Gravity in minesmdashAn investigation of Newton's law.

Abstract

The evidence that the value of the Newtonian gravitational constant G inferred from measurements of gravity g in mines and boreholes is of order 1% higher than the laboratory value is hardened with new and improved data from two mines in northwest Queensland. Surface-gravity surveys and more than 14 000 bore-core density values have been used to establish density structures for the mines, permitting full three-dimensional inversion to obtain G. Further constraint is imposed by requiring that the density structure give the same value of G for several vertical profiles of g, separated by hundreds of meters. The only residual doubt arises from the possibility of bias by an anomalous regional gravity gradient. Neither measurements of gravity gradient above ground level (in tall chimneys) nor surface surveys are yet adequate to remove this doubt, but the coincidence of conclusions derived from mine data obtained in different parts of the world makes such an anomaly appear an improbable explanation. If Newton's law is modified by adding a Yukawa term to the gravitational potential of a point mass m at distance r, V=-(${G}_{\ensuremath{\infty}}$m/r)(1+\ensuremath{\alpha}${e}^{\mathrm{\ensuremath{-}}r/\ensuremath{\lambda}}$), then the mine data provide a mutual constraint on the values of \ensuremath{\alpha} and \ensuremath{\lambda}, although they cannot be determined independently. Our results give \ensuremath{\alpha}\ensuremath{\approxeq}-0.0075 if \ensuremath{\lambda}\ensuremath{\le}200 m and \ensuremath{\alpha}\ensuremath{\approxeq}-0.014 if \ensuremath{\lambda}\ensuremath{\ge}${10}^{4}$ m, with intermediate values of \ensuremath{\alpha} between these ranges, but values greater than \ensuremath{\alpha}=-0.010, \ensuremath{\lambda}=800 m appear to be disallowed by a comparison of satellite and land-surface estimates of gravity. Gravity experiments over a range of several kilometers are needed for a better constraint. Recent consideration of the E\"otv\"os experiment in terms of a short-range force dependent upon the nuclear mass defect invites plans for similar experiments at sites where extreme topography ensures that the short-range force is directed at a substantial angle to normal gravity.