Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback

The Newtonian gravitational constant has still 150 parts per million of uncertainty. This paper examines the linear and nonlinear equations governing the rotational dynamics of the torsion gravitational balance. A nonlinear effect modifying the oscillation period of the torsion gravitational balance is carefully explored.

A precision measurement of the gravitational constant $G$ has been made using a beam balance. Special attention has been given to determining the calibration, the effect of a possible nonlinearity of the balance and the zero-point variation of the balance. The equipment, the measurements and the analysis are described in detail. The value obtained for G is 6.674252(109)(54) 10^{-11} m3 kg-1 s-2. The relative statistical and systematic uncertainties of this result are 16.3 10^...

We determined the Newtonian Constant of Gravitation G by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for G of (6.672 34 +/- 0.000 14) x 10^-11 m^3 kg^-1 s^-2. This value is in good agreement with the 1986 Committee on Data for Science and Technology (CODATA) value of (6.672 59 +/- 0.000 85) x 10^-11 m^3 kg^-1 s^-2 [Rev. Mod. Phys. 59, 1121 (198...

Recent experimental results for the gravitational constant G from Cavendish-type experiments were analysed in the framework of Modified Newtonian Dynamics (MOND). MOND corrections were applied to the equation of motion of a pendulum, under the assumption that the magnitude of the horizontal time dependent gravitational acceleration determines the amount of MOND corrections. The large vertical component of the local gravitational field of the earth is fully compensated by the ...

The torsion pendulum at the heart of the apparatus to measure the gravitational constant, $G$ at the Bureau International des Poids et Mesures (BIPM) is used to measure the gravitational torque between source and test-mass assemblies with two methods. In the Cavendish method, the pendulum moves freely. In the electrostatic-servo method, the pendulum is maintained at a constant angle by applying an electrostatic torque equal and opposite to any gravitational torque on the pend...

An astatized symmetrical vertical pendulum is monitoring torque {\Gamma}(M) resulting of gravitational attractions exerted by two external masses M moving up down. Local gravity field g produce the main pendulum restoring torque combined with a very weak variable torque {\Gamma}(c) induced by rotation of watch needles fixed to the pendulum. Transfer of fundamental units to calibrate the {\Gamma}(c) torques is obtained by a reference torque {\Gamma}({\mu}) resulting of precise...

Newton's gravitational constant G, which determines the strength of gravitational interactions both in Newton's theory and in Einstein's General Relativity, is the least well known of all the fundamental constants. Given its importance, and with recent disparities between experimental measurements, a new approach is suggested. It is based on a purely gravitational oscillator without any non-gravitational restoring forces. The suggested technique is based on the oscillation pe...

In 2006, a final result of a measurement of the gravitational constant $G$ performed by researchers at the University of Z\"urich was published. A value of $G=6.674\,252(122)\times 10^{-11}\,\mbox{m}^3\,\mbox{kg}^{-1}\,\mbox{s}^{-2}$ was obtained after an experimental effort that lasted over one decade. Here, we briefly summarize the measurement and discuss the strengths and weaknesses of this approach.

Many theories which unify gravity with the other known forces of nature predict the existence of an intermediate-range ``fifth force'' similar to gravity. Such a force could be manifest as a deviation from the gravitational inverse-square law. Currently, at distances near $10^{-1}$m, the inverse-square law is known to be correct to about one part per thousand. I present the design of an experiment that will improve this limit by two orders of magnitude. This is accomplished b...

The Newtonian constant of gravitation $G$ historically has the largest relative uncertainty over all other fundamental constants with some discrepancies in values between different measurements. We propose a new scheme to measure $G$ by detecting the position of a test mass in a precision displacement sensor induced by a force modulation from periodically rotating source masses. To seek different kinds of experimental setups, laser interferometers for the gravitational wave d...