Gravitational constant - wikipedia Gravitational constant Not to be confused with Gravitational coupling constant. Further information : Gravity of Earth and Standard gravity The gravitational constant G is a key quantity in Newton 's law of universal gravitation. The gravitational constant, also known as the universal gravitational constant, or as Newton 's constant, denoted by the letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton 's law of universal gravitation and in Albert Einstein 's general theory of relativity. Its measured value is approximately 6989667400000000000 ♠ 6.674 × 10 m ⋅ kg ⋅ s. Contents 1 Law of gravitation 2 Value and dimensions 2.1 Natural units 2.2 Orbital mechanics 3 History of measurement 4 The GM product 5 See also 6 Notes 7 References 8 External links Law of gravitation According to Newton 's law of universal gravitation, the attractive force ( F ) between two point - like bodies is directly proportional to the product of their masses ( m and m ), and inversely proportional to the square of the distance, r, ( inverse - square law ) between them : F = G m 1 × m 2 r 2. ( displaystyle F = G ( \frac ( m_ ( 1 ) \times m_ ( 2 ) ) ( r ^ ( 2 ) ) ) ,. ) The constant of proportionality, G, is the gravitational constant. Colloquially, the gravitational constant is also called `` Big G '', for disambiguation with `` small g '' ( g ), which is the local gravitational field of Earth ( equivalent to the free - fall acceleration ). The two quantities are related by g = GM / r ( where M is the mass of the Earth and r is the radius of the Earth ). In the general theory of relativity, the Einstein field equations, R μ ν − 1 2 R g μ ν = 8 π G c 4 T μ ν, ( displaystyle R_ ( mu \nu ) - ( \tfrac ( 1 ) ( 2 ) ) R , g_ ( mu \nu ) = ( \frac ( 8 pi G ) ( c ^ ( 4 ) ) ) T_ ( mu \nu ) ,, ) Newton 's constant appears in the proportionality between the spacetime curvature and the energy density component of the stress -- energy tensor. The scaled gravitational constant κ = 8π / c G ≈ 6957207100000000000 ♠ 2.071 × 10 s ⋅ m ⋅ kg ( depending on the choice of definition of the stress -- energy tensor it can also be normalized as κ = 8π / c G ≈ 6974186600000000000 ♠ 1.866 × 10 m ⋅ kg ) is also known as Einstein 's constant. Value and dimensions The gravitational constant is a physical constant that is difficult to measure with high accuracy. This is because the gravitational force is extremely weak compared with other fundamental forces. In SI units, the 2014 CODATA - recommended value of the gravitational constant ( with standard uncertainty in parentheses ) is : G = 6.67408 ( 31 ) × 10 − 11 m 3 k g − 1 s − 2 ( displaystyle G = 6.67408 ( 31 ) \times 10 ^ ( - 11 ) ( \rm ( m ^ ( 3 ) kg ^ ( - 1 ) s ^ ( - 2 ) ) ) ) This corresponds to a relative standard uncertainty of 6995470000000000000 ♠ 4.7 × 10. The dimensions assigned to the gravitational constant are force times length squared divided by mass squared ; this is equivalent to length cubed, divided by mass and by time squared : ( G ) = ( F ) ( L ) 2 ( M ) 2 = ( L ) 3 ( M ) ( T ) 2 ( displaystyle ( G ) = ( \frac ( ( F ) ( L ) ^ ( 2 ) ) ( ( M ) ^ ( 2 ) ) ) = ( \frac ( ( L ) ^ ( 3 ) ) ( ( M ) ( T ) ^ ( 2 ) ) ) ) In SI base units, this amounts to meters cubed per kilogram per second squared : N m 2 k g − 2 = m 3 k g − 1 s − 2 ( displaystyle ( \rm ( \N m ^ ( 2 ) kg ^ ( - 2 ) ) ) = ( \rm ( m ^ ( 3 ) kg ^ ( - 1 ) s ^ ( - 2 ) ) ) ). In cgs, G can be written as G ≈ 6992667400000000000 ♠ 6.674 × 10 cm ⋅ g ⋅ s. Natural units Further information : Natural units and Gravitational coupling constant The gravitational constant is taken as the basis of the Planck units : it is equal to the cube of the Planck length divided by the product of the Planck mass and the square of Planck time : G = l P 3 m P t P 2. ( displaystyle G = ( \frac ( l_ ( \rm ( P ) ) ^ ( 3 ) ) ( m_ ( \rm ( P ) ) t_ ( \rm ( P ) ) ^ ( 2 ) ) ). ) In other words, in Planck units, G has the numerical value of 7000100000000000000 ♠ 1. Thus, in Planck units, and other natural units taking G as their basis, the gravitational constant can not be measured as it is set to its value by definition. Depending on the choice of units, variation in a physical constant in one system of units shows up as variation of another constant in another system of units ; variation in dimensionless physical constants is preserved independently of the choice of units ; in the case of the gravitational constant, such a dimensionless value is the gravitational coupling constant, α G = G m e 2 ħ c = ( m e m P ) 2 ≈ 1.7518 × 10 − 45 ( displaystyle alpha _ ( \text ( G ) ) = ( \frac ( Gm_ ( \text ( e ) ) ^ ( 2 ) ) ( hbar c ) ) = left ( ( \frac ( m_ ( \text ( e ) ) ) ( m_ ( \text ( P ) ) ) ) \right ) ^ ( 2 ) approx 1.7518 \times 10 ^ ( - 45 ) ), a measure for the gravitational attraction between a pair of electrons, proportional to the square of the electron rest mass. Orbital mechanics In astrophysics, it is convenient to measure distances in parsecs ( pc ), velocities in kilometers per second ( km / s ) and masses in solar units M. In these units, the gravitational constant is : G ≈ 4.302 × 10 − 3 p c M ⊙ − 1 ( k m / s ) 2. ( displaystyle G approx 4.302 \times 10 ^ ( - 3 ) ( \rm ( pc ) ) M_ ( odot ) ^ ( - 1 ) ( \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 : G ≈ 1.90809 × 10 5 R ⊙ M ⊙ − 1 ( k m / s ) 2. ( displaystyle G approx 1.90809 \times 10 ^ ( 5 ) ( \rm ( R_ ( odot ) ) ) M_ ( odot ) ^ ( - 1 ) ( \rm ( ( km / s ) ^ ( 2 ) ) ). , ) In orbital mechanics, the period P of an object in circular orbit around a spherical object obeys G M = 3 π V P 2 ( displaystyle GM = ( \frac ( 3 pi V ) ( P ^ ( 2 ) ) ) ) where V is the volume inside the radius of the orbit. It follows that P 2 = 3 π G V M ≈ 10.896 h r 2 g c m − 3 V M. ( displaystyle P ^ ( 2 ) = ( \frac ( 3 pi ) ( G ) ) ( \frac ( V ) ( M ) ) approx 10.896 ( \rm ( hr ^ ( 2 ) g cm ^ ( - 3 ) ) ) ( \frac ( V ) ( M ) ). ) This way of expressing G 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 's 3rd law, expressed in units characteristic of Earth 's orbit : G = 4 π 2 A U 3 y r − 2 M ⊙ − 1 ( displaystyle G = 4 pi ^ ( 2 ) ( \rm ( AU ^ ( 3 ) ) ) ( \rm ( yr ^ ( - 2 ) ) ) M_ ( odot ) ^ ( - 1 ) , ), where distance is measured in astronomical units ( AU ), time in years, and mass in solar masses ( M ). History of measurement Diagram of torsion balance used in the Cavendish experiment 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 gravitational constant appears in Newton 's law of universal gravitation, but it was not measured until 1798, seventy - one years after Newton 's death, when Henry Cavendish performed his Cavendish experiment ( Philosophical Transactions 1798 ). Cavendish measured G implicitly, using a torsion balance invented by the geologist Rev. John Michell. 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. Cavendish 's aim was not actually to measure the gravitational constant, but rather to measure Earth 's density relative to water, through the precise knowledge of the gravitational interaction. In modern units, the density that Cavendish calculated implied a value for G of 6989667400000000000 ♠ 6.674 × 10 m ⋅ kg ⋅ s. The accuracy of the measured value of G has increased only modestly since the original Cavendish experiment. G is quite difficult to measure because gravity is much weaker than other fundamental forces, and an experimental apparatus can not be separated from the gravitational influence of other bodies. Furthermore, gravity has no established relation to other fundamental forces, so it does not appear possible to calculate it indirectly from other constants that can be measured more accurately, as is done in some other areas of physics. Published values of G have varied rather broadly, and some recent measurements of high precision are, in fact, mutually exclusive. This led to the 2010 CODATA value by NIST having 20 % increased uncertainty than in 2006. For the 2014 update, CODATA reduced the uncertainty to less than half the 2010 value. In the January 2007 issue of Science, Fixler et al. described a new measurement of the gravitational constant by atom interferometry, reporting a value of G = 6989669300000000000 ♠ 6.693 ( 34 ) × 10 m ⋅ kg ⋅ s. An improved cold atom measurement by Rosi et al. was published in 2014 of G = 6989667191000000000 ♠ 6.671 91 ( 99 ) × 10 m kg s. A controversial 2015 study of some previous measurements of G, by Anderson et al., suggested that most of the mutually exclusive values can be explained by a periodic variation. The variation was measured as having a period of 5.9 years, similar to that observed in length - of - day ( LOD ) measurements, hinting at a common physical cause which is not necessarily a variation in G. A response was produced by some of the original authors of the G measurements used in Anderson et al. This response notes that Anderson et al. not only omitted measurements, they also used the time of publication not the time the experiments were performed. A plot with estimated time of measurement from contacting original authors seriously degrades the length of day correlation. Also taking the data collected over a decade by Karagioz and Izmailov shows no correlation with length of day measurements. As such the variations in G most 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 type Ia supernovae has shown that the gravitational constant has varied by less than one part in ten billion per year over the last nine billion years. The GM product Main article : Standard gravitational parameter The quantity GM -- 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 is denoted μ. Depending on the body concerned, it may also be called the geocentric or heliocentric gravitational constant, among other names. This quantity gives a convenient simplification of various gravity - related formulas. Also, for celestial bodies such as Earth and the Sun, the value of the product GM is known much more accurately than each factor independently. Indeed, the limited accuracy available for G limits the accuracy of determination of such masses in the first place. For Earth, using M as the symbol for the mass of Earth, we have μ = G M ⊕ = ( 398 600.4415 ± 0.0008 ) k m 3 s − 2. ( displaystyle mu = GM_ ( oplus ) = ( 398 600.4415 pm 0.0008 ) ( \rm ( km ^ ( 3 ) s ^ ( - 2 ) ) ). ) For Sun, we have μ = G M ⊙ = ( 1.327 124 400 × 10 11 ) k m 3 s − 2. ( displaystyle mu = GM_ ( odot ) = ( 1.327 124 400 \times 10 ^ ( 11 ) ) ( \rm ( km ^ ( 3 ) s ^ ( - 2 ) ) ). ) Calculations in celestial mechanics can also be carried out using the units of solar masses, mean solar days and astronomical units rather than standard SI units. In this case we use the Gaussian gravitational constant k, where k = 0.017 202 098 95 A U 3 2 d a y − 1 M ⊙ − 1 2 ( displaystyle k = 0.017 202 098 95 ( \rm ( ( AU ) ^ ( \frac ( 3 ) ( 2 ) ) ( \rm ( ( day ) ^ ( - 1 ) M_ ( odot ) ^ ( - ( \frac ( 1 ) ( 2 ) ) ) ) ) ) ) ) If instead of mean solar day we use the sidereal year as our time unit, the value of ks is very close to 2π ( k = 7000628315000000000 ♠ 6.283 15 ). The standard gravitational parameter GM appears as above in Newton 's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler 's laws of planetary motion, and in the formula for escape velocity. See also Physics portal Dirac large numbers hypothesis Accelerating universe Gravity expressed in terms of orbital period Lunar Laser Ranging experiment Cosmological constant Gravitational coupling constant Strong gravitational constant Notes Jump up ^ For example, the gravitational force between an electron and proton one meter apart is approximately 6933099999999999999 ♠ 10 N, whereas the electromagnetic force between the same two particles is approximately 6972100000000000000 ♠ 10 N. The electromagnetic force in this example is some 39 orders of magnitude ( i.e. 10 ) greater than the force of gravity -- roughly the same ratio as the mass of the Sun to a microgram. References Jump up ^ `` CODATA Value : Newtonian constant of gravitation ''. The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015 - 09 - 25. 2014 CODATA recommended values Jump up ^ Gundlach, Jens H. ; Merkowitz, Stephen M. ( 2002 - 12 - 23 ). `` University of Washington Big G Measurement ''. Astrophysics Science Division. Goddard Space Flight Center. Since Cavendish first measured Newton 's Gravitational constant 200 years ago, `` Big G '' remains one of the most elusive constants in physics Jump up ^ Halliday, David ; Resnick, Robert ; Walker, Jearl. Fundamentals of Physics ( 8th ed. ). p. 336. ISBN 978 - 0 - 470 - 04618 - 0. Jump up ^ Grøn, Øyvind ; Hervik, Sigbjorn ( 2007 ). Einstein 's General Theory of Relativity : With Modern Applications in Cosmology ( illustrated ed. ). Springer Science & Business Media. p. 180. ISBN 978 - 0 - 387 - 69200 - 5. Jump up ^ Einstein, Albert ( 1916 ). `` The Foundation of the General Theory of Relativity ''. Annalen der Physik. 354 ( 7 ) : 769. Bibcode : 1916AnP... 354... 769E. doi : 10.1002 / andp. 19163540702. Archived from the original ( PDF ) on 2012 - 02 - 06. Jump up ^ Adler, Ronald ; Bazin, Maurice ; Schiffer, Menahem ( 1975 ). Introduction to General Relativity ( 2nd ed. ). New York : McGraw - Hill. p. 345. ISBN 0 - 07 - 000423 - 4. ^ Jump up to : Gillies, George T. ( 1997 ). `` The Newtonian gravitational constant : recent measurements and related studies ''. Reports on Progress in Physics. 60 ( 2 ) : 151 -- 225. Bibcode : 1997RPPh... 60... 151G. doi : 10.1088 / 0034 - 4885 / 60 / 2 / 001... A lengthy, detailed review. See Figure 1 and Table 2 in particular. Jump up ^ Mohr, Peter J. ; Newell, David B. ; Taylor, Barry N. ( 2015 - 07 - 21 ). `` CODATA Recommended Values of the Fundamental Physical Constants : 2014 ''. Reviews of Modern Physics. 88. arXiv : 1507.07956 ( physics. atom - ph ). Bibcode : 2016RvMP... 88c5009M. doi : 10.1103 / RevModPhys. 88.035009. Jump up ^ `` Newtonian constant of gravitation G ''. CODATA, NIST. Jump up ^ Brush, Stephen G. ; Holton, Gerald James ( 2001 ). Physics, the human adventure : from Copernicus to Einstein and beyond. New Brunswick, NJ : Rutgers University Press. p. 137. ISBN 0 - 8135 - 2908 - 5. Jump up ^ Mohr, Peter J. ; Taylor, Barry N. ( January 2005 ). `` CODATA recommended values of the fundamental physical constants : 2002 '' ( PDF ). Reviews of Modern Physics. 77 ( 1 ) : 1 -- 107. Bibcode : 2005RvMP... 77... 1M. doi : 10.1103 / RevModPhys. 77.1. Retrieved 2006 - 07 - 01... Section Q ( pp. 42 -- 47 ) describes the mutually inconsistent measurement experiments from which the CODATA value for G was derived. Jump up ^ `` CODATA recommended values of the fundamental physical constants : 2010 '' ( PDF ). Reviews of Modern Physics. 84 : 1527 -- 1605. 13 November 2012. arXiv : 1203.5425. Bibcode : 2012RvMP... 84.1527 M. doi : 10.1103 / RevModPhys. 84.1527. Jump up ^ Fixler, J.B. ; Foster, G.T. ; McGuirk, J.M. ; Kasevich, M.A. ( 2007 - 01 - 05 ). `` Atom Interferometer Measurement of the Newtonian Constant of Gravity ''. Science. 315 ( 5808 ) : 74 -- 77. Bibcode : 2007Sci... 315... 74F. doi : 10.1126 / science. 1135459. PMID 17204644. Jump up ^ Schlamminger, Stephan ( 18 June 2014 ). `` Fundamental constants : A cool way to measure big G ''. Nature. 510 : 478 -- 480. Bibcode : 2014Natur. 510... 478S. doi : 10.1038 / nature13507. PMID 24965646. Jump up ^ Anderson, J.D. ; Schubert, G. ; Trimble, 3 = V. ; Feldman, M.R. ( April 2015 ). `` Measurements of Newton 's gravitational constant and the length of day '' ( PDF ). EPL. 110 : 10002. arXiv : 1504.06604. Bibcode : 2015EL... 11010002A. doi : 10.1209 / 0295 - 5075 / 110 / 10002. ^ Jump up to : Schlamminger, S. ; Gundlach, J. H. ; Newman, R. D. ( 2015 ). `` Recent measurements of the gravitational constant as a function of time ''. Physical Review D. 91 ( 12 ). arXiv : 1505.01774. Bibcode : 2015PhRvD... 91l1101S. doi : 10.1103 / PhysRevD. 91.121101. ISSN 1550 - 7998. Jump up ^ Karagioz, O.V. ; 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. Jump up ^ Mould, J. ; Uddin, S.A. ( 2014 - 04 - 10 ). `` Constraining a Possible Variation of G with Type Ia Supernovae ''. Publications of the Astronomical Society of Australia. 31 : e015. arXiv : 1402.1534. Bibcode : 2014PASA... 31... 15M. doi : 10.1017 / pasa. 2014.9. Jump up ^ Ries, J.C. ; Eanes, R.J. ; Shum, C.K. ; Watkins, M.M. ( 20 March 1992 ). `` Progress in the determination of the gravitational coefficient of the Earth ''. Geophysical Research Letters. 19 ( 6 ) : 529 -- 531. Bibcode : 1992GeoRL... 19... 529R. doi : 10.1029 / 92GL00259. Retrieved 5 February 2016. Standish., E. Myles ( 1995 ). `` Report of the IAU WGAS Sub-group on Numerical Standards ''. In Appenzeller, I. Highlights of Astronomy. Dordrecht : Kluwer Academic Publishers. ( Complete report available online : PostScript ; PDF. Tables from the report 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 ( 14 ) : 2869 -- 2872. arXiv : gr - qc / 0006043. Bibcode : 2000PhRvL... 85.2869 G. doi : 10.1103 / PhysRevLett. 85.2869. PMID 11005956. External links Newtonian constant of gravitation G at the National Institute of Standards and Technology References on Constants, Units, and Uncertainty The Controversy over Newton 's Gravitational Constant -- additional commentary on measurement problems Isaac Newton Publications De analysi per aequationes numero terminorum infinitas ( 1669, published 1711 ) Method of Fluxions ( 1671 ) De motu corporum in gyrum ( 1684 ) Philosophiæ Naturalis Principia Mathematica ( 1687 ) General Scholium ( 1713 ) Opticks ( 1704 ) The Queries ( 1704 ) Arithmetica Universalis ( 1707 ) Other writings Notes on the Jewish Temple Quaestiones quaedam philosophicae The Chronology of Ancient Kingdoms Amended ( 1728 ) An Historical Account of Two Notable Corruptions of Scripture ( 1754 ) Discoveries and inventions Calculus Fluxions Newton disc Newton polygon Newton -- Okounkov body Newton 's reflector Newtonian telescope Newton scale Newton 's metal Newton 's cradle Sextant Theory expansions Kepler 's laws of planetary motion Problem of Apollonius Newtonianism Bucket argument Newton 's inequalities Newton 's law of cooling Newton 's law of universal gravitation Post-Newtonian expansion Parameterized post-Newtonian formalism Newton -- Cartan theory Schrödinger -- Newton equation Gravitational constant Newton 's laws of motion Newtonian dynamics Newton 's method in optimization Gauss -- Newton algorithm Truncated Newton method Newton 's rings Newton 's theorem about ovals Newton -- Pepys problem Newtonian potential Newtonian fluid Classical mechanics Newtonian fluid Corpuscular theory of light Leibniz -- Newton calculus controversy Newton 's notation Rotating spheres Newton 's cannonball Newton -- Cotes formulas Newton 's method Newton fractal Generalized Gauss -- Newton method Newton 's identities Newton polynomial Newton 's theorem of revolving orbits Newton -- Euler equations Newton number Kissing number problem Power number Newton 's quotient Parallelogram of force Newton -- Puiseux theorem Solar mass Dynamics Absolute space and time Finite difference Table of Newtonian series Impact depth Structural coloration Inertia Spectrum Phrases `` Hypotheses non fingo '' `` Standing on the shoulders of giants '' Life Cranbury Park Woolsthorpe Manor Early life Later life Religious views Occult studies The Mysteryes of Nature and Art Scientific revolution Copernican Revolution Friends and family Catherine Barton John Conduitt William Clarke Benjamin Pulleyn William Stukeley William Jones Isaac Barrow Abraham de Moivre John Keill Cultural depictions Newton ( Blake ) Newton ( Paolozzi ) In popular culture Related Writing of Principia Mathematica List of things named after Newton Isaac Newton Institute Isaac Newton Medal Isaac Newton Group of Telescopes Isaac Newton Telescope Newton ( unit ) Elements of the Philosophy of Newton Isaac Newton S / O Philipose GND : 4593074 - 0 Retrieved from `` https://en.wikipedia.org/w/index.php?title=Gravitational_constant&oldid=841223434 '' Categories : Gravitation Fundamental constants Hidden categories : Wikipedia articles with GND identifiers Talk Contents About Wikipedia Asturianu বাংলা Bân - lâm - gú Беларуская Беларуская ( тарашкевіца ) ‎ Български Català Čeština Dansk Deutsch Eesti Ελληνικά Español Esperanto Euskara فارسی Français Gaeilge Galego 한국어 Հայերեն हिन्दी Hrvatski Bahasa Indonesia Italiano עברית ქართული Қазақша Latviešu Lietuvių Magyar Македонски മലയാളം मराठी Bahasa Melayu မြန်မာဘာသာ Nederlands नेपाली 日本 語 Norsk Norsk nynorsk Polski Português Română Русский Scots Simple English Slovenčina Slovenščina کوردی Српски / srpski Srpskohrvatski / српскохрватски Suomi Svenska Tagalog தமிழ் Татарча / tatarça ไทย Türkçe Українська Tiếng Việt 粵語 中文 55 more Edit links This page was last edited on 14 May 2018, at 17 : 30. 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Question: in the universal law of gravitation what does the symbol r stand for
Answer: distance