Space probe of the gravitational constant G

Abstract

The empirical Gravitational constant G is of fundamental interest in metrology, Newtonian physics, and the field equations in General Relativity, particle physics, geophysics, and astrophysics. The precise value of G has yet to be known with the desired level of accuracy. In the 233 years since Cavendish, hundreds of experiments sought more accurate results but produced inconsistent results. Although they have had much more advanced supporting technology, past experiments have mostly stayed the same from the Cavendish approach. This paper shows that a different method is feasible to enhance the accuracy of G. A sphere made of metal with a large uniform mass density having a channel through the center with a bead oscillating back and forth in a simple-harmonic fashion. Monitoring the positions of the bead experimentally and comparing the predictions of the channel model will allow refining the value of G. The study develops a gravitational force function for the bead in a channeled sphere to provide more accuracy in the prediction of the bead's motion. This study determines that the best place to perform future gravitation constant experiments is in space far away from interfering effects. A near-perfect place is likely to be in outer space at the Sun-Earth Lagrange point L1, located about 1.5 million kilometers from the Earth on a line toward the Sun where other probes reside. It is estimated that three to six significant figures may be added to the current value of G.