G measurements with time-of-swing method at HUST

Abstract

We review the G measurements with time-of-swing method at HUST. Two independent experiments have been completed and an improved experiment is in progress. The first G value was determined as 6.6699(7)×10^-11 m³ kg^-1 s^-2 with a relative standard uncertainty (u_r) of 105 ppm by using a long period torsion pendulum and two cylindrical source masses. Later, this result was corrected to be 6.6723(9)×10^-11 m³ kg^-1 s^-2 with u_r=130 ppm after considering the density distribution of the cylinders and the air buoyancy, which was 360 ppm larger than the previous value. In 2009, a new experiment by using a simple block pendulum and spherical source masses with more homogeneous density was carried out. A series of improvements were performed, and the G value was determined to be 6.67349(18)×10^-11 m³ kg^-1 s^-2 with u_r=26 ppm. To reduce the anelasticity of the torsion fibre, fused silica fibres with Q's of approximately 5×10⁴ are used to measure G in the ongoing experiment. These fibres are coated with thin layers of germanium and bismuth in turn to reduce the electrostatic effect. Some other improvements include the gravity compensation, reduction of the coating layer effect, etc. The prospective uncertainty of the next G value is 20 ppm or lower.

Keywords: CODATA; gravitational constant G; precision measurement; time-of-swing method; torsion pendulum.

Figure 1.

Seven G values with claimed uncertainties of less than 50 ppm [–10] and CODATA-2010 recommended G value [3].

Figure 2.

Sketch of the two positions of the pendulum and source masses in the time-of-swing method. At the near position, the pendulum's equilibrium position is in line with the centre line of the source masses (a). While at the far position, it is perpendicular (b). (Online version in colour.)

Figure 3.

Schematic of the apparatus used in determining G of HUST-99 (in [11]). (Online version in colour.)

Figure 4.

The schematic diagram of the pendulum system and source masses in HUST-09 G measurement with time-of-swing method (in [8,16]). (Online version in colour.)

Figure 5.

Photos (a,b) show the entire experimental apparatus and the pendulum and source masses in the vacuum chamber, respectively (in [8,16]). (Online version in colour.)