New null experiment to test the inverse square law of gravitation

A ''source-independent'' null experiment for the Newtonian law of gravity is proposed. The new scheme involves detection of the Laplacian of the gravitational potential del2phi (r) in free space, i.e., where rho (r) < 0. This quantity should vanish identically regardless of the mass distribution in the rest of the universe if the inverse square law is exact. A departure from null in del2phi (r) could be measured by monitoring the breathing mode of a sphere or by summing three gravity gradients at a single point along any three orthogonal directions. The ''source-independent'' behavior of the proposed technique will allow a test of the inverse square law in the intermediate range between 1 m and 10 km in which large geological objects might be used as sources