Correction of source mass effects in the HUST-99 measurement of $G$

Eccentricities of the mass center from the geometric center of two cylindrical source masses used in the HUST-99 measurement of the Newtonian gravitational constant $G$ are determined by means of an electronic balance. Considering a linear density distribution of source masses as well as the effect of the air buoyancy, our value of $G$ should be revised to be $6.6723(9)\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$, which is 0.036% larger than our previous published value in Phys. Rev. D 59, 042001 (1999).

Figure 1

Apparatus for measuring the eccentricity of the center of mass $C_m$ of the cylinder A from its geometric center $C_g$. An aluminum alloy weighbridge with span $L$ is put on a beam balance and a heavy brass cylinder. The cylindrical source mass A is positioned on the U-shaped notch of the weighbridge with one face against a fixed micrometer gauge.

Figure 2

The value of $M_L$ versus the cylinder relative position $x$. Circle points represent the experimental data, and the solid line represents the linear fitting result of $M_L$ varying with $x$.