Abstract The Newtonian gravitational constant G is one of the most fundamental constants in nature. In the measurement of G with the angular acceleration feedback (AAF) method, the largest error comes from the distances between the geometric centers (GC) of the source masses. In the on-going experiment, the silicon spheres with a more homogeneous density are used as the source masses. Here a scheme of measuring the GC distances between the silicon spheres with the laser interferometer is proposed. The measurement principle is analyzed in detail, and the error sources, such as the laser, the sphere, the alignment of optical path, and the environment are evaluated in detail. With this method, the horizontal and vertical GC distances can be measured with uncertainties of 11 nm and 9 nm, respectively. The simulation with the ZEMAX software is performed to verify the theoretical model of measuring the GC distance, where the maximum deviation of the distance between the simulation result and the theoretical one is only -2.7 nm. When the sphericities of the four silicon spheres are at the level of 0.1 m, the uncertainty of each GC distance after considering the sphericity is about 0.1 m, corresponds to a combined uncertainty of 0.6 ppm for the G measurement with the AAF method. This provides an effective method to reduce the measurement uncertainty of GC distance, and makes it possible to measure G with a higher precision.
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