Application of internal gravitational field equations to geophysical measurement of G

Abstract

We present the spherical harmonic equation for the gravitational potential inside the Earth. The equation satisfies Poisson's equation and converges uniformly. It obviates the need for downward continuation of the exterior potential with its attendant convergence difficulties but of course requires some knowledge of the Earth's density distribution. Equipped with the equation, we derive the general expression for the geophysical measurement of the gravitational constant G made inside the Earth, such as in boreholes and mine shafts. We also present numerical evidence that the long‐ to intermediate‐wavelength gravity anomalies can masquerade as the “fifth force” if not properly corrected for.