Early history The existence of the constant is implied in
Newton's law of universal gravitation as published in the 1680s (although its notation as dates to the 1890s), Nevertheless, he had the opportunity to estimate the order of magnitude of the constant when he surmised that "the mean density of the earth might be five or six times as great as the density of water", which is equivalent to a gravitational constant of the order: : ≈ A measurement was attempted in 1738 by
Pierre Bouguer and
Charles Marie de La Condamine in their "
Peruvian expedition". Bouguer downplayed the significance of their results in 1740, suggesting that the experiment had at least proved that the Earth could not be a
hollow shell, as some thinkers of the day, including
Edmond Halley, had suggested. The
Schiehallion experiment, proposed in 1772 and completed in 1776, was the first successful measurement of the mean density of the Earth, and thus indirectly of the gravitational constant. The result reported by
Charles Hutton (1778) suggested a density of (4.5 times the density of water), about 20% below the modern value. This immediately led to estimates on the densities and masses of the
Sun,
Moon and
planets, sent by Hutton to
Jérôme Lalande for inclusion in his planetary tables. As discussed above, establishing the average density of Earth is equivalent to measuring the gravitational constant, given
Earth's mean radius and the
mean gravitational acceleration at Earth's surface, by setting G = g\frac{R_\oplus^2}{M_\oplus} = \frac{3g}{4\pi R_\oplus\rho_\oplus}. Based on this, Hutton's 1778 result is equivalent to . performed by
Henry Cavendish in 1798, to measure G, with the help of a pulley, large balls hung from a frame were rotated into position next to the small balls. The first direct measurement of gravitational attraction between two bodies in the laboratory was performed in 1798, seventy-one years after Newton's death, by Henry Cavendish. He determined a value for implicitly, using a
torsion balance invented by the geologist Rev.
John Michell (1753). He used a horizontal
torsion beam with lead balls whose inertia (in relation to the torsion constant) he could tell by timing the beam's oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused. In spite of the experimental design being due to Michell, the experiment is now known as the Cavendish experiment for its first successful execution by Cavendish. Cavendish's stated aim was the "weighing of Earth", that is, determining the average density of Earth and the
Earth's mass. His result, , corresponds to value of . It is remarkably accurate, being about 1% above the modern
CODATA recommended value , consistent with the claimed relative standard uncertainty of 0.6%.
19th century The accuracy of the measured value of has increased only modestly since the original Cavendish experiment. is quite difficult to measure because gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies. Measurements with pendulums were made by
Francesco Carlini (1821, ),
Edward Sabine (1827, ), Carlo Ignazio Giulio (1841, ) and
George Biddell Airy (1854, ). Cavendish's experiment was first repeated by
Ferdinand Reich (1838, 1842, 1853), who found a value of , less accurate than Cavendish's result, differing from the modern value by 1.5%. Cornu and Baille (1873), found . Cavendish's experiment proved to result in more reliable measurements than pendulum experiments of the "Schiehallion" (deflection) type or "Peruvian" (period as a function of altitude) type. Pendulum experiments still continued to be performed, by
Robert von Sterneck (1883, results between ) and
Thomas Corwin Mendenhall (1880, ). Cavendish's result was first improved upon by
John Henry Poynting (1891), who published a value of , differing from the modern value by 0.2%, but compatible with the modern value within the cited relative standard uncertainty of 0.55%. In addition to Poynting, measurements were made by
C. V. Boys (1895) and
Carl Braun (1897), with compatible results suggesting = . The modern notation involving the constant was introduced by Boys in 1894
Arthur Stanley Mackenzie in
The Laws of Gravitation (1899) reviews the work done in the 19th century. Poynting is the author of the article "Gravitation" in the
Encyclopædia Britannica Eleventh Edition (1911). Here, he cites a value of = with a relative uncertainty of 0.2%.
Modern value Paul R. Heyl (1930) published the value of (relative uncertainty 0.1%), improved to (relative uncertainty 0.045% = 450 ppm) in 1942. However, Heyl used the statistical spread as his standard deviation, and he admitted himself that measurements using the same material yielded very similar results while measurements using different materials yielded vastly different results. He spent the next 12 years after his 1930 paper to do more precise measurements, hoping that the composition-dependent effect would go away, but it did not, as he noted in his final paper from the year 1942. Published values of derived from high-precision measurements since the 1950s have remained compatible with Heyl (1930), but within the relative uncertainty of about 0.1% (or 1000 ppm) have varied rather broadly, and it is not entirely clear whether the uncertainty has been reduced at all since the 1942 measurement. Some measurements published in the 1980s to 2000s were, in fact, mutually exclusive. Establishing a standard value for with a relative standard uncertainty better than 0.1% has therefore remained rather speculative. By 1969, the value recommended by the
National Institute of Standards and Technology (NIST) was cited with a relative standard uncertainty of 0.046% (460 ppm), lowered to 0.012% (120 ppm) by 1986. But the continued publication of conflicting measurements led NIST to considerably increase the standard uncertainty in the 1998 recommended value, by a factor of 12, to a standard uncertainty of 0.15%, larger than the one given by Heyl (1930). The uncertainty was again lowered in 2002 and 2006, but once again raised, by a more conservative 20%, in 2010, matching the relative standard uncertainty of 120 ppm published in 1986. For the 2014 update, CODATA reduced the uncertainty to 46 ppm, less than half the 2010 value, and one order of magnitude below the 1969 recommendation. The following table shows the NIST recommended values published since 1969: In the January 2007 issue of
Science, Fixler et al. described a measurement of the gravitational constant by a new technique,
atom interferometry, reporting a value of , 0.28% (2800 ppm) higher than the 2006 CODATA value. An improved cold atom measurement by Rosi et al. was published in 2014 of . Although much closer to the accepted value (suggesting that the Fixler
et al. measurement was erroneous), this result was 325 ppm below the recommended 2014 CODATA value, with non-overlapping
standard uncertainty intervals. As of 2018, efforts to re-evaluate the conflicting results of measurements are underway, coordinated by NIST, notably a repetition of the experiments reported by Quinn et al. (2013). In August 2018, a Chinese research group announced new measurements based on torsion balances, and based on two different methods. These are claimed as the most accurate measurements ever made, with standard uncertainties cited as low as 12 ppm. The difference of 2.7
σ between the two results suggests there could be sources of error unaccounted for. == Constancy ==