Determination of the Newtonian Gravitational Constant $G$ with Time-of-Swing Method

We present a new value of the Newtonian gravitational constant $G$ by using the time-of-swing method. Several improvements greatly reduce the uncertainties: (1) measuring the anelasticity of the fiber directly; (2) using spherical source masses minimizes the effects of density inhomogeneity and eccentricities; (3) using a quartz block pendulum simplifies its vibration modes and minimizes the uncertainty of inertial moment; (4) setting the pendulum and source masses both in a vacuum chamber reduces the error of measuring the relative positions. By two individual experiments, we obtain $G=6.67349(18)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$ with a standard uncertainty of about 2.6 parts in ${10}^5$.

Figure 1

Schematic view of the pendulum system used to measure $G$ by time-of-swing method. The directions ($X,Y,Z$) used in text were also defined in this figure.

Figure 2

Periods of the ten sets of experimental data extracted by the correlative method with uncertainty of $\sim 0.01\mathrm{ms}$. After being corrected by the thermoelastic and nonlinear properties of the fiber and the gravitational nonlinearity of the source masses, the slopes of the two dashed lines, representing the linear drifts of the pendulum’s periods at near and far positions, are almost same. The “$A\mathrm{\text{−}}B\mathrm{\text{−}}A$” method is also shown in the figure.

Figure 3

A comparison of this work with others of uncertainties within 50 ppm [3] and the CODATA recommended values [1].