Constraint on the planetary scale value of the Newtonian gravitational constant from the gravity profile within a mine

Abstract

Measurements of gravity down a 950-m vertical line within the mine at Mount Isa, Queensland, are used to estimate the value of the Newtonian gravitational constant $G$ on a geophysical scale. The value obtained is (6.71±0.13)×${10}^{-11\mathrm{}}$ ${\mathrm{m}}^3$ ${\mathrm{kg}}^{-1\mathrm{}}$ ${\sec }^{-2\mathrm{}}$. The assigned uncertainty is the possible (but not probable) systematic error arising from density inhomogeneity and indicated by local variations in gravity gradient, and is several times as large as the formal error of a least-squares fit to the gravity-depth data. A dramatic improvement in accuracy can be anticipated if measurements can be made in a flat-lying sedimentary basin, or even better within the sea in a gravitationally featureless area.