G&g Cm16 Mod 0 Aeg Combat Machine Black Airsoft Rifle

G&g Cm16 Mod 0 Aeg Combat Machine Black Airsoft Rifle

Concrete constant relating the gravitational force between objects to their mass and altitude

Notations for the gravitational constant

Values of G	Units
half dozen.674xxx(fifteen)×10−xi [i]	N thousand2⋅kg–2
6.67430(15)×10−8	dyne cm2⋅g–2
4.30091(25)×10−3	pc⋅M ⊙ –1⋅(km/s)two

The gravitational constant (also known every bit the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant),^[a] denoted by the capital letter letter M , is an empirical concrete constant involved in the calculation of gravitational effects in Sir Isaac Newton's constabulary of universal gravitation and in Albert Einstein's general theory of relativity.

In Newton's police force, it is the proportionality abiding connecting the gravitational force betwixt two bodies with the product 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 free energy–momentum tensor (too referred to as the stress–free energy tensor).

The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately six.674×10^−eleven 1000³⋅kg⁻¹⋅s⁻² .^[1]

The mod notation of Newton'due south constabulary involving One thousand was introduced in the 1890s by C. 5. Boys. The first implicit measurement with an accurateness inside about 1% is attributed to Henry Cavendish in a 1798 experiment.^[b]

Definition [edit]

According to Newton'due south law of universal gravitation, the attractive force ( F ) betwixt 2 bespeak-like bodies is directly proportional to the product of their masses ( thou _i and m ₂ ) and inversely proportional to the foursquare of the distance, r , betwixt their centers of mass.:

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

The constant of proportionality, G , is the gravitational abiding. Colloquially, the gravitational constant is likewise called "Big G", distinct from "pocket-sized yard" ( one thousand ), which is the local gravitational field of Earth (equivalent to the free-autumn acceleration).^{[2] [iii]} Where ${\displaystyle M_{\oplus }}$ is the mass of the Globe and ${\displaystyle r_{\oplus }}$ is the radius of the World, the two quantities are related by:

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

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

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

where Thousand _μν is the Einstein tensor, Λ is the cosmological constant, one thousand_μν is the metric tensor, T_μν is the stress–energy tensor, and κ is a abiding originally introduced by Einstein that is directly related to the Newtonian abiding of gravitation:^{[5] [6] [c]}

$${\displaystyle \kappa ={\frac {eight\pi Yard}{c^{two}}}\approx ane.866\times x^{-26}\mathrm {\,k{\cdot }kg^{-1}} .}$$

Value and uncertainty [edit]

The gravitational constant is a physical constant that is difficult to mensurate with high accuracy.^[vii] This is because the gravitational forcefulness is an extremely weak forcefulness as compared to other key forces.^[d]

In SI units, the 2018 Committee on Information for Science and Technology (CODATA)-recommended value of the gravitational constant (with standard uncertainty in parentheses) is:^{[1] [8]}

$${\displaystyle G=6.67430(15)\times 10^{-11}{\rm {\ m^{3}{\cdot }kg^{-i}{\cdot }south^{-ii}}}}$$

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, specially geometrized unit of measurement systems, such as Planck units and Stoney units. When expressed in terms of such units, the value of the gravitational constant will generally accept a numeric value of 1 or a value close to it. Due to the significant doubt in the measured value of Yard in terms of other known fundamental constants, a similar level of incertitude will testify up in the value of many quantities when expressed in such a unit system.

Orbital mechanics [edit]

In astrophysics, it is convenient to measure distances in parsecs (pc), velocities in kilometres per second (km/s) and masses in solar units Yard _⊙ . In these units, the gravitational abiding is:

$${\displaystyle G\approx iv.3009\times 10^{-3}{\rm {}}{\frac {pc}{M_{\odot }}}{\rm {\ (km/southward)^{2}}}.\,}$$

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

$${\displaystyle Thousand\approx 1.90809\times 10^{5}R_{\odot }M_{\odot }^{-1}{\rm {\ (km/due south)^{ii}}}.\,}$$

In orbital mechanics, the period P of an object in circular orbit effectually a spherical object obeys

$${\displaystyle GM={\frac {3\pi V}{P^{2}}}}$$

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

${\displaystyle P^{2}={\frac {3\pi }{Yard}}{\frac {5}{M}}\approx ten.896\ \mathrm {h^{two}{\cdot }k{\cdot }cm^{-iii}} {\frac {V}{M}}.}$

This style of expressing One thousand shows the relationship betwixt the average density of a planet and the period of a satellite orbiting just above its surface.

For elliptical orbits, applying Kepler'south 3rd police force, expressed in units characteristic of Globe's orbit:

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

where distance is measured in terms of the semi-major axis of Earth'southward orbit (the astronomical unit of measurement, AU), time in years, and mass in the total mass of the orbiting arrangement ( Yard = M _☉ + M _Earth + One thousand _☾ ^[eastward]).

The above equation is verbal only within the approximation of the Earth'southward orbit around the Sun as a ii-body trouble in Newtonian mechanics, the measured quantities comprise corrections from the perturbations from other bodies in the solar system and from general relativity.

From 1964 until 2012, however, it was used every bit the definition of the astronomical unit and thus held by definition:

$${\displaystyle one\ \mathrm {AU} =\left({\frac {GM}{four\pi ^{ii}}}{\rm {yr}}^{two}\correct)^{\frac {1}{3}}\approx ane.495979\times 10^{11}{\rm {m}}.}$$

Since 2012, the AU is divers as 1.495978 707 ×10^xi 1000 exactly, and the equation tin can no longer be taken as holding precisely.

The quantity GM —the production of the gravitational constant and the mass of a given astronomical body such as the Sun or World—is known equally the standard gravitational parameter (too denoted μ ). The standard gravitational parameter GM appears as above in Newton's police of universal gravitation, too as in formulas for the deflection of light caused by gravitational lensing, in Kepler'southward laws of planetary movement, and in the formula for escape velocity.

This quantity gives a convenient simplification of various gravity-related formulas. The production GM is known much more accurately than either factor is.

Values for GM

Trunk	μ = GM	Value	Relative uncertainty
Sun	M 1000 ☉	one.327124 400 18(8)×1020 m3⋅s−2 [9]	6×10−11
Earth	G M World	3.986004 418(8)×tenfourteen mthree⋅southward−2 [10]	2×ten−nine

Calculations in celestial mechanics can likewise be carried out using the units of solar masses, hateful solar days and astronomical units rather than standard SI units. For this purpose, the Gaussian gravitational constant was historically in widespread apply, k = 0.017202 098 95 , expressing the mean angular velocity of the Sun–Earth organization measured in radians per twenty-four hours.^{[ citation needed ]} The use of this constant, and the unsaid definition of the astronomical unit discussed above, has been deprecated by the IAU since 2012.^{[ commendation needed ]}

History of measurement [edit]

Early history [edit]

The existence of the constant is implied in Newton's police of universal gravitation equally published in the 1680s (although its notation every bit G dates to the 1890s),^[11] but is not calculated in his Philosophiæ Naturalis Principia Mathematica where information technology postulates the inverse-square law of gravitation. In the Principia, Newton considered the possibility of measuring gravity'due south force past measuring the deflection of a pendulum in the vicinity of a big loma, just thought that the consequence would be as well pocket-size to exist measurable.^[12] Nevertheless, he estimated the order of magnitude of the constant when he surmised that "the mean density of the earth might exist five or six times as great as the density of water", which is equivalent to a gravitational constant of the order:^[13]

G ≈ (half-dozen.vii±0.6)×10^−xi m³⋅kg^–one⋅s⁻²

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, equally some thinkers of the mean solar day, 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 constant. The outcome reported by Charles Hutton (1778) suggested a density of iv.five g/cm³ (4+ i / ii times the density of h2o), nigh 20% below the mod value.^[15] 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. Equally discussed higher up, establishing the average density of Earth is equivalent to measuring the gravitational constant, given Earth's mean radius and the mean gravitational dispatch at World'southward surface, by setting^[11]

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

Based on this, Hutton's 1778 result is equivalent to G ≈ 8×10⁻¹¹ mⁱⁱⁱ⋅kg^–1⋅s⁻² .

Diagram of torsion balance used in the Cavendish experiment performed by Henry Cavendish in 1798, to measure out M, with the assist of a caster, large balls hung from a frame were rotated into position next to the pocket-sized balls.

The first direct measurement of gravitational attraction between two bodies in the laboratory was performed in 1798, seventy-1 years after Newton's death, past Henry Cavendish.^[16] He determined a value for K 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 axle'southward oscillation. Their faint attraction to other balls placed alongside the beam was detectable past 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 past Cavendish.

Cavendish's stated aim was the "weighing of Earth", that is, determining the boilerplate density of World and the Earth's mass. His effect, ρ _🜨 = five.448(33) grand·cm⁻³ , corresponds to value of One thousand = 6.74(4)×10⁻¹¹ g^three⋅kg^–1⋅s⁻² . It is surprisingly accurate, about 1% above the modern value (comparable to the claimed standard uncertainty of 0.6%).^[17]

19th century [edit]

The accurateness of the measured value of Grand has increased only modestly since the original Cavendish experiment.^[xviii] G is quite difficult to measure because gravity is much weaker than other cardinal forces, and an experimental apparatus cannot exist separated from the gravitational influence of other bodies.

Measurements with pendulums were made by Francesco Carlini (1821, 4.39 m/cm³ ), Edward Sabine (1827, iv.77 chiliad/cmⁱⁱⁱ ), Carlo Ignazio Giulio (1841, 4.95 g/cm^three ) and George Biddell Airy (1854, six.6 thou/cm³ ).^[19]

Cavendish's experiment was outset repeated by Ferdinand Reich (1838, 1842, 1853), who found a value of 5.5832(149) m·cm⁻ⁱⁱⁱ ,^[20] which is actually worse than Cavendish's result, differing from the modern value by ane.5%. Cornu and Baille (1873), found 5.56 m·cm⁻ⁱⁱⁱ .^[21]

Cavendish's experiment proved to result in more than reliable measurements than pendulum experiments of the "Schiehallion" (deflection) type or "Peruvian" (flow as a role of altitude) type. Pendulum experiments still continued to exist performed, by Robert von Sterneck (1883, results betwixt 5.0 and 6.3 grand/cm³ ) and Thomas Corwin Mendenhall (1880, five.77 thou/cm³ ).^[22]

Cavendish's outcome was first improved upon by John Henry Poynting (1891),^[23] who published a value of 5.49(3) m·cm⁻³ , differing from the modern value past 0.2%, but uniform with the modern value within the cited standard uncertainty of 0.55%. In add-on to Poynting, measurements were made by C. Five. Boys (1895)^[24] and Carl Braun (1897),^[25] with compatible results suggesting Thousand = 6.66(1)×ten⁻¹¹ g³⋅kg^−one⋅s⁻² . The modern notation involving the constant Yard was introduced past Boys in 1894^[11] and becomes standard past the end of the 1890s, with values normally cited in the cgs system. Richarz and Krigar-Menzel (1898) attempted a repetition of the Cavendish experiment using 100,000 kg of atomic number 82 for the attracting mass. The precision of their effect of 6.683(11)×10^−eleven m³⋅kg^−ane⋅southward⁻² was, withal, of the same order of magnitude equally the other results at the fourth dimension.^[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 commodity "Gravitation" in the Encyclopædia Britannica Eleventh Edition (1911). Here, he cites a value of M = 6.66×x⁻¹¹ grand³⋅kg^−one⋅s⁻² with an uncertainty of 0.2%.

Modern value [edit]

Paul R. Heyl (1930) published the value of vi.670(v)×10^−eleven k³⋅kg^–one⋅s⁻² (relative uncertainty 0.1%),^[28] improved to half dozen.673(iii)×10⁻¹¹ k³⋅kg^–1⋅s⁻² (relative dubiousness 0.045% = 450 ppm) in 1942.^[29]

Published values of G derived from loftier-precision measurements since the 1950s have remained compatible with Heyl (1930), merely within the relative uncertainty of about 0.1% (or 1,000 ppm) accept varied rather broadly, and it is not entirely clear if the doubt has been reduced at all since the 1942 measurement. Some measurements published in the 1980s to 2000s were, in fact, mutually sectional.^{[seven] [30]} Establishing a standard value for G with a standard dubiety improve than 0.1% has therefore remained rather speculative.

By 1969, the value recommended by the National Constitute of Standards and Applied science (NIST) was cited with a standard uncertainty of 0.046% (460 ppm), lowered to 0.012% (120 ppm) past 1986. But the continued publication of conflicting measurements led NIST to considerably increase the standard doubt in the 1998 recommended value, past a factor of 12, to a standard uncertainty of 0.15%, larger than the ane given past Heyl (1930).

The doubt was again lowered in 2002 and 2006, but one time again raised, by a more bourgeois xx%, in 2010, matching the standard doubtfulness of 120 ppm published in 1986.^[31] For the 2014 update, CODATA reduced the incertitude to 46 ppm, less than half the 2010 value, and one order of magnitude below the 1969 recommendation.

The post-obit table shows the NIST recommended values published since 1969:

Timeline of measurements and recommended values for G since 1900: values recommended based on a literature review are shown in red, private torsion residuum experiments in blue, other types of experiments in green.

Recommended values for Grand

Twelvemonth	G (x−11·grand3⋅kg−ane⋅south−2)	Standard uncertainty	Ref.
1969	half dozen.6732(31)	460 ppm	[32]
1973	half-dozen.6720(49)	730 ppm	[33]
1986	half-dozen.67449(81)	120 ppm	[34]
1998	6.673(ten)	ane,500 ppm	[35]
2002	half-dozen.6742(10)	150 ppm	[36]
2006	half dozen.67428(67)	100 ppm	[37]
2010	6.67384(80)	120 ppm	[38]
2014	6.67408(31)	46 ppm	[39]
2018	6.67430(fifteen)	22 ppm	[40]

In the Jan 2007 outcome of Scientific discipline, Fixler et al. described a measurement of the gravitational constant by a new technique, atom interferometry, reporting a value of G = 6.693(34)×ten^−xi g³⋅kg⁻ⁱ⋅s^−two , 0.28% (2800 ppm) college than the 2006 CODATA value.^[41] An improved common cold cantlet measurement by Rosi et al. was published in 2014 of Thou = vi.67191(99)×10⁻¹¹ m³⋅kg⁻¹⋅s⁻² .^{[42] [43]} Although much closer to the accepted value (suggesting that the Fixler et. al. measurement was erroneous), this consequence was 325 ppm below the recommended 2014 CODATA value, with non-overlapping standard dubiety intervals.

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

In August 2018, a Chinese research group announced new measurements based on torsion balances, 6.674184(78)×ten⁻¹¹ m³⋅kg^–1⋅s⁻² and 6.674484(78)×10⁻¹¹ mⁱⁱⁱ⋅kg^–ane⋅s⁻² based on two different methods.^[45] These are claimed equally the about accurate measurements ever made, with a standard uncertainties cited as low as 12 ppm. The difference of 2.7σ between the two results suggests at that place could be sources of mistake unaccounted for.

Suggested time-variation [edit]

A controversial 2015 study of some previous measurements of G , by Anderson et al., suggested that near of the mutually sectional values in high-precision measurements of G can be explained past a periodic variation.^[46] The variation was measured as having a period of 5.nine years, similar to that observed in length-of-day (LOD) measurements, hinting at a common physical crusade that is not necessarily a variation in M . A response was produced by some of the original authors of the Thousand 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 time the experiments were performed. A plot with estimated fourth dimension of measurement from contacting original authors seriously degrades the length of solar day correlation. Also, consideration of the information collected over a decade by Karagioz and Izmailov shows no correlation with length of solar day measurements.^{[47] [48]} As such, the variations in G well-nigh likely ascend from systematic measurement errors which take not properly been deemed for. Under the supposition that the physics of type Ia supernovae are universal, analysis of observations of 580 of them has shown that the gravitational abiding has varied by less than one part in 10 billion per yr over the last ix billion years co-ordinate to Mould et al. (2014).^[49]

See as well [edit]

• Gravity of Earth
• Standard gravity
• Gaussian gravitational abiding
• Orbital mechanics
• Escape velocity
• Gravitational potential
• Gravitational wave
• Stiff gravitational constant
• 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 G by Boys (1894). Use of the term by T.E. Stern (1928) was misquoted every bit "Newton's constant of gravitation" in Pure Scientific discipline Reviewed for Profound and Unsophisticated Students (1930), in what is manifestly the first use of that term. Use of "Newton's abiding" (without specifying "gravitation" or "gravity") is more recent, equally "Newton'southward abiding" was also used for the oestrus transfer coefficient in Newton's law of cooling, but has by at present become quite common, e.g. Calmet et al, Quantum Blackness Holes (2013), p. 93; P. de Aquino, Beyond Standard Model Phenomenology at the LHC (2013), p. 3. The name "Cavendish gravitational constant", sometimes "Newton–Cavendish gravitational abiding", appears to have been common in the 1970s to 1980s, especially in (translations from) Soviet-era Russian literature, e.thousand. Sagitov (1970 [1969]), Soviet Physics: Uspekhi 30 (1987), Problems 1–6, p. 342 [etc.]. "Cavendish constant" and "Cavendish gravitational constant" is also used in Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, "Gravitation", (1973), 1126f. Colloquial use of "Large Chiliad", 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 "Big Yard'south" vs. "little g's" every bit early on as the 1940s of the Einstein tensor G _μν vs. the metric tensor g _μν , Scientific, medical, and technical books published in the United states: a selected list of titles in print with annotations: supplement of books published 1945–1948, Commission on American Scientific and Technical Bibliography National Inquiry Quango, 1950, p. 26).
2. ^ Cavendish determined the value of G indirectly, by reporting a value for the Earth's mass, or the average density of World, as v.448 g⋅cm⁻³ .
3. ^ Depending on the choice of definition of the Einstein tensor and of the stress–free energy tensor it can alternatively be defined as κ = 8πG / c ⁴ ≈ 2.077×x⁻⁴³ southward²⋅m⁻¹⋅kg^−one
4. ^ For example, the gravitational force between an electron and a proton ane k apart is approximately 10⁻⁶⁷ N, whereas the electromagnetic force between the same two particles is approximately 10⁻²⁸ N. The electromagnetic force in this example is in the order of 10³⁹ times greater than the forcefulness of gravity—roughly the same ratio as the mass of the Dominicus to a microgram.
5. ^ M ≈ 1.000003040433 Thou _☉ , so that Thousand = M _☉ tin be used for accuracies of five or fewer pregnant digits.

Citations

1. ^ ^{a b c} "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Doubtfulness. NIST. xx May 2019. Retrieved xx May 2019.
2. ^ Gundlach, Jens H.; Merkowitz, Stephen Yard. (23 Dec 2002). "Academy of Washington Big K Measurement". Astrophysics Science Division. Goddard Space Flying Center. Since Cavendish start measured Newton's Gravitational constant 200 years agone, "Big G" 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 Mod Applications in Cosmology (illustrated ed.). Springer Science & Business Media. p. 180. ISBN978-0-387-69200-5.
5. ^ ^{a b} Einstein, Albert (1916). "The Foundation of the 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 6 February 2012.
6. ^ Adler, Ronald; Bazin, Maurice; Schiffer, Menahem (1975). Introduction to General Relativity (2d ed.). New York: McGraw-Loma. p. 345. ISBN978-0-07-000423-8.
7. ^ ^{a b} Gillies, George T. (1997). "The Newtonian gravitational constant: recent measurements and related studies". Reports on Progress in Physics. threescore (2): 151–225. Bibcode:1997RPPh...lx..151G. doi:10.1088/0034-4885/60/2/001. . A lengthy, detailed review. See Figure 1 and Table 2 in particular.
8. ^ Mohr, Peter J.; Newell, David B.; Taylor, Barry North. (21 July 2015). "CODATA Recommended Values of the Central Physical Constants: 2014". Reviews of Modern 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 abiding". Numerical Standards for Fundamental Astronomy. IAU Partition I Working Group on Numerical Standards for Central Astronomy. Retrieved 24 June 2021 – via iau-a3.gitlab.io. Citing
    • Ries JC, Eanes RJ, Shum CK, Watkins MM (20 March 1992). "Progress in the determination of the gravitational coefficient of the Earth". Geophysical Research Letters. 19 (half-dozen): 529–531. Bibcode:1992GeoRL..19..529R. doi:10.1029/92GL00259. S2CID 123322272.
11. ^ ^{a b c} Boys 1894, p.330 In this lecture before the Regal Society, Boys introduces K and argues for its credence. See: Poynting 1894, p. 4, MacKenzie 1900, p.vi
12. ^ Davies, R.D. (1985). "A Celebration of Maskelyne at Schiehallion". Quarterly Journal of the Majestic Astronomical Guild. 26 (iii): 289–294. Bibcode:1985QJRAS..26..289D.
13. ^ "Sir Isaac Newton idea it probable, that the mean density of the earth might be v or six times as slap-up as the density of h2o; and we take now constitute, by experiment, that information technology is very little less than what he had thought it to be: so much justness was even in the surmises of this wonderful man!" Hutton (1778), p. 783
14. ^ Poynting, J.H. (1913). The Earth: 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 Regal Society. 68: 689–788. doi:x.1098/rstl.1778.0034.
16. ^ Published in Philosophical Transactions of the Royal Society (1798); reprint: Cavendish, Henry (1798). "Experiments to Decide the Density of the Earth". In MacKenzie, A. S., Scientific Memoirs Vol. 9: The Laws of Gravitation. American Book Co. (1900), pp. 59–105.
17. ^ 2014 CODATA value 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻² .
18. ^ Castor, Stephen Chiliad.; Holton, Gerald James (2001). Physics, the human adventure: from Copernicus to Einstein and beyond . New Brunswick, NJ: Rutgers University Printing. pp. 137. ISBN978-0-8135-2908-0. Lee, Jennifer Lauren (16 November 2016). "Big G Redux: Solving the Mystery of a Perplexing Result". NIST.
19. ^ Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin. pp. 22–24.
20. ^ F. Reich, On the Repetition of the Cavendish Experiments for Determining the hateful density of the Globe" 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 Constant of Gravitation". Philosophical Transactions of the Imperial Lodge A: Mathematical, Concrete and Engineering Sciences. The Royal Society. 186: 1–72. Bibcode:1895RSPTA.186....1B. doi:10.1098/rsta.1895.0001. ISSN 1364-503X.
25. ^ Carl Braun, Denkschriften der 1000. Akad. d. Wiss. (Wien), math. u. naturwiss. Classe, 64 (1897). Braun (1897) quoted an optimistic standard uncertainty of 0.03%, 6.649(two)×10^−eleven gⁱⁱⁱ⋅kg⁻¹⋅due south⁻² merely his result was significantly worse than the 0.2% feasible at the fourth dimension.
26. ^ Sagitov, M. U., "Current Condition of Determinations of the Gravitational Abiding and the Mass of the Globe", Soviet Astronomy, Vol. 13 (1970), 712–718, translated from Astronomicheskii Zhurnal Vol. 46, No. 4 (July–August 1969), 907–915 (tabular array of historical experiments p. 715).
27. ^ Mackenzie, A. Stanley, The laws of gravitation; memoirs by 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 Research. 5 (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 Northward. (2012). "CODATA recommended values of the key physical constants: 2002" (PDF). Reviews of Modern Physics. 77 (one): i–107. arXiv:1203.5425. Bibcode:2005RvMP...77....1M. CiteSeerX10.ane.one.245.4554. doi:10.1103/RevModPhys.77.1. Archived from the original (PDF) on 6 March 2007. Retrieved 1 July 2006. Section Q (pp. 42–47) describes the mutually inconsistent measurement experiments from which the CODATA value for Thousand was derived.
31. ^ Mohr, Peter J.; Taylor, Barry Due north.; Newell, David B. (13 November 2012). "CODATA recommended values of the primal 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, Due west. H.; Langenberg, D. North. (1 July 1969). "Decision of e/h, Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Key Concrete 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, East. Richard; Taylor, B. N. (1973). "The 1973 Least‐Squares Adjustment of the Fundamental Constants". Periodical of Physical and Chemical Reference Data. AIP Publishing. 2 (4): 663–734. Bibcode:1973JPCRD...2..663C. doi:10.1063/1.3253130. hdl:2027/pst.000029951949. ISSN 0047-2689.
34. ^ Cohen, E. Richard; Taylor, Barry N. (1 Oct 1987). "The 1986 adjustment of the fundamental physical constants". Reviews of Modern Physics. American Physical Club (APS). 59 (four): 1121–1148. Bibcode:1987RvMP...59.1121C. doi:x.1103/revmodphys.59.1121. ISSN 0034-6861.
35. ^ Mohr, Peter J.; Taylor, Barry Northward. (2012). "CODATA recommended values of the fundamental physical constants: 1998". Reviews of Modern Physics. 72 (2): 351–495. arXiv:1203.5425. Bibcode:2000RvMP...72..351M. doi:10.1103/revmodphys.72.351. ISSN 0034-6861.
36. ^ Mohr, Peter J.; Taylor, Barry N. (2012). "CODATA recommended values of the fundamental physical constants: 2002". Reviews of Modern Physics. 77 (ane): 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 concrete constants: 2006". Journal of Physical and Chemical Reference Data. 37 (3): 1187–1284. arXiv:1203.5425. Bibcode:2008JPCRD..37.1187M. doi:ten.1063/1.2844785. ISSN 0047-2689.
38. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2012). "CODATA Recommended Values of the Central Concrete Constants: 2010". Journal of Concrete and Chemic Reference Data. 41 (iv): 1527–1605. arXiv:1203.5425. Bibcode:2012JPCRD..41d3109M. doi:10.1063/one.4724320. ISSN 0047-2689.
39. ^ Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (2016). "CODATA Recommended Values of the Primal Concrete Constants: 2014". Journal of Physical and Chemical Reference Data. 45 (4): 1527–1605. arXiv:1203.5425. Bibcode:2016JPCRD..45d3102M. doi:10.1063/1.4954402. ISSN 0047-2689.
40. ^ Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry North. Taylor (2019), "The 2018 CODATA Recommended Values of the Primal Concrete Constants" (Web Version 8.0). Database developed by J. Baker, M. Douma, and Southward. Kotochigova. National Plant of Standards and Technology, Gaithersburg, Doc 20899.
41. ^ Fixler, J. B.; Foster, G. T.; McGuirk, J. Thou.; Kasevich, M. A. (five January 2007). "Atom Interferometer Measurement of the Newtonian Constant of Gravity". Scientific discipline. 315 (5808): 74–77. Bibcode:2007Sci...315...74F. doi:ten.1126/science.1135459. PMID 17204644. S2CID 6271411.
42. ^ Rosi, K.; Sorrentino, F.; Cacciapuoti, L.; Prevedelli, Yard.; Tino, G. M. (26 June 2014). "Precision measurement of the Newtonian gravitational abiding using common 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 cool way to measure big 1000" (PDF). Nature. 510 (7506): 478–480. Bibcode:2014Natur.510..478S. doi:10.1038/nature13507. PMID 24965646.
44. ^ C. Rothleitner; S. Schlamminger (2017). "Invited Review Commodity: Measurements of the Newtonian abiding of gravitation, One thousand". Review of Scientific Instruments. 88 (11): 111101. Bibcode:2017RScI...88k1101R. doi:x.1063/1.4994619. PMC8195032. PMID 29195410. 111101. Nevertheless, re-evaluating or repeating experiments that have already been performed may provide insights into hidden biases or dark uncertainty. NIST has the unique opportunity to repeat the experiment of Quinn et al. [2013] with an virtually identical setup. Past mid-2018, NIST researchers volition publish their results and assign a number likewise as an dubiousness to their value. Referencing:
    • T. Quinn; H. Parks; C. Speake; R. Davis (2013). "Improved determination of G using two methods" (PDF). Phys. Rev. Lett. 111 (10): 101102. Bibcode:2013PhRvL.111j1102Q. doi:10.1103/PhysRevLett.111.101102. PMID 25166649. 101102.
    The 2018 experiment was described past C. Rothleitner. Newton's Gravitational Constant 'Big' Chiliad – A proposed Free-fall Measurement (PDF). CODATA Fundamental Constants Coming together, Eltville – 5 Feb 2015.
45. ^ Li, Qing; et al. (2018). "Measurements of the gravitational constant using two independent methods". Nature. 560 (7720): 582–588. Bibcode:2018Natur.560..582L. doi:10.1038/s41586-018-0431-5. PMID 30158607. S2CID 52121922. . See also: "Physicists simply made the well-nigh precise measurement ever of Gravity's strength". 31 Baronial 2018. Retrieved thirteen October 2018.
46. ^ Anderson, J. D.; Schubert, G.; Trimble, iii=V.; Feldman, G. R. (Apr 2015). "Measurements of Newton's gravitational abiding and the length of day". EPL. 110 (1): 10002. arXiv:1504.06604. Bibcode:2015EL....11010002A. doi:x.1209/0295-5075/110/10002. S2CID 119293843.
47. ^ ^{a b} Schlamminger, South.; 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. Five.; Izmailov, V. P. (1996). "Measurement of the gravitational abiding with a torsion rest". Measurement Techniques. 39 (10): 979–987. doi:10.1007/BF02377461. ISSN 0543-1972. S2CID 123116844.
49. ^ Mould, J.; Uddin, Due south. A. (10 Apr 2014). "Constraining a Possible Variation of Yard with Type Ia Supernovae". Publications of the Astronomical Society of Commonwealth of australia. 31: e015. arXiv:1402.1534. Bibcode:2014PASA...31...15M. doi:ten.1017/pasa.2014.9. S2CID 119292899.

Sources [edit]

• Standish., East. Myles (1995). "Report of the IAU WGAS Sub-group on Numerical Standards". In Appenzeller, I. (ed.). Highlights of Astronomy. Dordrecht: Kluwer Bookish Publishers. (Complete report available online: PostScript; PDF. Tables from the study also available: Astrodynamic Constants and Parameters)
• Gundlach, Jens H.; Merkowitz, Stephen M. (2000). "Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback". Physical Review Letters. 85 (xiv): 2869–2872. arXiv:gr-qc/0006043. Bibcode:2000PhRvL..85.2869G. doi:x.1103/PhysRevLett.85.2869. PMID 11005956. S2CID 15206636.

External links [edit]

• Newtonian abiding of gravitation G at the National Institute of Standards and Engineering science References on Constants, Units, and Dubiety
• The Controversy over Newton's Gravitational Constant — additional commentary on measurement problems

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