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Measurement of "G".

Determination of Newton’s constant of Gravitation.

Contact C. C. Speake

Research at the International Bureau of Weights and Measures in France (BIPM) into the fundamental limitations to the resolution of force measurements due to anelasticity led to the development of a ‘torsion-strip’ balance (see Meas Sci Technol 10 430-234 1999 for a review). We rediscovered that the restoring torque of a strip, whose thickness is much less than its width, is essentially determined by the weight of the suspended torsion bob rather than the elastic properties of the material from which the strip is made. This observation allowed us to design a determination of Newton’s constant of gravitation with the following features:

·      A four test mass configuration, rather than the usual 2-mass dumbell, to give much reduced sensitivity to external gravitational perturbations. The torque due to a point source mass falls off as the inverse fifth power of distance rather than the 3rd power for the 2-mass case.

·      The torsion strip has a restoring torque that is 96% gravitational. This gives the balance a quality factor of 3x105. The ringdown time is about 5 months.

·      The test masses weigh approximately 1.2 kg. Four source masses of approximately 12kg are mounted on a carousel and generate a gravitational signal torque of approximately 3x10-5 Nm. This torque is some 4 orders of magnitude larger than employed by other G determinations that use classical torsion fibres.

·      We can use the torsion-strip balance in 3 modes. The first method is that first implemented by Henry Cavendish in 1798, where the deflection of the balance is readout using an autocollimator. Accurate timing of the period of oscillation together with a calculation of the moment of inertia of the bob are used to determine G. The torsion strip design effectively eliminates the effects of anelasticity on this measurement. In the second method the force of gravity is measured (servoed) against the torque due to electrostatic actuators. The actuators have a novel geometry such that their capacitance varies linearly with the angular displacement. This slope is determined using a three terminal technique and an accurate Andeen-Hagerling capacitance bridge together with accurate measurement of angular motion using an Elcomat autocollimator. The third method uses the change in the oscillation period of the torsion balance as the source masses add or subtract from the restoring torque of the torsion strip.

·      The complete apparatus is mounted on a Coordinate Measuring Machine that enables the relative positions of the masses to be determined with sub-micrometer accuracy.

We published results from the Cavendish and the Servo methods in 2001 (Phys Rev Letts 87 111101-1 September 2001). The combined result for Newton’s constant for the 2 methods was 6.667559(67)x10-11 m3kg-1s-2 (a relative accuracy of 41ppm). This number differed by 200ppm from the result of Gundlach and Merkowitz. We have rebuilt the apparatus and we are now performing another determination of G to cast light on the discrepancy

Figure showing the Torsion strip balance at BIPM that was used for the 2001

determination of G.