A new precise determination of Newton's gravitational constant

Abstract

A new determination of the numerical value of the gravitational constant G was carried out by means of an apparatus consisting of a fibreless torsion balance which was carried by the buoyancy of a floater in a liquid; the angular deflection of the balance was compensated with the aid of a control loop and an electrostatic torque transmitter; the reacting bodies were cylinders. The result obtained for G differs from the CODATA value by about +6 × 10-3 in relative value. No dependence on the materials or on the distance between the cylinders was found. The apparatus is described, the methods of evaluation and the results are reported, the possible sources of errors are discussed.

The search for Newton’s constant

“…10 Michaelis and his colleagues used a novel torsion balance in which the test masses were floated in a mercury bath rather than hung from a wire. Instead of measuring the displacement or change in period due to the gravitational pull of nearby source masses, the researchers used feedback control to apply an electrostatic torque just strong enough to hold the test masses in place (see figure 2c).…”

Status of the experiments on measurement of the Newtonian gravitational constant

“…These results are partly summarized in Table. Nevertheless, the discrepancies between the values of the gravitational constant obtained in these experiments remained large enough. In particular, the value of G = 6.7146 obtained in the Physikalish Technische Bundesanstalt (Germany) [6], was more than by 40 standard deviations (i.e., more than 5000 ppm) above the value of G recommended by CODATA in 1986. As a result of such a scatter of G values, CODATA had to increase the uncertainty significantly and in 1998 recommended the value G = (6.673 ± 0.010) × 10 −11 m 3 kg −1 s −2 [11], with a relative error of 1500 ppm.…”

“…Oscillations in the torsion degree of freedom are described by Eq. (6). The terms in the right-hand side of this equation are nonlinear combinations of random quasi-harmonic swing modes.…”

The curious case of the gravitational constant

“…But then an experiment in 1995, shockingly, came up with a value for G that differed from the accepted value by 0.7%, in addition to causing a 12-fold increase in its uncertainty (4).…”