Experimental test of a spatial variation of Newtonian gravitational constant at large distance

Abstract

The Poisson equation of Newtonian gravitational potential provides a source-independent null test of the Inverse Square Law. A convenient Laplacian detector consists of superconducting gravity gradiometers in three orthogonal directions. Matching and stability of the cryogenic detector are achieved by utilizing superconducting circuits. Since the Laplacian of the gravitational potential produced by an arbitrary source is zero outside the source in the Inverse Square Law, this experiment becomes a source-independent null test for the constancy of the gravitational constant. This characteristic allows a precision test of the Inverse Square Law at geological distances using natural objects like an ocean or the earth. We discuss experimental procedures and expected sensitivities of the null experiment for three different sources: a swinging pendulum, an ocean tide, and the earth itself. It appears that the empirical limits in the Inverse Square Law could be improved by three to six orders of magnitude in the range between 1 m and 10^ km by this new null experiment.