Nevertheless, he estimated 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.
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.
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 first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment. ==Definition== According to Newton's law of universal gravitation, the attractive force () between two point-like bodies is directly proportional to the product of their masses ( and ) and inversely proportional to the square of the distance, , between them: F = G\frac{m_1m_2}{r^2} \,. The constant of proportionality, , is the gravitational constant.
In SI units, its value is approximately The modern notation of Newton's law involving was introduced in the 1890s by C.
The use of this constant, and the implied definition of the astronomical unit discussed above, has been deprecated by the IAU since 2012. ==History of measurement== ===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), but is not calculated in his Philosophiæ Naturalis Principia Mathematica where it postulates the inverse-square law of gravitation.
The modern notation involving the constant was introduced by Boys in 1894 and becomes standard by the end of the 1890s, with values usually cited in the cgs system.
The modern notation involving the constant was introduced by Boys in 1894 and becomes standard by the end of the 1890s, with values usually cited in the cgs system.
Heyl (1930) published the value of (relative uncertainty 0.1%), improved to (relative uncertainty 0.045% = 450 ppm) in 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 1,000 ppm) have varied rather broadly, and it is not entirely clear if the uncertainty has been reduced at all since the 1942 measurement.
Heyl (1930) published the value of (relative uncertainty 0.1%), improved to (relative uncertainty 0.045% = 450 ppm) in 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 1,000 ppm) have varied rather broadly, and it is not entirely clear if the uncertainty has been reduced at all since the 1942 measurement.
Establishing a standard value for with a 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 standard uncertainty of 0.046% (460 ppm), lowered to 0.012% (120 ppm) by 1986.
Some measurements published in the 1980s to 2000s were, in fact, mutually exclusive.
Establishing a standard value for with a 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 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 standard uncertainty of 120 ppm published in 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 standard uncertainty of 120 ppm published in 1986.
Some measurements published in the 1980s to 2000s were, in fact, mutually exclusive.
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 standard uncertainty of 120 ppm published in 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 standard uncertainty of 120 ppm published in 1986.
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.
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 standard uncertainty of 120 ppm published in 1986.
Since 2012, the AU is defined as exactly, and the equation can no longer be taken as holding precisely. The quantity —the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter and (also denoted ).
The use of this constant, and the implied definition of the astronomical unit discussed above, has been deprecated by the IAU since 2012. ==History of measurement== ===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), but is not calculated in his Philosophiæ Naturalis Principia Mathematica where it postulates the inverse-square law of gravitation.
was published in 2014 of .
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.
The difference of 2.7σ between the two results suggests there could be sources of error unaccounted for. ==Suggested time-variation== A controversial 2015 study of some previous measurements of , by Anderson et al., suggested that most of the mutually exclusive values in high-precision measurements of G can be explained by a periodic variation.
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.
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