
Photograph of the preliminary apparatus. The torsion balance is located in the vacuum chamber, which is installed on the air bearing turntable. The source masses are supported by another separate gear bearing turntable. The two turntables rotate in opposite directions (see [30]). (Online version in colour.)
Figure 3.
Figure 3.
Feedback control system. Feedback loop I is used to control the air bearing turntable to keep the fibre untwisted. Feedback loop II is used to control the gear bearing turntable to hold the difference angular velocity constant (see [30]).
Figure 4.
Figure 4.
The typical PSD of the pendulum twist angle. The random noise is less than 7.3×10−7 rad Hz−1/2, which contributes 0.4 ppm to the value of G. (Online version in colour.)
Figure 5.
Figure 5.
A 2 h segment of the angular acceleration of the inner turntable. The signal frequency is 2 mHz.
Figure 6.
Figure 6.
The typical PSD of the turntable angular acceleration. The 2.0 mHz gravitational acceleration signal is nearly four orders of magnitude larger than the random noise. The two peaks at 4.0 and 6.0 mHz are the higher harmonic signals. The primary laboratory-fixed gravitational background is cleanly separated.

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