Measurement of Eccentricity of the Centre of Mass from the Geometric Centre of a Sphere

The eccentricity of the centre of mass from the geometric centre of a spherical attracting mass in determining the Newtonian gravitational constant G is tested by means of an electronic balance. The experimental result shows that the eccentricity of the sample is about 0.31 μm with uncertainty of 0.05 μm. Two density distribution models are discussed to estimate the uncertainty to G by the eccentricities of the attracting masses.