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Physical abiding relating the gravitational strength betwixt objects to their mass and distance

Notations for the gravitational constant

Values of 1000	Units
six.67430(15)×x−11 [one]	N m2⋅kg–2
6.67430(15)×ten−8	dyne cm2⋅yard–2
iv.30091(25)×ten−3	pc⋅M ⊙ –i⋅(km/s)2

The gravitational abiding (also known as the universal gravitational abiding, the Newtonian constant of gravitation, or the Cavendish gravitational constant),^[a] denoted past the majuscule letter K , is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton'south police of universal gravitation and in Albert Einstein's general theory of relativity.

In Newton's law, information technology is the proportionality constant connecting the gravitational force betwixt two bodies with the production of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (too referred to as the stress–energy tensor).

The measured value of the abiding is known with some certainty to four significant digits. In SI units, its value is approximately six.674×x⁻¹¹ yard^three⋅kg⁻¹⋅southward⁻² .^[1]

The modern annotation of Newton'south police involving G was introduced in the 1890s by C. V. Boys. The offset implicit measurement with an accuracy within about ane% is attributed to Henry Cavendish in a 1798 experiment.^[b]

Definition [edit]

Co-ordinate to Newton's law of universal gravitation, the attractive forcefulness ( F ) between two signal-like bodies is directly proportional to the product of their masses ( 1000 _one and m ₂ ) and inversely proportional to the foursquare of the distance, r , between their centers of mass.:

$${\displaystyle F=G{\frac {m_{1}m_{two}}{r^{2}}}.}$$

The constant of proportionality, G , is the gravitational abiding. Colloquially, the gravitational constant is also chosen "Large G", distinct from "small one thousand" ( g ), which is the local gravitational field of Earth (equivalent to the gratis-fall acceleration).^{[2] [three]} Where ${\displaystyle M_{\oplus }}$ is the mass of the Earth and ${\displaystyle r_{\oplus }}$ is the radius of the Earth, the two quantities are related by:

$${\displaystyle k={\frac {GM_{\oplus }}{r_{\oplus }^{two}}}.}$$

The gravitational constant appears in the Einstein field equations of full general relativity,^{[4] [5]}

$${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }\,,}$$

where M _μν is the Einstein tensor, Λ is the cosmological constant, 1000_μν is the metric tensor, T_μν is the stress–energy tensor, and κ is a constant originally introduced past Einstein that is directly related to the Newtonian constant of gravitation:^{[5] [half dozen] [c]}

$${\displaystyle \kappa ={\frac {8\pi Yard}{c^{two}}}\approx 1.866\times ten^{-26}\mathrm {\,m{\cdot }kg^{-i}} .}$$

Value and incertitude [edit]

The gravitational constant is a concrete constant that is difficult to measure with high accuracy.^[7] This is because the gravitational strength is an extremely weak force as compared to other fundamental forces.^[d]

In SI units, the 2018 CODATA-recommended value of the gravitational constant (with standard doubtfulness in parentheses) is:^{[1] [8]}

$${\displaystyle G=6.67430(15)\times x^{-eleven}{\rm {\ thousand^{3}{\cdot }kg^{-1}{\cdot }s^{-2}}}}$$

This corresponds to a relative standard uncertainty of 2.two×ten⁻⁵ (22 ppm).

Natural units [edit]

The gravitational abiding is a defining abiding in some systems of natural units, particularly geometrized unit systems, such as Planck units and Stoney units. When expressed in terms of such units, the value of the gravitational constant will generally have a numeric value of 1 or a value shut to it. Due to the significant dubiousness in the measured value of Chiliad in terms of other known key constants, a similar level of incertitude will show upwards in the value of many quantities when expressed in such a unit system.

Orbital mechanics [edit]

In astrophysics, information technology is convenient to mensurate distances in parsecs (pc), velocities in kilometres per second (km/south) and masses in solar units M _⊙ . In these units, the gravitational constant is:

$${\displaystyle G\approx 4.3009\times 10^{-3}{\rm {}}{\frac {pc}{M_{\odot }}}{\rm {\ (km/s)^{2}}}.\,}$$

For situations where tides are important, the relevant length scales are solar radii rather than parsecs. In these units, the gravitational constant is:

$${\displaystyle G\approx i.90809\times 10^{five}R_{\odot }M_{\odot }^{-1}{\rm {\ (km/south)^{2}}}.\,}$$

In orbital mechanics, the menstruation P of an object in round orbit around a spherical object obeys

$${\displaystyle GM={\frac {3\pi Five}{P^{two}}}}$$

where 5 is the volume inside the radius of the orbit. It follows that

${\displaystyle P^{2}={\frac {three\pi }{G}}{\frac {V}{Yard}}\approx 10.896\ \mathrm {h^{2}{\cdot }yard{\cdot }cm^{-3}} {\frac {5}{K}}.}$

This way of expressing 1000 shows the relationship between the average density of a planet and the period of a satellite orbiting just above its surface.

For elliptical orbits, applying Kepler'due south tertiary law, expressed in units feature of Earth'south orbit:

${\displaystyle K=4\pi ^{ii}{\rm {\ AU^{3}{\cdot }yr^{-ii}}}\ M^{-1}\approx 39.478{\rm {\ AU^{iii}{\cdot }yr^{-2}}}\ M_{\odot }^{-ane},}$

where distance is measured in terms of the semi-major axis of Earth's orbit (the astronomical unit of measurement, AU), time in years, and mass in the full mass of the orbiting system ( M = Thou _☉ + M _Globe + K _☾ ^{[due east]}).

The above equation is exact only within the approximation of the Earth's orbit around the Sun as a two-torso problem in Newtonian mechanics, the measured quantities comprise corrections from the perturbations from other bodies in the solar arrangement and from general relativity.

From 1964 until 2012, however, it was used as the definition of the astronomical unit and thus held past definition:

$${\displaystyle i\ \mathrm {AU} =\left({\frac {GM}{four\pi ^{2}}}{\rm {twelvemonth}}^{2}\right)^{\frac {1}{iii}}\approx 1.495979\times 10^{11}{\rm {m}}.}$$

Since 2012, the AU is defined every bit 1.495978 707 ×10¹¹ grand exactly, and the equation can no longer be taken as holding precisely.

The quantity GM —the product of the gravitational abiding and the mass of a given astronomical body such every bit the Sun or Earth—is known as the standard gravitational parameter (also denoted μ ). The standard gravitational parameter GM appears as above in Newton's law of universal gravitation, likewise every bit in formulas for the deflection of light caused past gravitational lensing, in Kepler'due south laws of planetary motion, and in the formula for escape velocity.

This quantity gives a convenient simplification of diverse gravity-related formulas. The product GM is known much more accurately than either gene is.

Values for GM

Trunk	μ = GM	Value	Relative uncertainty
Dominicus	1000 M ☉	one.327124 400 18(8)×10twenty m3⋅s−two [nine]	6×ten−11
Earth	G M Earth	iii.986004 418(8)×1014 grand3⋅due south−ii [10]	2×10−9

Calculations in celestial mechanics can besides be carried out using the units of solar masses, mean solar days and astronomical units rather than standard SI units. For this purpose, the Gaussian gravitational constant was historically in widespread apply, grand = 0.017202 098 95 , expressing the mean angular velocity of the Lord's day–Earth organisation measured in radians per twenty-four hour period.^{[ citation needed ]} The use of this abiding, and the implied definition of the astronomical unit of measurement discussed in a higher place, has been deprecated past the IAU since 2012.^{[ citation needed ]}

History of measurement [edit]

Early history [edit]

The existence of the abiding is unsaid in Newton'southward law of universal gravitation as published in the 1680s (although its notation as G dates to the 1890s),^[11] but is non calculated in his Philosophiæ Naturalis Principia Mathematica where it postulates the inverse-square constabulary of gravitation. In the Principia, Newton considered the possibility of measuring gravity's strength by measuring the deflection of a pendulum in the vicinity of a large hill, but thought that the issue would be too small-scale to be measurable.^[12] Nevertheless, he estimated the society of magnitude of the abiding when he surmised that "the mean density of the earth might be five or six times as nifty every bit the density of water", which is equivalent to a gravitational constant of the guild:^[13]

G ≈ (6.7±0.6)×ten^−eleven 1000³⋅kg^–1⋅southward⁻²

A measurement was attempted in 1738 past 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 to the lowest degree proved that the Earth could not be a hollow shell, equally some thinkers of the twenty-four hour period, including Edmond Halley, had suggested.^[14]

The Schiehallion experiment, proposed in 1772 and completed in 1776, was the beginning successful measurement of the mean density of the Earth, and thus indirectly of the gravitational abiding. The result reported past Charles Hutton (1778) suggested a density of 4.5 g/cm³ (iv+ ane / 2 times the density of water), about twenty% beneath the mod value.^[15] This immediately led to estimates on the densities and masses of the Sunday, Moon and planets, sent by Hutton to Jérôme Lalande for inclusion in his planetary tables. Every bit discussed above, establishing the average density of Earth is equivalent to measuring the gravitational constant, given Earth's mean radius and the hateful gravitational acceleration at Earth's surface, past setting^[11]

$${\displaystyle K=1000{\frac {R_{\oplus }^{2}}{M_{\oplus }}}={\frac {3g}{4\pi R_{\oplus }\rho _{\oplus }}}.}$$

Based on this, Hutton's 1778 result is equivalent to G ≈ 8×10⁻¹¹ m³⋅kg^–ane⋅s⁻² .

Diagram of torsion residual used in the Cavendish experiment performed by Henry Cavendish in 1798, to measure out 1000, with the help of a pulley, large assurance hung from a frame were rotated into position side by side to the small assurance.

The commencement direct measurement of gravitational attraction betwixt ii bodies in the laboratory was performed in 1798, seventy-1 years subsequently Newton'southward expiry, past Henry Cavendish.^[xvi] He adamant a value for G implicitly, using a torsion balance invented past the geologist Rev. John Michell (1753). He used a horizontal torsion beam with atomic number 82 assurance 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 information technology caused. In spite of the experimental design being due to Michell, the experiment is at present known as the Cavendish experiment for its get-go successful execution past Cavendish.

Cavendish's stated aim was the "weighing of World", that is, determining the average density of Earth and the Earth'south mass. His upshot, ρ _🜨 = 5.448(33) g·cm⁻ⁱⁱⁱ , corresponds to value of K = half-dozen.74(4)×10^−eleven m³⋅kg^–one⋅s⁻ⁱⁱ . Information technology is surprisingly accurate, about 1% higher up the modern value (comparable to the claimed standard uncertainty of 0.vi%).^[17]

19th century [edit]

The accurateness of the measured value of G has increased but modestly since the original Cavendish experiment.^[18] G is quite difficult to measure out because gravity is much weaker than other fundamental forces, and an experimental appliance cannot be separated from the gravitational influence of other bodies.

Measurements with pendulums were made by Francesco Carlini (1821, 4.39 g/cm³ ), Edward Sabine (1827, 4.77 m/cm³ ), Carlo Ignazio Giulio (1841, 4.95 grand/cm³ ) and George Biddell Airy (1854, half dozen.half dozen 1000/cm³ ).^[nineteen]

Cavendish'due south experiment was first repeated by Ferdinand Reich (1838, 1842, 1853), who constitute a value of 5.5832(149) grand·cm⁻³ ,^[xx] which is actually worse than Cavendish's issue, differing from the mod value by 1.5%. Cornu and Baille (1873), establish 5.56 grand·cm⁻³ .^[21]

Cavendish's experiment proved to result in more reliable measurements than pendulum experiments of the "Schiehallion" (deflection) blazon or "Peruvian" (catamenia as a office of altitude) blazon. Pendulum experiments still continued to be performed, by Robert von Sterneck (1883, results between 5.0 and vi.3 g/cm^three ) and Thomas Corwin Mendenhall (1880, v.77 thousand/cm³ ).^[22]

Cavendish'south result was first improved upon by John Henry Poynting (1891),^[23] who published a value of v.49(3) m·cm⁻³ , differing from the modern value past 0.2%, but compatible with the modern value within the cited standard uncertainty of 0.55%. In addition to Poynting, measurements were made by C. V. Boys (1895)^[24] and Carl Braun (1897),^[25] with compatible results suggesting G = vi.66(i)×10^−xi m³⋅kg^−ane⋅due south⁻ⁱⁱ . The modern note involving the constant Chiliad was introduced past Boys in 1894^[xi] and becomes standard past the cease of the 1890s, with values usually cited in the cgs system. Richarz and Krigar-Menzel (1898) attempted a repetition of the Cavendish experiment using 100,000 kg of lead for the attracting mass. The precision of their result of 6.683(11)×10⁻¹¹ mⁱⁱⁱ⋅kg⁻¹⋅s⁻² was, however, of the same club of magnitude every bit the other results at the time.^[26]

Arthur Stanley Mackenzie in The Laws of Gravitation (1899) reviews the work done in the 19th century.^[27] Poynting is the writer of the article "Gravitation" in the Encyclopædia Britannica Eleventh Edition (1911). Here, he cites a value of 1000 = 6.66×10⁻¹¹ g³⋅kg^−one⋅s⁻² with an dubiety of 0.2%.

Mod value [edit]

Paul R. Heyl (1930) published the value of 6.670(5)×10⁻¹¹ m³⋅kg^–i⋅s⁻² (relative uncertainty 0.1%),^[28] improved to 6.673(3)×ten⁻¹¹ chiliad³⋅kg^–1⋅due south⁻² (relative uncertainty 0.045% = 450 ppm) in 1942.^[29]

Published values of G derived from loftier-precision measurements since the 1950s accept remained compatible with Heyl (1930), merely within the relative uncertainty of about 0.1% (or i,000 ppm) take varied rather broadly, and information technology is non entirely clear if the incertitude has been reduced at all since the 1942 measurement. Some measurements published in the 1980s to 2000s were, in fact, mutually exclusive.^{[7] [30]} Establishing a standard value for G with a standard uncertainty better than 0.1% has therefore remained rather speculative.

By 1969, the value recommended past the National Constitute of Standards and Technology (NIST) was cited with a standard dubiety of 0.046% (460 ppm), lowered to 0.012% (120 ppm) by 1986. Simply the continued publication of conflicting measurements led NIST to considerably increase the standard doubt 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 again raised, by a more conservative twenty%, in 2010, matching the standard uncertainty of 120 ppm published in 1986.^[31] For the 2014 update, CODATA reduced the uncertainty to 46 ppm, less than half the 2010 value, and one social club of magnitude below the 1969 recommendation.

The following tabular array shows the NIST recommended values published since 1969:

Timeline of measurements and recommended values for One thousand since 1900: values recommended based on a literature review are shown in red, individual torsion remainder experiments in blue, other types of experiments in green.

Recommended values for G

Yr	Thousand (x−xi·mthree⋅kg−1⋅s−2)	Standard uncertainty	Ref.
1969	6.6732(31)	460 ppm	[32]
1973	6.6720(49)	730 ppm	[33]
1986	half-dozen.67449(81)	120 ppm	[34]
1998	vi.673(x)	1,500 ppm	[35]
2002	half-dozen.6742(x)	150 ppm	[36]
2006	vi.67428(67)	100 ppm	[37]
2010	half-dozen.67384(eighty)	120 ppm	[38]
2014	6.67408(31)	46 ppm	[39]
2018	6.67430(15)	22 ppm	[40]

In the January 2007 result of Science, Fixler et al. described a measurement of the gravitational constant past a new technique, cantlet interferometry, reporting a value of G = six.693(34)×10⁻¹¹ thou³⋅kg⁻¹⋅due south⁻² , 0.28% (2800 ppm) higher than the 2006 CODATA value.^[41] An improved cold cantlet measurement by Rosi et al. was published in 2014 of G = 6.67191(99)×ten^−eleven grandⁱⁱⁱ⋅kg^−one⋅s⁻² .^{[42] [43]} Although much closer to the accepted value (suggesting that the Fixler et. al. measurement was erroneous), this issue was 325 ppm below the recommended 2014 CODATA value, with non-overlapping standard uncertainty intervals.

Equally of 2018, efforts to re-evaluate the alien results of measurements are underway, coordinated past NIST, notably a repetition of the experiments reported past Quinn et al. (2013).^[44]

In August 2018, a Chinese research group appear new measurements based on torsion balances, 6.674184(78)×10⁻¹¹ g³⋅kg^–1⋅s⁻² and six.674484(78)×10⁻¹¹ grand^three⋅kg^–1⋅south⁻² based on two different methods.^[45] These are claimed every bit the most accurate measurements ever fabricated, with a standard uncertainties cited every bit low as 12 ppm. The difference of 2.7σ betwixt the two results suggests there could be sources of fault unaccounted for.

Suggested time-variation [edit]

A controversial 2015 study of some previous measurements of G , by Anderson et al., suggested that most of the mutually exclusive values in high-precision measurements of Chiliad can be explained by a periodic variation.^[46] The variation was measured every bit having a period of 5.9 years, like to that observed in length-of-day (LOD) measurements, hinting at a common physical crusade that is not necessarily a variation in K . A response was produced by some of the original authors of the Yard measurements used in Anderson et al.^[47] This response notes that Anderson et al. not only omitted measurements, but that they also used the time of publication rather than the fourth dimension the experiments were performed. A plot with estimated time of measurement from contacting original authors seriously degrades the length of 24-hour interval correlation. Besides, consideration of the data collected over a decade by Karagioz and Izmailov shows no correlation with length of day measurements.^{[47] [48]} As such, the variations in G almost likely arise from systematic measurement errors which have not properly been accounted for. Under the assumption that the physics of type Ia supernovae are universal, analysis of observations of 580 of them has shown that the gravitational constant has varied past less than i role in ten billion per twelvemonth over the last nine billion years co-ordinate to Mould et al. (2014).^[49]

See too [edit]

• Gravity of World
• Standard gravity
• Gaussian gravitational abiding
• Orbital mechanics
• Escape velocity
• Gravitational potential
• Gravitational moving ridge
• Potent gravitational abiding
• Dirac large numbers hypothesis
• Accelerating universe
• Lunar Laser Ranging experiment
• Cosmological constant

References [edit]

Footnotes

1. ^ "Newtonian constant of gravitation" is the name introduced for Thousand by Boys (1894). Use of the term by T.Eastward. Stern (1928) was misquoted every bit "Newton's constant of gravitation" in Pure Science Reviewed for Profound and Unsophisticated Students (1930), in what is apparently the first apply of that term. Use of "Newton'south constant" (without specifying "gravitation" or "gravity") is more recent, equally "Newton's constant" was besides used for the heat transfer coefficient in Newton'due south law of cooling, but has by now go quite common, e.1000. Calmet et al, Quantum Blackness Holes (2013), p. 93; P. de Aquino, Beyond Standard Model Phenomenology at the LHC (2013), p. 3. The proper name "Cavendish gravitational constant", sometimes "Newton–Cavendish gravitational constant", appears to have been common in the 1970s to 1980s, especially in (translations from) Soviet-era Russian literature, e.g. Sagitov (1970 [1969]), Soviet Physics: Uspekhi 30 (1987), Issues i–half dozen, p. 342 [etc.]. "Cavendish constant" and "Cavendish gravitational constant" is besides used in Charles W. Misner, Kip South. Thorne, John Archibald Wheeler, "Gravitation", (1973), 1126f. Colloquial use of "Large G", as opposed to "lilliputian g" for gravitational dispatch dates to the 1960s (R.W. Fairbridge, The encyclopedia of atmospheric sciences and astrogeology, 1967, p. 436; note use of "Large Thou's" vs. "little g's" as early on as the 1940s of the Einstein tensor Yard _μν vs. the metric tensor thousand _μν , Scientific, medical, and technical books published in the United states of America: a selected list of titles in print with annotations: supplement of books published 1945–1948, Committee on American Scientific and Technical Bibliography National Enquiry Quango, 1950, p. 26).
2. ^ Cavendish determined the value of Thou indirectly, by reporting a value for the Earth's mass, or the average density of Earth, as 5.448 thousand⋅cm⁻³ .
3. ^ Depending on the choice of definition of the Einstein tensor and of the stress–free energy tensor it can alternatively exist defined as κ = 8πG / c ^four ≈ 2.077×ten⁻⁴³ south²⋅thousand⁻¹⋅kg⁻¹
4. ^ For case, the gravitational forcefulness between an electron and a proton 1 m autonomously is approximately ten⁻⁶⁷ North, whereas the electromagnetic force between the same 2 particles is approximately 10⁻²⁸ N. The electromagnetic strength in this example is in the lodge of 10³⁹ times greater than the strength of gravity—roughly the same ratio equally the mass of the Sun to a microgram.
5. ^ K ≈ 1.000003040433 K _☉ , so that M = M _☉ can be used for accuracies of five or fewer meaning digits.

Citations

1. ^ ^{a b c} "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Dubiety. NIST. 20 May 2019. Retrieved 20 May 2019.
2. ^ Gundlach, Jens H.; Merkowitz, Stephen M. (23 Dec 2002). "Academy of Washington Big Chiliad Measurement". Astrophysics Science Division. Goddard Infinite Flight Heart. Since Cavendish beginning measured Newton's Gravitational abiding 200 years ago, "Big Grand" remains ane of the most elusive constants in physics
3. ^ Halliday, David; Resnick, Robert; Walker, Jearl (September 2007). Fundamentals of Physics (8th ed.). p. 336. ISBN978-0-470-04618-0.
4. ^ Grøn, Øyvind; Hervik, Sigbjorn (2007). Einstein's General Theory of Relativity: With Modern Applications in Cosmology (illustrated ed.). Springer Science & Business Media. p. 180. ISBN978-0-387-69200-v.
5. ^ ^{a b} Einstein, Albert (1916). "The Foundation of the Full general Theory of Relativity". Annalen der Physik. 354 (7): 769–822. Bibcode:1916AnP...354..769E. doi:10.1002/andp.19163540702. Archived from the original (PDF) on six February 2012.
6. ^ Adler, Ronald; Bazin, Maurice; Schiffer, Menahem (1975). Introduction to General Relativity (second ed.). New York: McGraw-Hill. p. 345. ISBN978-0-07-000423-8.
7. ^ ^{a b} Gillies, George T. (1997). "The Newtonian gravitational abiding: recent measurements and related studies". Reports on Progress in Physics. 60 (2): 151–225. Bibcode:1997RPPh...threescore..151G. doi:10.1088/0034-4885/60/2/001. . A lengthy, detailed review. Encounter Figure i and Tabular array ii in particular.
8. ^ Mohr, Peter J.; Newell, David B.; Taylor, Barry Due north. (21 July 2015). "CODATA Recommended Values of the Fundamental Physical Constants: 2014". Reviews of Mod Physics. 88 (3): 035009. arXiv:1507.07956. Bibcode:2016RvMP...88c5009M. doi:10.1103/RevModPhys.88.035009. S2CID 1115862.
9. ^ "Astrodynamic Constants". NASA/JPL. 27 Feb 2009. Retrieved 27 July 2009.
10. ^ "Geocentric gravitational constant". Numerical Standards for Fundamental Astronomy. IAU Division I Working Group on Numerical Standards for Fundamental Astronomy. Retrieved 24 June 2021 – via iau-a3.gitlab.io. Citing
    • Ries JC, Eanes RJ, Shum CK, Watkins MM (xx March 1992). "Progress in the decision of the gravitational coefficient of the World". Geophysical Research Letters. 19 (6): 529–531. Bibcode:1992GeoRL..nineteen..529R. doi:10.1029/92GL00259. S2CID 123322272.
11. ^ ^{a b c} Boys 1894, p.330 In this lecture earlier the Imperial Guild, Boys introduces G and argues for its credence. See: Poynting 1894, p. iv, MacKenzie 1900, p.vi
12. ^ Davies, R.D. (1985). "A Commemoration of Maskelyne at Schiehallion". Quarterly Journal of the Purple Astronomical Society. 26 (three): 289–294. Bibcode:1985QJRAS..26..289D.
13. ^ "Sir Isaac Newton thought information technology probable, that the mean density of the earth might be five or six times as smashing equally the density of water; and we take at present establish, by experiment, that information technology is very little less than what he had thought information technology to be: so much justness was even in the surmises of this wonderful man!" Hutton (1778), p. 783
14. ^ Poynting, J.H. (1913). The Globe: its shape, size, weight and spin. Cambridge. pp. 50–56.
15. ^ Hutton, C. (1778). "An Account of the Calculations Made from the Survey and Measures Taken at Schehallien". Philosophical Transactions of the Royal Society. 68: 689–788. doi:ten.1098/rstl.1778.0034.
16. ^ Published in Philosophical Transactions of the Royal Order (1798); reprint: Cavendish, Henry (1798). "Experiments to Determine the Density of the Globe". In MacKenzie, A. Southward., Scientific Memoirs Vol. 9: The Laws of Gravitation. American Volume Co. (1900), pp. 59–105.
17. ^ 2014 CODATA value half dozen.674×ten^−xi thou^three⋅kg⁻¹⋅south⁻ⁱⁱ .
18. ^ Brush, Stephen G.; Holton, Gerald James (2001). Physics, the homo adventure: from Copernicus to Einstein and beyond . New Brunswick, NJ: Rutgers University Press. pp. 137. ISBN978-0-8135-2908-0. Lee, Jennifer Lauren (xvi Nov 2016). "Big G Redux: Solving the Mystery of a Perplexing Result". NIST.
19. ^ Poynting, John Henry (1894). The Mean Density of the Globe. London: Charles Griffin. pp. 22–24.
20. ^ F. Reich, On the Repetition of the Cavendish Experiments for Determining the hateful density of the Earth" Philosophical Magazine 12: 283–284.
21. ^ Mackenzie (1899), p. 125.
22. ^ A.S. Mackenzie , The Laws of Gravitation (1899), 127f.
23. ^ Poynting, John Henry (1894). The hateful density of the globe. Gerstein - University of Toronto. London.
24. ^ Boys, C. V. (1 Jan 1895). "On the Newtonian Abiding of Gravitation". Philosophical Transactions of the Royal Social club A: Mathematical, Concrete and Engineering Sciences. The Majestic Gild. 186: 1–72. Bibcode:1895RSPTA.186....1B. doi:ten.1098/rsta.1895.0001. ISSN 1364-503X.
25. ^ Carl Braun, Denkschriften der thou. Akad. d. Wiss. (Wien), math. u. naturwiss. Classe, 64 (1897). Braun (1897) quoted an optimistic standard dubiousness of 0.03%, 6.649(2)×ten⁻¹¹ g³⋅kg⁻¹⋅due south⁻ⁱⁱ but his result was significantly worse than the 0.2% feasible at the time.
26. ^ Sagitov, Grand. U., "Current Condition of Determinations of the Gravitational Constant and the Mass of the Globe", Soviet Astronomy, Vol. 13 (1970), 712–718, translated from Astronomicheskii Zhurnal Vol. 46, No. four (July–Baronial 1969), 907–915 (table of historical experiments p. 715).
27. ^ Mackenzie, A. Stanley, The laws of gravitation; memoirs past Newton, Bouguer and Cavendish, together with abstracts of other important memoirs, American Book Company (1900 [1899]).
28. ^ Heyl, P. R. (1930). "A redetermination of the constant of gravitation". Bureau of Standards Journal of Inquiry. v (6): 1243–1290. doi:10.6028/jres.005.074.
29. ^ P. R. Heyl and P. Chrzanowski (1942), cited after Sagitov (1969:715).
30. ^ Mohr, Peter J.; Taylor, Barry N. (2012). "CODATA recommended values of the fundamental physical constants: 2002" (PDF). Reviews of Modern Physics. 77 (1): 1–107. arXiv:1203.5425. Bibcode:2005RvMP...77....1M. CiteSeerXten.1.1.245.4554. doi:10.1103/RevModPhys.77.ane. Archived from the original (PDF) on half dozen March 2007. Retrieved 1 July 2006. Section Q (pp. 42–47) describes the mutually inconsistent measurement experiments from which the CODATA value for G was derived.
31. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (xiii November 2012). "CODATA recommended values of the fundamental physical constants: 2010" (PDF). Reviews of Modern Physics. 84 (iv): 1527–1605. arXiv:1203.5425. Bibcode:2012RvMP...84.1527M. CiteSeerX10.1.1.150.3858. doi:10.1103/RevModPhys.84.1527. S2CID 103378639.
32. ^ Taylor, B. N.; Parker, West. H.; Langenberg, D. N. (1 July 1969). "Determination of e/h, Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Fundamental Physical Constants". Reviews of Modern Physics. American Physical Society (APS). 41 (three): 375–496. Bibcode:1969RvMP...41..375T. doi:10.1103/revmodphys.41.375. ISSN 0034-6861.
33. ^ Cohen, E. Richard; Taylor, B. N. (1973). "The 1973 To the lowest degree‐Squares Aligning of the Fundamental Constants". Periodical of Physical and Chemical Reference Information. AIP Publishing. 2 (four): 663–734. Bibcode:1973JPCRD...2..663C. doi:10.1063/one.3253130. hdl:2027/pst.000029951949. ISSN 0047-2689.
34. ^ Cohen, Due east. Richard; Taylor, Barry N. (i October 1987). "The 1986 adjustment of the key physical constants". Reviews of Modern Physics. American Physical Gild (APS). 59 (4): 1121–1148. Bibcode:1987RvMP...59.1121C. doi:ten.1103/revmodphys.59.1121. ISSN 0034-6861.
35. ^ Mohr, Peter J.; Taylor, Barry N. (2012). "CODATA recommended values of the primal concrete constants: 1998". Reviews of Modern Physics. 72 (2): 351–495. arXiv:1203.5425. Bibcode:2000RvMP...72..351M. doi:x.1103/revmodphys.72.351. ISSN 0034-6861.
36. ^ Mohr, Peter J.; Taylor, Barry Due north. (2012). "CODATA recommended values of the fundamental physical constants: 2002". Reviews of Modern Physics. 77 (1): 1–107. arXiv:1203.5425. Bibcode:2005RvMP...77....1M. doi:10.1103/revmodphys.77.ane. ISSN 0034-6861.
37. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2012). "CODATA recommended values of the fundamental physical constants: 2006". Periodical of Physical and Chemical Reference Data. 37 (3): 1187–1284. arXiv:1203.5425. Bibcode:2008JPCRD..37.1187M. doi:10.1063/i.2844785. ISSN 0047-2689.
38. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2012). "CODATA Recommended Values of the Cardinal Concrete Constants: 2010". Journal of Physical and Chemic Reference Data. 41 (4): 1527–1605. arXiv:1203.5425. Bibcode:2012JPCRD..41d3109M. doi:x.1063/1.4724320. ISSN 0047-2689.
39. ^ Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (2016). "CODATA Recommended Values of the Cardinal Concrete Constants: 2014". Journal of Physical and Chemical Reference Information. 45 (four): 1527–1605. arXiv:1203.5425. Bibcode:2016JPCRD..45d3102M. doi:10.1063/one.4954402. ISSN 0047-2689.
40. ^ Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor (2019), "The 2018 CODATA Recommended Values of the Cardinal Physical Constants" (Web Version viii.0). Database developed past J. Bakery, K. Douma, and Due south. Kotochigova. National Constitute of Standards and Engineering, Gaithersburg, Medico 20899.
41. ^ Fixler, J. B.; Foster, G. T.; McGuirk, J. M.; Kasevich, Grand. A. (5 Jan 2007). "Atom Interferometer Measurement of the Newtonian Constant of Gravity". Scientific discipline. 315 (5808): 74–77. Bibcode:2007Sci...315...74F. doi:10.1126/science.1135459. PMID 17204644. S2CID 6271411.
42. ^ Rosi, Grand.; Sorrentino, F.; Cacciapuoti, L.; Prevedelli, M.; Tino, G. M. (26 June 2014). "Precision measurement of the Newtonian gravitational constant using cold atoms" (PDF). Nature. 510 (7506): 518–521. arXiv:1412.7954. Bibcode:2014Natur.510..518R. doi:10.1038/nature13433. PMID 24965653. S2CID 4469248.
43. ^ Schlamminger, Stephan (eighteen June 2014). "Fundamental constants: A absurd way to measure big G" (PDF). Nature. 510 (7506): 478–480. Bibcode:2014Natur.510..478S. doi:ten.1038/nature13507. PMID 24965646.
44. ^ C. Rothleitner; S. Schlamminger (2017). "Invited Review Article: Measurements of the Newtonian constant of gravitation, G". Review of Scientific Instruments. 88 (11): 111101. Bibcode:2017RScI...88k1101R. doi:10.1063/1.4994619. PMC8195032. PMID 29195410. 111101. All the same, re-evaluating or repeating experiments that have already been performed may provide insights into subconscious biases or dark uncertainty. NIST has the unique opportunity to echo the experiment of Quinn et al. [2013] with an virtually identical setup. By mid-2018, NIST researchers volition publish their results and assign a number too as an uncertainty to their value. Referencing:
    • T. Quinn; H. Parks; C. Speake; R. Davis (2013). "Improved determination of M using ii methods" (PDF). Phys. Rev. Lett. 111 (10): 101102. Bibcode:2013PhRvL.111j1102Q. doi:x.1103/PhysRevLett.111.101102. PMID 25166649. 101102.
    The 2018 experiment was described by C. Rothleitner. Newton's Gravitational Constant 'Large' G – A proposed Free-fall Measurement (PDF). CODATA Fundamental Constants Meeting, Eltville – v February 2015.
45. ^ Li, Qing; et al. (2018). "Measurements of the gravitational constant using 2 independent methods". Nature. 560 (7720): 582–588. Bibcode:2018Natur.560..582L. doi:10.1038/s41586-018-0431-5. PMID 30158607. S2CID 52121922. . Come across also: "Physicists just fabricated the most precise measurement ever of Gravity'south strength". 31 August 2018. Retrieved 13 October 2018.
46. ^ Anderson, J. D.; Schubert, Thousand.; Trimble, iii=V.; Feldman, M. R. (April 2015). "Measurements of Newton'due south gravitational constant and the length of twenty-four hours". EPL. 110 (i): 10002. arXiv:1504.06604. Bibcode:2015EL....11010002A. doi:10.1209/0295-5075/110/10002. S2CID 119293843.
47. ^ ^{a b} Schlamminger, Southward.; Gundlach, J. H.; Newman, R. D. (2015). "Recent measurements of the gravitational constant as a function of fourth dimension". Physical Review D. 91 (12): 121101. arXiv:1505.01774. Bibcode:2015PhRvD..91l1101S. doi:ten.1103/PhysRevD.91.121101. ISSN 1550-7998. S2CID 54721758.
48. ^ Karagioz, O. 5.; Izmailov, V. P. (1996). "Measurement of the gravitational constant with a torsion balance". Measurement Techniques. 39 (10): 979–987. doi:10.1007/BF02377461. ISSN 0543-1972. S2CID 123116844.
49. ^ Mould, J.; Uddin, S. A. (10 April 2014). "Constraining a Possible Variation of Grand with Type Ia Supernovae". Publications of the Astronomical Club of Commonwealth of australia. 31: e015. arXiv:1402.1534. Bibcode:2014PASA...31...15M. doi:ten.1017/pasa.2014.9. S2CID 119292899.

Sources [edit]

• Standish., E. Myles (1995). "Written report of the IAU WGAS Sub-group on Numerical Standards". In Appenzeller, I. (ed.). Highlights of Astronomy. Dordrecht: Kluwer Academic Publishers. (Complete study available online: PostScript; PDF. Tables from the study as well available: Astrodynamic Constants and Parameters)
• Gundlach, Jens H.; Merkowitz, Stephen M. (2000). "Measurement of Newton's Abiding Using a Torsion Rest with Angular Dispatch Feedback". Physical Review Letters. 85 (fourteen): 2869–2872. arXiv:gr-qc/0006043. Bibcode:2000PhRvL..85.2869G. doi:10.1103/PhysRevLett.85.2869. PMID 11005956. S2CID 15206636.

External links [edit]

• Newtonian constant of gravitation G at the National Institute of Standards and Technology References on Constants, Units, and Doubt
• The Controversy over Newton's Gravitational Abiding — additional commentary on measurement problems

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