New Measurements of $G$ Using the Measurement Standards Laboratory Torsion Balance

This Letter presents the results of a series of measurements of the Newtonian gravitational constant $G$ using the compensated torsion balance developed at the Measurement Standards Laboratory. Since our last published result using the torsion balance in the compensated mode of operation [Meas. Sci. Technol. 10, 439 (1999)], several improvements have been made to reduce the uncertainty in the final result. The new measurements have used both stainless steel and copper large masses. The values of $G$ for the two sets of masses are in good agreement. After combining all of the measurements we get a value of $G=6.67387(0.00027)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{s}}^{-2}$. This new value is 5 parts in ${10}^5$ smaller than our previous published values.

Figure 1

A schematic diagram of the MSL torsion balance. SM, small mass; LM, large masses; T, turntable; A, autocollimator; F, fiber; AB, air bearing; E, electrometer; M, mirror.

Figure 2

The measured values of $dC/d\theta$ for one side of the electrometer for one of the recent measurements of $G$ plotted with $+$’s. Also shown are the values for the same side of the electrometer measured during the 1999 measurement of $G$ (indicated by x’s).

Figure 3

A measurement of the angular variation of the torque to determine the maximum angle.

Figure 4

Recent measurements of $G$. The measurements are (from left to right), the earlier MSL measurements using the compensated torsion balance, the measurements of Gundlach and Merkowitz [2], Quinn et al. [4], Schlamminger et al. [3], and the four current MSL values with their type $A$ uncertainties. The rightmost point is the average value of the current measurements with its type $A$ and type $B$ uncertainties included.