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Fundamental constants

# Measuring big G

Newton's constant, G, which governs the strength of the gravitational attraction between two masses, is difficult to measure accurately. A new set of experiments aims to end 200 years of uncertainty.

Newton's gravitational constant, G, differs from all the other fundamental constants of physics in that there is no complete theory that links gravity to the other forces of nature. Hence there is no definitive relationship between G and the other fundamental constants. It also stands apart in that the accepted uncertainty of 0.15% for G is many orders of magnitude larger than for the other fundamental constants (as given in the 1998 CODATA report1). It is astonishing that 200 years after the famous experiment of Henry Cavendish to 'weigh the Earth' we seem to have improved on his result by only a factor of ten. Now, in Physical Review Letters, Gundlach and Merkowitz2 report a value for G with an uncertainty of about 0.001% — so is G finally becoming respectable?

The measurement of G is simple in theory: take two spherical masses M1 and M2 at a known distance r apart, and measure the gravitational attractive force between them, F=GM1M2/r2. The problem is that the gravitational attraction between any two laboratory-sized masses is simply too small to measure accurately. For example, if we take two 1-kg masses, 10 cm apart, the gravitational attraction between them is about 6×10−9 N. Put another way, if one of the masses is fixed, the acceleration of the other towards it is 6×10−9 m s−2 . Such an acceleration is infinitesimal compared with the local acceleration due to Earth's gravity, g, of 9.8 m s−2.

From the time of Cavendish, the preferred method of measuring G has been the torsion balance, in which the restoring force of a twisted fibre balances the weak gravitational torque (twisting force) produced by the attraction between several test masses and a pendulum suspended at the end of the fibre (Fig. 1, overleaf). This method provides an excellent way of decoupling the gravitational attraction from the effects of g. However, whether G is measured using a torsion balance or any other device, it is necessary to construct test masses whose dimensions and density are known with sufficient accuracy. If spherical or cylindrical masses are used that have perfect geometry, the effects of density variation can be eliminated by random changes in orientation. But this does not work if the geometry is not perfect and, in any case, becomes more difficult with larger masses.

In the absence of any advances in physics linking gravity to the rest of science, there have been no really new methods of measuring G since the time of Cavendish. Despite a flurry of excitement over the 'fifth force' in the 1980s, or apparently strange gravitational effects acting on spinning rotors reported in the 1990s, Newton continues to reign supreme in laboratory gravitation. Nevertheless, measurements of G hold great interest for both cosmology and particle physics; in the latter case it has been suggested that the compact dimensions predicted by 'superstring theory' might show up in the behaviour of G at small (<1 mm) distances3.

The current interest in measuring G was stimulated by the publication4 in 1996 of a value for G that differed by 0.6% from the accepted value given in the previous 1986 CODATA report. To take account of this, the 1998 CODATA report recommends a value for G of 6.673×10−11 m3 kg−1 s−2 with an uncertainty of 0.15%, some ten times worse than in 1986. Whereas the other fundamental constants were more accurately known in 1998 than in 1986, the uncertainty in G increased dramatically. The G community appeared to be going backwards rather than forwards.

Since 1998, several groups around the world have set about measuring G, using a range of different methods. At a symposium held in London in 1998 to celebrate the bicentenary of Cavendish's experiment, reports of eight experiments then under way were presented5, some of which are shown in Fig. 1. The target uncertainty for these experiments is between 0.01% and 0.001%. Mostly preliminary results have been published so far, but all, including the new result of Gundlach and Merkowitz2, are in rough agreement and do not support the controversial 1996 value. This is good news because the different techniques have different sources of error, reducing the likelihood of systematic errors affecting the final result.

But not all the improvements in accuracy have resulted from new techniques — there have also been similar advances in torsion balance experiments6,7,8,9. Gundlach and Merkowitz's result is based on a torsion- balance method that has several advantages over previous experiments. The design eliminates much of the uncertainty resulting from the distribution of the pendulum mass suspended from the torsion fibre (Fig. 1a). If this suspended mass is a thin flat plate, corrections due to the shape, the total mass and the mass distribution of the plate cancel out in the analysis. Using a set of eight spherical test masses, almost all effects resulting from the suspended mass become negligible.

Gundlach and Merkowitz measure the angular acceleration of their suspended mass by rotating the whole system on a turntable. This has the advantage that the torsion wire is never twisted, so the measurement of G is independent of anelasticity in the fibre properties10. The rotation also averages out the effects of local gravity gradients. The result has an uncertainty of 0.001%, well below anything claimed before. But their value for G is 0.024% above the original 1986 CODATA value. Is it right?

The only way we can generate confidence in a result is by having several independent measurements made using different experimental techniques. Agreement has yet to be achieved at the 0.01% level, let alone 0.001%. Although we do not yet have a theoretical prediction for G against which to test the results, a reliable and accurate experimental value is important for testing future theories. The G community awaits with great interest the final results of the other measurements in progress. In the meantime, the result of Gundlach and Merkowitz sets a new standard for all G experiments to match.

## References

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Mohr, P. J. & Taylor, B. N. J. Phys. Chem. Ref. Data 28, 1713–1852 (1999); http://physics.nist.gov/cuu/Constants/index.html

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Gundlach, J. H. & Merkowitz, S. M. Phys. Rev. Lett. 85, 2869–2872 (2000).

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Correspondence to Terry Quinn.

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Quinn, T. Measuring big G. Nature 408, 919–920 (2000). https://doi.org/10.1038/35050187

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