Null Test of the Gravitational Inverse Square Law

Abstract

An experiment has been performed to demonstrate a new source-independent null test of the inverse square law of gravitation. A single-axis superconducting gravity gradiometer was rotated into three orthogonal orientations to measure the Laplacian of the gravitational potential produced by a 1600-kg lead pendulum at an average distance of 2.3 m. The result is that if one assumes a potential of the form $\varphi \left(\mathcal{r}\right)=-\left(\frac{\mathrm{GM}}{\mathcal{r}}\right)[1+\alpha \exp (-\mu \mathcal{r}\left)\right]$, the value of $\alpha$ is + 0.024±0.036 at ${\mu }^{-1\mathrm{}}=1\mathrm{}$ m.