Editing Gravitational constant (section)

== Definition ==
According to Newton's law of universal gravitation, the [[Norm (mathematics)#Euclidean norm|magnitude]] of the attractive [[force]] ({{math|''F''}}) between two bodies each with a spherically symmetric [[density]] distribution is directly proportional to the product of their [[mass]]es, {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}}, and inversely proportional to the square of the distance, {{math|''r''}}, directed along the line connecting their [[centre of mass|centres of mass]]:
<math display="block">F=G\frac{m_1m_2}{r^2}.</math>
The [[Proportionality (mathematics)|constant of proportionality]], {{math|''G''}}, in this non-relativistic formulation is the gravitational constant. Colloquially, the gravitational constant is also called "Big G", distinct from "small g" ({{math|''g''}}), which is the local gravitational field of Earth (also referred to as free-fall acceleration).<ref>{{cite web |first1=Jens H. |last1=Gundlach |first2=Stephen M. |last2=Merkowitz |title=University of Washington Big G Measurement |work=Astrophysics Science Division |publisher=Goddard Space Flight Center |date=23 December 2002 |url=http://asd.gsfc.nasa.gov/Stephen.Merkowitz/G/Big_G.html |quote=Since Cavendish first measured Newton's Gravitational constant 200 years ago, 'Big G' remains one of the most elusive constants in physics }}</ref><ref>{{cite book|title=Fundamentals of Physics|edition=8th |last1=Halliday |first1=David |last2=Resnick |first2=Robert |last3=Walker |first3=Jearl |isbn=978-0-470-04618-0 |page=336|title-link=Fundamentals of Physics |date=September 2007 |publisher=John Wiley & Sons, Limited }}</ref> Where <math>M_\oplus</math> is the [[mass of Earth]] and <math>r_\oplus</math> is the [[Earth radius|radius of Earth]], the two quantities are related by:
<math display="block">g = G\frac{M_\oplus}{r_\oplus^2}.</math>

The gravitational constant is a constant term in the [[Einstein field equations]] of [[general relativity]],<ref>{{cite book |title=Einstein's General Theory of Relativity: With Modern Applications in Cosmology |edition=illustrated |first1=Øyvind |last1=Grøn |first2=Sigbjorn |last2=Hervik |publisher=Springer Science & Business Media |year=2007 |isbn=978-0-387-69200-5 |page=180 |url=https://books.google.com/books?id=IyJhCHAryuUC&pg=PA180}}</ref><ref name="ein">{{cite journal |last=Einstein |first=Albert |title=The Foundation of the General Theory of Relativity |journal=[[Annalen der Physik]] |volume=354 |issue=7 |pages=769–822 |year=1916 |url=http://www.alberteinstein.info/gallery/science.html |doi=10.1002/andp.19163540702 |format=[[PDF]] |bibcode=1916AnP...354..769E |archive-url=https://web.archive.org/web/20120206225139/http://www.alberteinstein.info/gallery/gtext3.html |archive-date=6 February 2012}}</ref>
<math display="block">G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu} \,,</math>
where {{math|''G''{{sub|''μν''}}}} is the [[Einstein tensor]] (not the gravitational constant despite the use of {{mvar|G}}), {{math|Λ}} is the [[cosmological constant]], {{mvar|g{{sub|μν}}}} is the [[metric tensor (general relativity)|metric tensor]], {{mvar|T{{sub|μν}}}} is the [[stress–energy tensor]],  and {{math|''κ''}} is the [[Einstein gravitational constant]], a constant originally introduced by [[Albert Einstein|Einstein]] that is directly related to the Newtonian constant of gravitation:<ref name="ein" /><ref>{{cite book |title= Introduction to General Relativity |url= https://archive.org/details/introductiontoge00adle |url-access= limited |first1=Ronald |last1=Adler |first2=Maurice |last2=Bazin |first3=Menahem |last3=Schiffer |publisher= McGraw-Hill |location= New York |year= 1975 |edition= 2nd |isbn= 978-0-07-000423-8 |page= [https://archive.org/details/introductiontoge00adle/page/n360 345]}}</ref>{{efn|Depending on the choice of definition of the Einstein tensor and of the stress–energy tensor it can alternatively be defined as {{math|1=''κ'' = {{sfrac|8π''G''|''c''<sup>2</sup>}} ≈ {{val|1.866|e=-26|u=m⋅kg<sup>−1</sup>}}}}}}
<math display="block">\kappa = \frac{8\pi G}{c^4} \approx 2.076\,647(46) \times 10^{-43} \mathrm{~N^{-1}}.</math>