This Letter describes new work on the determination of the Newtonian constant of gravitation, G, carried out at the BIPM since publication of the first results in 2001. The apparatus has been completely rebuilt and extensive tests carried out on the key parameters needed to produce a new value for G. The basic principles of the experiment remain the same, namely a torsion balance suspended from a wide, thin Cu-Be strip with two modes of operation, free deflection (Cavendish) and electrostatic servo control. The result from the new work is: G=6.67545(18)×10(-11)  m3 kg(-1) s(-2) with a standard uncertainty of 27 ppm. This is 21 ppm below our 2001 result but 241 ppm above The CODATA 2010 value, which has an assigned uncertainty of 120 ppm. This confirms the discrepancy of our results with the CODATA value and highlights the wide divergence that now exists in recent values of G. The many changes made to the apparatus lead to the formal correlation between our two results being close to zero. Being statistically independent and statistically consistent, the two results taken together provide a unique contribution to determinations of G.

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) × 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) × 10 −11 m 3 kg −1 s −2 [Rev. Mod. Phys. 59, 1121(1987 but differs from some more recent determinations as well as the latest CODATA recommendation of (6.674 28 ± 0.000 67) × 10 −11 m 3 kg −1 s −2 [Rev. Mod. Phys. 80, 633 (2008)].

Three errors appeared in our recent publication of the BIPM G result. Two affect our result by less than 10 ppm, but one is more significant and together they increase our value of G by 13 ppm.The more significant error concerns the effect of density gradients in the source masses which was inadvertently applied twice. In our Letter, we quote the magnitude of the effect as −32, −0.4, and þ36 ppm depending on the orientation of the source masses. These figures come from analytical expressions given in Ref. [1]. For the 2013 result, more accurate values were obtained by including them in the numerical calculation of the gravitational coupling, they were found to be −22, þ2, and þ26 ppm. The orientation of the source masses was such that for the servo result the effect was −22 ppm and the Cavendish þ2 ppm. Unfortunately, in the final calculation of G an additional correction of −32 ppm was added to the Cavendish value; i.e., the effects of density gradients were included twice and also to the result where the effect was actually smallest. To correct this, the Cavendish value should be increased by 32 ppm. The two small errors are:(a) A correction of −13 ppm made to the Cavendish result, which was assigned an uncertainty of 4 ppm in Table 1 of the Letter, has been recalculated and it should now be −6 ppm with an uncertainty of 6 ppm. To correct this, the Cavendish result should be increased by 7 ppm.(b) A correction of þ8 ppm included in the calculation for G in both servo and Cavendish methods for an offset in the alignment of the source masses with respect to that of the test masses should not exist because the alignment procedure eliminates such a misalignment. To correct this, the results of both should be reduced by 8 ppm.Also, a more accurate accounting for thermal effects in the dimensional metrology has decreased the correlation coefficient from −0.58 to −0.63; this has in turn reduced the uncertainty on the final value of G from 27 to 25 ppm without changing its value.The net result of these changes is that we must increase the Cavendish result by 31 ppm and reduce the servo by 8 ppm. We thus find for the Cavendish method G ¼ 6.67586ð36Þ × 10 −11 kg −1 m 3 s −2 (54 ppm) and for the servo 6.67515ð41Þ × 10 −11 kg −1 m 3 s −2 (61 ppm). The weighted average is G ¼ 6.67554ð16Þ × 10 −11 kg −1 m 3 s −2 (25 ppm). This is 13 ppm above our published result in the Letter. The difference between the Cavendish and servo results becomes 106 ppm, still compatible with the uncertainty of the difference, namely, 104 ppm.A detailed description of the experiment, which includes the above errata, has been accepted for publication [2].[1] T.

in which we presented the results of the two BIPM determinations of the Newtonian constant of gravitation G. While this review contains no new results, it includes more detailed descriptions of certain key parameters that enter into the determination of G. Following a description of the overall method and the two versions of the experiment, we discuss the properties of the torsion strip, including the effects of anelasticity, then the electrostatic torque transducer, the source and test masses, dimensional metrology, angle measurement, the calculation and measurement of the moment of inertia, calculation of the torque, possible magnetic interactions and finally we discuss uncertainties and correlations in the derivation of a value for G.