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 $\ensuremath{\phi}(\mathcal{r})=\ensuremath{-}(\frac{\mathrm{GM}}{\mathcal{r}})[1+\ensuremath{\alpha}\mathrm{exp}(\ensuremath{-}\ensuremath{\mu}\mathcal{r})]$, the value of $\ensuremath{\alpha}$ is + 0.024\ifmmode\pm\else\textpm\fi{}0.036 at ${\ensuremath{\mu}}^{\ensuremath{-}1}=1$ m.