G

For the unit of acceleration, see G.

The gravitational constant, or Newtonian constant of gravitation. The constant of proportionality in Newton’s equation describing the force of attraction between two bodies. It is equal to the force of attraction due to gravity between any two bodies, times the square of the distance between their centers of mass, divided by the product of their masses.

Of all the fundamental constants, the value of G is known with the least precision. In 1970 Taylor remarked on “the fact that a precise value of G is irrelevant for most of physics.”¹

Source Value (× 10⁻¹¹ m³·kg⁻¹·s⁻²)
2010 CODATA Recommended Values of the Fundamental Constants 6.673 84;
standard uncertainty of 0.000 80
IAU (1976) System of Astronomical Constants 6.672
1986 Recommended Values of the Fundamental Constants 6.67259(85);
relative uncertainty of 128 parts per million
Mark P. Fitzgerald et al, Measurement Standards Laboratory, Lower Hutt, New Zealand. 6.6656(6)
Gabriel G. Luther et al, Los Alamos National Laboratory, New Mexico.  
Hinrich Meyer et al, University of Wuppertal, Germany. 6.6685
Winfried Michaelis et al, Physikalisch-Technische Bundesanstalt, Braunsweig, Germany. 6.71540

For the most recent accepted value for this constant, look under "Newtonian constant of gravitation" at  www.physics.nist.gov/cuu/Constants/index.html

1. B. N. Taylor.
Report on the International Conference on Precision Measurement and Fundamental Constants.
Metrologia, vol 7, no 1, 1971.
Page 42.

The 2018 measurements

In 2018 physicists reported the most precise measurements yet made, using two different methods. The results were “6.674184 × 10⁻¹¹ and 6.674484 × 10⁻¹¹ cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively.”¹

1. Qing Li, Chao Xue, Jian-Ping Liu, Jun-Fei Wu, Shan-Qing Yang, Cheng-Gang Shao, Li-Di Quan, Wen-Hai Tan, Liang-Cheng Tu, Qi Liu, Hao Xu, Lin-Xia Liu, Qing-Lan Wang, Zhong-Kun Hu, Ze-Bing Zhou, Peng-Shun Luo, Shu-Chao Wu, Vadim Milyukov and Jun Luo.
Measurements of the gravitational constant using two independent methods.
Nature, 560, pages 582–588 (2018).

Some commentary:

Hamish Johnston.
Gravitational-constant mystery deepens with new precision measurements.
Physics World, 30 Aug 2018.
https://physicsworld.com/a/gravitational-constant-mystery-deepens-with-new-precision-measurements

Stephan Schlamminger.
Gravity measured with record precision.
Nature 560, 562-563 (29 August 2018)
doi: 10.1038/d41586-018-06028-6

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