Determination of the gravitational constant with a lake experiment: New constraints for non-Newtonian gravity.

Abstract

The gravitational constant G has been determined at two effective interaction distances 88 m and 112 m, respectively. The 1/${\mathit{r}}^{2}$ dependence of the Newtonian gravitational force law is tested by comparing these results with the currently accepted laboratory determination of G. A high-precision balance was used to measure the weight difference of two 1-kg stainless steel masses as a function of the variable water level of a pumped-storage lake. Water-level changes up to 44 m produced a maximum weight difference of 1390 \ensuremath{\mu}g, which could be measured with a resolution of 0.5 \ensuremath{\mu}g. The difference measurement was carried out to diminish several systematic effects; e.g., tides and balance drifts become negligible. Basically, the measurement directly yields the gravitational interaction between the test masses and the locally moved mass (water and air). Data of weight difference and water level were recorded over several months of the last three years. They yield values for G of (6.669\ifmmode\pm\else\textpm\fi{}0.005)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ ${\mathrm{m}}^{3}$ ${\mathrm{kg}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}2}$ at 112 m and (6.678\ifmmode\pm\else\textpm\fi{}0.007)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ ${\mathrm{m}}^{3}$ ${\mathrm{kg}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}2}$ at 88 m, both in agreement with laboratory determinations. New constraints on the strength and range of a composition-independent fifth force are set.