On determining G using a cryogenic torsion pendulum

A measurement of G which will use a torsion pendulum in the 'dynamic' (time -of-swing) mode, measuring the influence of field source masses on the pend ulum's oscillation period, is being prepared at UC Irvine. Features of the design include: (i) operation at cryogenic temperature (2 K) to reduce ther mal noise and increase frequency stability and for ease of magnetic shieldi ng, (ii) large pendulum oscillation amplitudes to increase signal-to-noise ratio and reduce the effect of amplitude-determination error (iii) use of a pair of source mass rings to produce an extremely uniform field gradient; and (iv) use of a thin quartz plate as a torsion pendulum to minimize sensi tivity to pendulum density inhomogeneity and dimensional uncertainties. The 'dynamic' method to be used has the great advantage of requiring no angula r displacement measurement or calibrating force, but, as pointed out by Kur oda, the method is subject to systematic error associated with the anelasti c properties of a torsion fibre. We demonstrate that, for the linear anelas ticity discussed by Kuroda, the fractional error introduced by anelasticity in such measurements of G is bounded by 0 less than or equal to delta G/G less than or equal to 1/2 Q(-1), where Q is the torsional oscillation quali ty factor of the pendulum. We report detailed studies of anelasticity in ca ndidate fibre materials at low temperature, concluding that anelastic behav iour should not limit our G measurement at a level of a few ppm.