The missing measurements of the gravitational constant

Abstract

In 1998, two centuries after Cavendish, a conference on theory and experiment of the G measurement pointed out the progress made in various experimental methods and discussed the effects on the accuracy of G. In spite of several measurements with torsion balance in vacuum to the aim of reducing some disturbances, no mention was made about a possible pressure effect in calm air. In 2000 J.Luo and Z.K.Hu firstly denounced the presence of some unknown systematic problem on G measurement. In the present work a new systematic error is analysed which arises from the non-zero balance of the overall momentum discharged by the air molecules upon the test mass within the vacuum chamber. This effect is normally negligible, but when the pressure is so low that the molecule mean free path is comparable to the thickness of the air meatus surrounding the test mass, the drawing force may become greater than the gravitational force. Considering the usual size of the meatus, the molecular effect becomes maximum when the pressure drops to about 0.01milli bar. Before Heyl measurement at 1 millibar (1927), the experiments were made at higher pressures. Conversely those made with recent vacuum techniques show pressures down to 0.1 nanobar (Gundlach and Merkowitz, 2000) and 0.01 nanobar (Gershteyn, 2002). In these experiments the effect of the vacuum pressure appears very little. As a matter of fact, we were not able to find in the literature some measurements made at vacuum pressures between the millibar and the nanobar. Why ? This lack appears embarrassing in absence of an adequate physical explanation.