Experimental tests of the gravitational inverse-square law for mass separations from 2 to 105 cm

Abstract

We report two experiments which test the inverse-square distance dependence of the Newtonian gravitational force law. One experiment uses a torsion balance consisting of a 60-cm-long copper bar suspended at its midpoint by a tungsten wire, to compare the torque produced by copper masses 105 cm from the balance axis with the torque produced by a copper mass 5 cm from the side of the balance bar, near its end. Defining ${R}_{\mathrm{expt}}$ to be the measured ratio of the torques due to the masses at 105 cm and 5 cm, and ${R}_{\mathrm{Newton}}$ to be the corresponding ratio computed assuming an inverse-square force law, we find \ensuremath{\delta}\ensuremath{\equiv}(${R}_{\mathrm{expt}}$/${R}_{\mathrm{Newton}}$-1)=(1.2 \ifmmode\pm\else\textpm\fi{}7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$. Assuming a force deviating from an inverse-square distance dependence by a factor [1+\ensuremath{\epsilon} lnr(cm)], this result implies \ensuremath{\epsilon}=(0.5 \ifmmode\pm\else\textpm\fi{}2.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$. An earlier experiment, which has been reported previously, is described here in detail. This experiment tested the inverse-square law over a distance range of approximately 2 to 5 cm, by probing the gravitational field inside a steel mass tube using a copper test mass suspended from the end of a torsion balance bar. This experiment yielded a value for the parameter \ensuremath{\epsilon} defined above: \ensuremath{\epsilon}=(1\ifmmode\pm\else\textpm\fi{}7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$. The results of both of these experiments are in good agreement with the Newton- ian prediction. Limits on the strength and range of a Yukawa potential term superimposed on the Newtonian gravitational potential are discussed.