Gauss’s law test of gravity at short range

Abstract

A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2\ensuremath{\sigma}) limit of \ensuremath{\alpha}=(0.9\ifmmode\pm\else\textpm\fi{}4.6)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ at \ensuremath{\lambda}=1.5 m, where \ensuremath{\alpha} and \ensuremath{\lambda} are parameters of the generalized potential \ensuremath{\varphi}=-(GM/r)(1+\ensuremath{\alpha}${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{r}/\ensuremath{\lambda}}$).