View source for Gravity

{{Short description|Attraction of masses and energy}}
{{Other uses}}
{{redirect-multi|2|Gravitation|Law of Gravity}}
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{{Use American English|date=December 2024}}
{{Use dmy dates|date=December 2024}}
[[File:UGC 1810 and UGC 1813 in Arp 273 (captured by the Hubble Space Telescope).jpg|thumb|upright=1.35|The shapes of two massive [[galaxies]] in this image evolved under the effects of gravity.]]
{{Classical mechanics}}

In physics, '''gravity''' ({{Etymology|lat|gravitas|weight}}<ref>{{cite web |url=https://browse.dict.cc/latin-english/gravitas.html |title=dict.cc dictionary :: gravitas :: English-Latin translation |access-date=11 September 2018 |archive-date=13 August 2021 |archive-url=https://web.archive.org/web/20210813203625/https://browse.dict.cc/latin-english/gravitas.html |url-status=live }}</ref>), also known as '''gravitation''' or a '''gravitational interaction''',<ref>{{cite book |title=Particles and Fundamental Interactions: An Introduction to Particle Physics |edition=illustrated |first1=Sylvie |last1=Braibant |first2=Giorgio |last2=Giacomelli |first3=Maurizio |last3=Spurio |publisher=Springer Science & Business Media |year=2011 |isbn=978-94-007-2463-1 |page=109 |url=https://books.google.com/books?id=0Pp-f0G9_9sC}} [https://books.google.com/books?id=0Pp-f0G9_9sC&pg=PA109 Extract of page 109]</ref> is a [[fundamental interaction]], which may be described as the effect of a field that is generated by a gravitational source such as mass.

The gravitational attraction between clouds of primordial [[hydrogen]] and clumps of [[dark matter]] in the early [[universe]] caused the hydrogen gas to [[coalescence (physics)|coalesce]], eventually condensing and fusing to [[star formation|form stars]]. At larger scales this resulted in galaxies and clusters, so gravity is a primary driver for the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.

Gravity is described by the [[general relativity|general theory of relativity]], proposed by [[Albert Einstein]] in 1915, which describes gravity in terms of the [[curvature]] of [[spacetime]], caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a [[black hole]], from which nothing—not even light—can escape once past the black hole's [[event horizon]].<ref>{{cite web |url=http://hubblesite.org/explore_astronomy/black_holes/home.html |title=HubbleSite: Black Holes: Gravity's Relentless Pull|website=hubblesite.org|access-date=7 October 2016 |archive-date=26 December 2018 |archive-url=https://web.archive.org/web/20181226185228/http://hubblesite.org/explore_astronomy/black_holes/home.html |url-status=live }}</ref> However, for most applications, gravity is sufficiently well approximated by [[Newton's law of universal gravitation]], which describes gravity as an attractive [[force]] between any two bodies that is [[proportionality (mathematics)|proportional]] to the product of their masses and [[inversely proportional]] to the [[square (algebra)|square]] of the [[distance]] between them.

Scientists are looking for a theory that describes gravity in the framework of [[quantum mechanics]] ([[quantum gravity]]),<ref name="NYT-20221010">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=10 October 2022 |title=Black Holes May Hide a Mind-Bending Secret About Our Universe – Take gravity, add quantum mechanics, stir. What do you get? Just maybe, a holographic cosmos. |url=https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html |url-status=live |archive-url=https://web.archive.org/web/20221116151210/https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html |archive-date=16 November 2022 |access-date=10 October 2022 |work=[[The New York Times]]}}</ref> which would unify gravity and the other known fundamental interactions of physics in a single mathematical framework (a [[theory of everything]]).<ref>{{cite news |last=Cartwright |first=Jon |date=May 17, 2025 |title=Defying gravity |work=New Scientist |pages=30–33 }}</ref>

On the surface of a planetary body such as [[Gravity of Earth|on Earth]], this leads to gravitational acceleration of all objects towards the body, modified by the centrifugal effects arising from the rotation of the body.<ref name=HWM/> In this context, gravity gives [[weight]] to [[physical object]]s and is essential to understanding the mechanisms that are responsible for surface water [[gravity wave|wave]]s, lunar [[tide]]s and substantially contributes to weather patterns. Gravitational weight also has many important biological functions, helping to guide the growth of plants through the process of [[gravitropism]] and influencing the [[Circulatory system|circulation]] of fluids in [[multicellular organism]]s.

== Characterization ==
Gravity is the word used to describe a [[physical law]], a [[fundamental interaction|fundamental physical interaction]] that derives primarily from [[mass]], and the observed consequences of that interaction on objects. Gravity is the law that every object with mass attracts every other object in the universe in proportion to each mass and inversely proportional to the square of the distance between them. The force of gravity, {{mvar|F}} is written using the [[gravitational constant]], {{mvar|G}}, as<ref name=Feynman-7>{{cite book |last1=Feynman |first1=Richard P. |title=The Feynman lectures on physics |last2=Leighton |first2=Robert B. |last3=Sands |first3=Matthew L. |date=2006 |publisher=Pearson Addison Wesley |isbn=978-0-8053-9045-2 |edition=Definitive |location=San Francisco, Calif. |chapter=The Theory of Gravitation |chapter-url=https://www.feynmanlectures.caltech.edu/I_07.html}}</ref> 
<math display="block">F=G\frac{mm'}{r^2}</math>
for two masses, {{mvar|m}}, and {{math|''m''′}} separated by a distance {{mvar|r}}.

Gravity is considered to be one of four fundamental interactions. The [[electromagnetic force]] law is similar to the force law for gravity: both depend upon the square of the inverse distance between objects in typical interactions. The ratio of gravitational attraction of two [[electrons]] to their electrical repulsion is 1 to {{val|4.17|e=42}}.<ref name=Feynman-7/> As a result, gravity can generally be neglected at the level of [[subatomic particle]]s.<ref>{{cite book |title=Scientific Development and Misconceptions Through the Ages: A Reference Guide |edition=illustrated |first1=Robert E. |last1=Krebs |publisher=Greenwood Publishing Group |year=1999 |isbn=978-0-313-30226-8 |page=[https://archive.org/details/scientificdevelo0000kreb/page/133 133] |url=https://archive.org/details/scientificdevelo0000kreb|url-access=registration }}</ref> Gravity becomes the most significant interaction between objects at the scale of astronomical bodies, and it determines the motion of [[satellite]]s, [[planet]]s, [[star]]s, [[Galaxy|galaxies]], and even [[Electromagnetic radiation|light]]. Gravity is also fundamental in another sense: the [[inertial mass]] that appears in [[Newton's second law]] is the same as the [[gravitational mass]]. This [[equivalence principle]] is a [[scientific hypothesis]] that has been tested experimentally to more than one part in a trillion.<ref>S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024) [https://pdg.lbl.gov/2024/reviews/rpp2024-rev-gravity-tests.pdf#page=2.39 21. Experimental Tests of Gravitational Theory]</ref>

==History==
{{main|History of gravitational theory}}

===Ancient world===
The nature and mechanism of gravity were explored by a wide range of ancient scholars. In [[Ancient Greece]], [[Aristotle]] believed that each of the [[classical elements]] had a [[Aristotelian physics#Natural place|natural place]] in the universe which it tends to move toward - earth at the center of the universe (the center of the Earth, which was known to be spherical); then water, air, fire, and aether in concentric shells from inner to outer.<ref>''[[De Caelo]]'' II. 13-14.</ref> He also thought that the speed of a falling object should increase with its weight, a conclusion that was later shown to be false.<ref>{{Cite web |last=Cappi |first=Alberto |title=The concept of gravity before Newton |url=http://www.cultureandcosmos.org/pdfs/16/Cappi_INSAPVII_Gravity_before_Newton.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.cultureandcosmos.org/pdfs/16/Cappi_INSAPVII_Gravity_before_Newton.pdf |archive-date=9 October 2022 |url-status=live |website=Culture and Cosmos}}</ref> While Aristotle's view was widely accepted throughout Ancient Greece, there were other thinkers such as [[Plutarch]] who correctly predicted that the attraction of gravity was not unique to the Earth.<ref>{{Cite journal |last1=Bakker |first1=Frederik |last2=Palmerino |first2=Carla Rita |date=1 June 2020 |title=Motion to the Center or Motion to the Whole? Plutarch's Views on Gravity and Their Influence on Galileo |url=https://www.journals.uchicago.edu/doi/abs/10.1086/709138 |journal=Isis |volume=111 |issue=2 |pages=217–238 |doi=10.1086/709138 |s2cid=219925047 |issn=0021-1753 |hdl=2066/219256 |hdl-access=free |access-date=2 May 2022 |archive-date=2 May 2022 |archive-url=https://web.archive.org/web/20220502172704/https://www.journals.uchicago.edu/doi/abs/10.1086/709138 |url-status=live |url-access=subscription }}</ref>

Although he did not understand gravity as a force, the ancient Greek philosopher [[Archimedes]] discovered the [[center of gravity]] of a triangle.<ref>{{cite book |last1=Neitz |first1=Reviel |url=https://books.google.com/books?id=ZC1MOaAkKnsC&pg=PT125 |title=The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest |last2=Noel |first2=William |date=13 October 2011 |publisher=Hachette UK |isbn=978-1-78022-198-4 |page=125 |access-date=10 April 2019 |archive-url=https://web.archive.org/web/20200107004958/https://books.google.com/books?id=ZC1MOaAkKnsC&pg=PT125 |archive-date=7 January 2020 |url-status=live}}</ref> He postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity.<ref>{{cite book |author=Tuplin |first1=CJ |url=https://books.google.com/books?id=ajGkvOo0egwC&pg=PR11 |title=Science and Mathematics in Ancient Greek Culture |last2=Wolpert |first2=Lewis |publisher=Hachette UK |year=2002 |isbn=978-0-19-815248-4 |page=xi |access-date=10 April 2019 |archive-url=https://web.archive.org/web/20200117170945/https://books.google.com/books?id=ajGkvOo0egwC&pg=PR11 |archive-date=17 January 2020 |url-status=live}}</ref> Two centuries later, the Roman engineer and architect [[Vitruvius]] contended in his ''[[De architectura]]'' that gravity is not dependent on a substance's weight but rather on its "nature".<ref>{{Cite book  | last = Vitruvius  | first = Marcus Pollio  | author-link = Marcus Vitruvius Pollio  | editor = Alfred A. Howard  | title = De Architectura libri decem  | trans-title = Ten Books on Architecture  | place = Harvard University, Cambridge  | publisher = Harvard University Press  | date = 1914  | chapter = 7  | page = 215  | chapter-url = http://www.gutenberg.org/files/20239/20239-h/29239-h.htm#Page_215  | others = Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan  | access-date = 10 April 2019 | archive-date = 13 October 2016 | archive-url = https://web.archive.org/web/20161013193438/http://www.gutenberg.org/files/20239/20239-h/29239-h.htm#Page_215  | url-status = live  }}</ref> In the 6th century CE, the [[Byzantine Empire|Byzantine]] Alexandrian scholar [[John Philoponus]] proposed the theory of impetus, which modifies Aristotle's theory that "continuation of motion depends on continued action of a force" by incorporating a causative force that diminishes over time.<ref>Philoponus' term for impetus is "ἑνέργεια ἀσώματος κινητική" ("incorporeal motive ''[[Potentiality and actuality|enérgeia]]''"); see ''[[Commentaria in Aristotelem Graeca|CAG]]'' XVII, [https://books.google.com/books?id=dVcqvVDiNVUC ''Ioannis Philoponi in Aristotelis Physicorum Libros Quinque Posteriores Commentaria''] {{Webarchive|url=https://web.archive.org/web/20231222224140/https://books.google.com/books?id=dVcqvVDiNVUC |date=22 December 2023 }}, [[Walter de Gruyter]], 1888, p. 642: "λέγω δὴ ὅτι ἑνέργειά τις ἀσώματος κινητικὴ ἑνδίδοται ὑπὸ τοῦ ῥιπτοῦντος τῷ ῥιπτουμένῳ [I say that impetus (incorporeal motive energy) is transferred from the thrower to the thrown]."</ref>

In 628 CE, the [[India]]n mathematician and astronomer [[Brahmagupta]] proposed the idea that gravity is an attractive force that draws objects to the Earth and used the term ''[[wikt:गुरुत्वाकर्षण|gurutvākarṣaṇ]]'' to describe it.<ref>{{cite book |last1=Pickover |first1=Clifford |url=https://books.google.com/books?id=SQXcpvjcJBUC&pg=PA105 |title=Archimedes to Hawking: Laws of Science and the Great Minds Behind Them |date=16 April 2008 |publisher=Oxford University Press |isbn=978-0-19-979268-9 |language=en |access-date=29 August 2017 |archive-url=https://web.archive.org/web/20170118060420/https://books.google.com/books?id=SQXcpvjcJBUC |archive-date=18 January 2017 |url-status=live}}</ref>{{rp|105}}<ref>{{cite book |last1=Bose |first1=Mainak Kumar |url=https://books.google.com/books?id=nbItAAAAMAAJ&q=gravity |title=Late classical India |publisher=A. Mukherjee & Co. |year=1988 |language=en |access-date=28 July 2021 |archive-url=https://web.archive.org/web/20210813203602/https://books.google.com/books?id=nbItAAAAMAAJ&q=gravity |archive-date=13 August 2021 |url-status=live}}</ref><ref>{{cite book |last=Sen |first=Amartya |title=The Argumentative Indian |date=2005 |publisher=Allen Lane |isbn=978-0-7139-9687-6 |page=29}}</ref>

In the ancient [[Middle East]], gravity was a topic of fierce debate. The [[Persians|Persian]] intellectual [[Al-Biruni]] believed that the force of gravity was not unique to the Earth, and he correctly assumed that other [[Astronomical object|heavenly bodies]] should exert a gravitational attraction as well.<ref>{{cite book |last1=Starr |first1=S. Frederick |title=Lost Enlightenment: Central Asia's Golden Age from the Arab Conquest to Tamerlane |date=2015 |publisher=Princeton University Press |isbn=978-0-691-16585-1 |page=260 |url=https://books.google.com/books?id=hWyYDwAAQBAJ&pg=PA260}}</ref> In contrast, [[Al-Khazini]] held the same position as Aristotle that all matter in the [[Universe]] is attracted to the center of the Earth.<ref>{{Cite encyclopedia|encyclopedia=Encyclopedia of the History of Arabic Science|editor-first=Rāshid|editor-last=Rushdī|date=1996|publisher=Psychology Press|isbn=978-0-415-12411-9|first1=Mariam |last1=Rozhanskaya |first2=I. S. |last2=Levinova |title=Statics |volume=2 |pages=614–642}}</ref>

[[File:The Leaning Tower of Pisa SB.jpeg|thumb|upright|The [[Leaning Tower of Pisa]], where according to legend Galileo performed an experiment about the speed of falling objects]]

===Scientific Revolution===
{{main|Scientific Revolution}}
In the mid-16th century, various European scientists experimentally disproved the [[Aristotelian physics|Aristotelian]] notion that heavier objects [[Free fall|fall]] at a faster rate.<ref name="Wallace-2018">{{Cite book|last=Wallace|first=William A.|url=https://books.google.com/books?id=8GxQDwAAQBAJ&pg=PR21|title=Domingo de Soto and the Early Galileo: Essays on Intellectual History|publisher=[[Routledge]]|year=2018|isbn=978-1-351-15959-3|location=Abingdon, UK|pages=119, 121–22|language=en|orig-date=2004|access-date=4 August 2021|archive-date=16 June 2021|archive-url=https://web.archive.org/web/20210616043300/https://books.google.com/books?id=8GxQDwAAQBAJ&pg=PR21|url-status=live}}</ref> In particular, the [[Spanish people|Spanish]] Dominican priest [[Domingo de Soto]] wrote in 1551 that bodies in [[free fall]] uniformly accelerate.<ref name="Wallace-2018"/> De Soto may have been influenced by earlier experiments conducted by other [[Dominican Order|Dominican]] priests in Italy, including those by [[Benedetto Varchi]], Francesco Beato, [[Luca Ghini]], and [[Giovan Battista Bellaso|Giovan Bellaso]] which contradicted Aristotle's teachings on the fall of bodies.<ref name="Wallace-2018"/>

The mid-16th century Italian physicist [[Giambattista Benedetti]] published papers claiming that, due to [[relative density|specific gravity]], objects made of the same material but with different masses would fall at the same speed.<ref name="Drabkin">{{Cite journal| doi = 10.1086/349706| issn = 0021-1753| volume = 54| issue = 2| pages = 259–262| last = Drabkin| first = I. E.| title = Two Versions of G. B. Benedetti's Demonstratio Proportionum Motuum Localium| journal = Isis| year = 1963| jstor = 228543| s2cid = 144883728}}</ref> With the 1586 [[Delft tower experiment]], the [[Flanders|Flemish]] physicist [[Simon Stevin]] observed that two cannonballs of differing sizes and weights fell at the same rate when dropped from a tower.<ref name="Stevin">{{Cite book|url=https://books.google.com/books?id=YicuDwAAQBAJ&dq=delft+tower+experiment&pg=PA26|title=Ripples in Spacetime: Einstein, Gravitational Waves, and the Future of Astronomy|last=Schilling|first=Govert|date=31 July 2017|publisher=Harvard University Press|isbn=978-0-674-97166-0|page=26|language=en|access-date=16 December 2021|archive-date=16 December 2021|archive-url=https://web.archive.org/web/20211216025328/https://books.google.com/books?id=YicuDwAAQBAJ&dq=delft+tower+experiment&pg=PA26|url-status=live}}</ref>

In the late 16th century, [[Galileo Galilei]]'s careful measurements of balls rolling down [[Inclined plane|inclines]] allowed him to firmly establish that gravitational acceleration is the same for all objects.<ref>[[Galileo]] (1638), ''[[Two New Sciences]]'', First Day Salviati speaks: "If this were what Aristotle meant you would burden him with another error which would amount to a falsehood; because, since there is no such sheer height available on earth, it is clear that Aristotle could not have made the experiment; yet he wishes to give us the impression of his having performed it when he speaks of such an effect as one which we see."</ref><ref>{{Cite book |last=Sobel |first=Dava |title=Galileo's daughter: a historical memoir of science, faith, and love |date=1993 |publisher=Walker |isbn=978-0-8027-1343-8 |location=New York}}</ref>{{rp|334}} Galileo postulated that [[air resistance]] is the reason that objects with a low density and high [[surface area]] fall more slowly in an atmosphere. In his 1638 work ''[[Two New Sciences]]'', Galileo proved that the distance traveled by a falling object is proportional to the [[Square (algebra)|square]] of the time elapsed. His method was a form of graphical numerical integration since concepts of algebra and calculus were unknown at the time.<ref>{{cite book|last=Gillispie|first=Charles Coulston|url=https://archive.org/details/edgeofobjectivit00char/page/n13/mode/2up|title=The Edge of Objectivity: An Essay in the History of Scientific Ideas|publisher=Princeton University Press|year=1960|isbn=0-691-02350-6|pages=3–6|author-link=Charles Coulston Gillispie}}</ref>{{rp|4}} This was later confirmed by Italian scientists [[Jesuits]] [[Francesco Maria Grimaldi|Grimaldi]] and [[Giovanni Battista Riccioli|Riccioli]] between 1640 and 1650. They also calculated the magnitude of [[Earth's gravity|the Earth's gravity]] by measuring the oscillations of a pendulum.<ref>J. L. Heilbron, ''Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics'' (Berkeley, California: University of California Press, 1979), p. 180.</ref>

Galileo also broke with incorrect ideas of Aristotelian philosophy by regarding [[inertia]] as persistence of motion, not a tendency to come to rest. By considering that the laws of physics appear identical on a moving ship to those on land, Galileo developed the concepts of [[reference frame]] and the [[principle of relativity]].<ref>{{Cite book |last=Ferraro |first=Rafael |title=Einstein's space-time: an introduction to special and general relativity |date=2007 |publisher=Springer |isbn=978-0-387-69946-2 |location=New York |oclc=141385334}}</ref>{{rp|5}} These concepts would become central to Newton's mechanics, only to be transformed in Einstein's theory of gravity, the general theory of relativity.<ref name=Weinberg-1972>{{cite book |last=Weinberg |first=Steven |url=https://archive.org/details/gravitationcosmo00stev_0 |title=Gravitation and cosmology |date=1972 |publisher=John Wiley & Sons |isbn=978-0-471-92567-5 |author-link=Steven Weinberg |url-access=registration}}</ref>{{rp|17}}

In last quarter of the 16th century [[Tycho Brahe]] created accurate tools for [[astrometry]], providing careful observations of the planets. His assistant and successor, [[Johannes Kepler]] analyzed these data into three empirical laws of planetary motion. These laws were central to the development of a theory of gravity a hundred years later.<ref>{{Cite journal |last=Høg |first=Erik |date=August 2009 |title=400 years of astrometry: from Tycho Brahe to Hipparcos |url=http://link.springer.com/10.1007/s10686-009-9156-7 |journal=Experimental Astronomy |language=en |volume=25 |issue=1–3 |pages=225–240 |doi=10.1007/s10686-009-9156-7 |bibcode=2009ExA....25..225H |issn=0922-6435|url-access=subscription }}</ref>
In his 1609 book [[Astronomia nova]] Kepler described gravity as a mutual attraction, claiming that if the Earth and Moon were not held apart by some force they would come together. He recognized that mechanical forces cause action, creating a kind of celestial machine. On the other hand Kepler viewed the force of the Sun on the planets as magnetic and acting tangential to their orbits and he assumed with Aristotle that inertia meant objects tend to come to rest.<ref>{{Cite journal |last=Holton |first=Gerald |date=1956-05-01 |title=Johannes Kepler's Universe: Its Physics and Metaphysics |url=https://pubs.aip.org/ajp/article/24/5/340/1036024/Johannes-Kepler-s-Universe-Its-Physics-and |journal=American Journal of Physics |language=en |volume=24 |issue=5 |pages=340–351 |doi=10.1119/1.1934225 |bibcode=1956AmJPh..24..340H |issn=0002-9505}}</ref><ref name=Dijksterhuss-1954>Dijksterhuis, E. J. (1954). History of Gravity and Attraction before Newton. Cahiers d'Histoire Mondiale. Journal of World History. Cuadernos de Historia Mundial, 1(4), 839.</ref>{{rp|846}}

In 1666, [[Giovanni Alfonso Borelli]] avoided the key problems that limited Kepler. By Borelli's time the concept of inertia had its modern meaning as the tendency of objects to remain in uniform motion and he viewed the Sun as just another heavenly body. Borelli developed the idea of mechanical equilibrium, a balance between inertia and gravity. Newton cited Borelli's influence on his theory.<ref name=Dijksterhuss-1954/>{{rp|848}}

In 1657, [[Robert Hooke]] published his ''[[Micrographia]]'', in which he hypothesized that the Moon must have its own gravity.<ref name=Gribbin-2017>{{Cite book |title=Out of the shadow of a giant: Hooke, Halley and the birth of British science |last1=Gribbin |last2=Gribbin |first1= John |first2=Mary |isbn=978-0-00-822059-4 |location=London |oclc=966239842 |year=2017 |publisher=William Collins |author-link=John Gribbin}}</ref>{{rp|57}} In a communication to the Royal Society in 1666 and his 1674 Gresham lecture, ''An Attempt to prove the Annual Motion of the Earth'', Hooke took the important step of combining related hypothesis and then forming predictions based on the hypothesis.<ref>{{cite book |last=Stewart |first=Dugald |date=1816 |author-link=Dugald Stewart |title=Elements of the Philosophy of the Human Mind |volume= 2 |url=https://archive.org/details/b28041604/page/n5/mode/2up |page=[https://archive.org/details/b28041604/page/434/mode/2up 434] |publisher=Constable & Co; Cadell & Davies |location=Edinburgh; London }}</ref> He wrote:
{{blockquote|I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having a simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it....<ref>{{cite book |last=Hooke |first=Robert |date=1679 |title=Lectiones Cutlerianae, or A collection of lectures, physical, mechanical, geographical & astronomical : made before the Royal Society on several occasions at Gresham Colledge [i.e. College]: to which are added divers miscellaneous discourses |url=https://archive.org/details/LectionesCutler00Hook/page/n23/mode/2up}}</ref>{{sfnp|Hooke|1679|loc='' An Attempt to prove the Annual Motion of the Earth'', [https://archive.org/details/LectionesCutler00Hook/page/n23/mode/2up page 2, 3]}}}} 
Hooke was an important communicator who helped reformulate the scientific enterprise.<ref name=Guicciardini>{{Cite journal |last=Guicciardini |first=Niccolò |date=2020-01-01 |title=On the invisibility and impact of Robert Hooke's theory of gravitation |url=https://www.degruyterbrill.com:443/document/doi/10.1515/opphil-2020-0131/html |journal=Open Philosophy |language=en |volume=3 |issue=1 |pages=266–282 |doi=10.1515/opphil-2020-0131 |issn=2543-8875|hdl=2434/746528 |hdl-access=free }}</ref> He was one of the first professional scientists and worked as the then-new [[Royal Society]]'s curator of experiments for 40 years.<ref>{{Cite book |last=Purrington |first=Robert D. |title=The first professional scientist: Robert Hooke and the Royal Society of London |date=2009 |publisher=Birkhäuser |isbn=978-3-0346-0037-8 |series=Science networks. Historical studies |location=Basel, Switzerland Boston}}</ref> However his valuable insights remained hypotheses and some of these were incorrect.<ref>{{Cite journal |last=Hecht |first=Eugene |date=July 2021 |title=The true story of Newtonian gravity |url=https://pubs.aip.org/aapt/ajp/article/89/7/683-692/1056900 |journal=American Journal of Physics |language=en |volume=89 |issue=7 |pages=683–692 |doi=10.1119/10.0003535 |issn=0002-9505|url-access=subscription }}</ref> He was unable develop a mathematical theory of gravity and work out the consequences.<ref name=Dijksterhuss-1954/>{{rp|853}} For this he turned to Newton, writing him a letter in 1679, outlining a model of planetary motion in a void or vacuum due to attractive action at a distance. This letter likely turned Newton's thinking in a new direction leading to his revolutionary work on gravity.<ref name=Guicciardini/> When Newton reported his results in 1686, Hooke claimed the [[Newton–Hooke priority controversy for the inverse square law|inverse square law portion was his "notion"]].

===Newton's theory of gravitation===
{{main|Newton's law of universal gravitation}}
[[File:Portrait of Sir Isaac Newton, 1689.jpg|thumb|upright|English physicist and mathematician, Sir [[Isaac Newton]] (1642–1727)]]

Before 1684, scientists including [[Christopher Wren]], [[Robert Hooke]] and [[Edmund Halley]] determined that [[Kepler's laws of planetary motion|Kepler's third law]], relating to planetary orbital periods, would prove the [[Inverse-square law|inverse square law]] if the orbits were circles. However the orbits were known to be ellipses. At Halley's suggestion, Newton tackled the problem and was able to prove that ellipses also proved the inverse square relation from Kepler's observations.<ref name=Weinberg-1972/>{{rp|13}} In 1684, [[Isaac Newton]] sent a manuscript to [[Edmond Halley]] titled ''[[De motu corporum in gyrum]] ('On the motion of bodies in an orbit')'', which provided a physical justification for [[Kepler's laws of planetary motion]].<ref name="Sagan-1997">{{cite book |last1=Sagan |first1=Carl |url=https://books.google.com/books?id=LhkoowKFaTsC |title=Comet |last2=Druyan |first2=Ann |publisher=Random House |year=1997 |isbn=978-0-3078-0105-0 |location=New York |pages=52–58 |author-link1=Carl Sagan |author-link2=Ann Druyan |access-date=5 August 2021 |archive-url=https://web.archive.org/web/20210615020250/https://books.google.com/books?id=LhkoowKFaTsC |archive-date=15 June 2021 |url-status=live |name-list-style=amp}}</ref> Halley was impressed by the manuscript and urged Newton to expand on it, and a few years later Newton published a groundbreaking book called ''[[Philosophiæ Naturalis Principia Mathematica]]'' (''Mathematical Principles of Natural Philosophy'').

The revolutionary aspect of Newton's theory of gravity was the unification of Earth-bound observations of acceleration with celestial mechanics.<ref name="Longair-2009"/>{{rp|4}} In his book, Newton described gravitation as a universal force, and claimed that it operated on objects "according to the quantity of solid matter which they contain and propagates on all sides to immense distances always at the inverse square of the distances".<ref name="Principa">{{Cite book |last=Newton |first=Isaac |author-link=Isaac Newton |title=The Principia, The Mathematical Principles of Natural Philosophy |date=1999 |publisher=University of California Press |location=Los Angeles |translator-last1=Cohen |translator-first1=I.B. |translator-last2=Whitman |translator-first2=A.}}</ref>{{rp|546}} This formulation had two important parts. First was [[Equivalence principle|equating inertial mass and gravitational mass]]. Newton's 2nd law defines force via <math>F=ma</math> for inertial mass, his [[Newton's law of universal gravitation|law of gravitational]] force uses the same mass. Newton did experiments with pendulums to verify this concept as best he could.<ref name=Weinberg-1972/>{{rp|11}}

The second aspect of Newton's formulation was the inverse square of distance. This aspect was not new: the astronomer [[Ismaël Bullialdus]] proposed it around 1640. Seeking proof, Newton made quantitative analysis around 1665, considering the period and distance of the Moon's orbit and considering the timing of objects falling on Earth. Newton did not publish these results at the time because he could not prove that the [[Shell theorem|Earth's gravity acts as if all its mass were concentrated at its center]]. That proof took him twenty years.<ref name=Weinberg-1972/>{{rp|13}}

Newton's ''Principia'' was well received by the scientific community, and his law of gravitation quickly spread across the European world.<ref>{{Cite web |title=The Reception of Newton's Principia |url=http://physics.ucsc.edu/~michael/newtonreception6.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://physics.ucsc.edu/~michael/newtonreception6.pdf |archive-date=9 October 2022 |url-status=live |access-date=6 May 2022}}</ref> More than a century later, in 1821, his theory of gravitation rose to even greater prominence when it was used to predict the existence of [[Neptune]]. In that year, the French astronomer [[Alexis Bouvard]] used this theory to create a table modeling the orbit of [[Uranus]], which was shown to differ significantly from the planet's actual trajectory. In order to explain this discrepancy, many astronomers speculated that there might be a large object beyond the orbit of Uranus which was disrupting its<!--Uranus's--> orbit. In 1846, the astronomers [[John Couch Adams]] and [[Urbain Le Verrier]] independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day.<ref>{{Cite web |title=This Month in Physics History |url=http://www.aps.org/publications/apsnews/202008/history.cfm |access-date=6 May 2022 |website=www.aps.org |language=en |archive-date=6 May 2022 |archive-url=https://web.archive.org/web/20220506231353/https://www.aps.org/publications/apsnews/202008/history.cfm |url-status=live }}</ref><ref>{{Cite journal |last=McCrea |first=W. H. |date=1976 |title=The Royal Observatory and the Study of Gravitation |url=https://www.jstor.org/stable/531749 |journal=Notes and Records of the Royal Society of London |volume=30 |issue=2 |pages=133–140 |doi=10.1098/rsnr.1976.0010 |jstor=531749 |issn=0035-9149}}</ref>

Newton's formulation was later condensed into the inverse-square law:<math display="block">F = G \frac{m_1 m_2}{r^2}, </math>where {{mvar|F}} is the force, {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}} are the masses of the objects interacting, {{mvar|r}} is the distance between the centers of the masses and {{math|''G''}} is the [[gravitational constant]] {{physconst|G|after=.|round=3}} While {{math|''G''}} is also called [[Gravitational constant|Newton's constant]], Newton did not use this constant or formula, he only discussed proportionality. But this allowed him to come to an astounding conclusion we take for granted today: the gravity of the Earth on the Moon is the same as the gravity of the Earth on an apple:<math display="block">M_\text{earth} \propto a_\text{apple}R_\text{radius of earth}^2 = a_\text{moon}R_\text{lunar orbit}^2 </math>Using the values known at the time, Newton was able to verify this form of his law. The value of {{math|''G''}} was eventually [[Cavendish experiment|measured]] by [[Henry Cavendish]] in 1797.<ref name="Zee-2013">{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1 |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|31}}

===Einstein's general relativity===
{{main| History of general relativity}}
{{General relativity sidebar}}
Eventually, astronomers noticed an eccentricity in the orbit of the planet [[Mercury (planet)|Mercury]] which could not be explained by Newton's theory: the [[perihelion]] of the orbit was increasing by about 42.98 [[arcseconds]] per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body, such as a planet orbiting the Sun even closer than Mercury, but all efforts to find such a body turned out to be fruitless. In 1915, [[Albert Einstein]] developed a theory of [[general relativity]] which was able to accurately model Mercury's orbit.<ref>{{Cite journal |last=Nobil |first=Anna M. |date=March 1986 |title=The real value of Mercury's perihelion advance |journal=Nature |volume=320 |issue=6057 |pages=39–41 |bibcode=1986Natur.320...39N |doi=10.1038/320039a0 |s2cid=4325839 | issn=0028-0836}}</ref>

Einstein's theory brought two other ideas with independent histories into the physical theories of gravity: the [[principle of relativity]] and [[non-Euclidean geometry]].

The principle of relativity, introduced by Galileo and used as a foundational principle by Newton, led to a long and fruitless search for a [[luminiferous aether]] after [[Maxwell's equations]] demonstrated that light propagated at a fixed speed independent of reference frame. In Newton's mechanics, velocities add: a cannon ball shot from a moving ship would travel with a trajectory which included the motion of the ship. Since light speed was fixed, it was assumed to travel in a fixed, absolute medium. Many experiments sought to reveal this medium but failed and in 1905 Einstein's [[special relativity]] theory showed the aether was not needed. Special relativity proposed that mechanics be reformulated to use the [[Lorentz transformation]] already applicable to light rather than the [[Galilean transformation]] adopted by Newton. Special relativity, as in [[special case]], specifically did not cover gravity.<ref name=Weinberg-1972/>{{rp|4}}

While relativity was associated with mechanics and thus gravity, the idea of altering geometry only joined the story of gravity once mechanics required the Lorentz transformations. [[Geometry]] was an [[history of geometry|ancient science]] that gradually broke free of Euclidean limitations when [[Carl Gauss]] discovered in the 1800s that [[hypersurface|surfaces in any number of dimensions]] could be characterized by a [[metric space|metric]], a distance measurement along the shortest path between two points that reduces to Euclidean distance at infinitesimal separation. Gauss' student [[Bernhard Riemann]] developed this into a complete geometry by 1854. These geometries are locally flat but have global [[curvature]].<ref name=Weinberg-1972/>{{rp|4}}

In 1907, Einstein took his first step by using special relativity to create a new form of the [[equivalence principle]]. The equivalence of inertial mass and gravitational mass was a known empirical law. The {{mvar|m}} in Newton's first law, <math>F=ma</math>, has the same value as the {{mvar|m}} in Newton's law of gravity on Earth, <math>F=GMm/r^2</math>. In what he later described as "the happiest thought of my life" Einstein realized this meant that in free-fall, an accelerated coordinate system exists with no local [[gravitational field]].<ref>{{Cite web |last1=Webb |first1=Joh |last2=Dougan |first2=Darren |date=23 November 2015 |title=Without Einstein it would have taken decades longer to understand gravity |url=https://phys.org/news/2015-11-einstein-decades-longer-gravity.html#:~:text=In%201907%2C%20Einstein%20had%20the,not%20feel%20his%20own%20weight. |access-date=21 May 2022 |archive-date=21 May 2022 |archive-url=https://web.archive.org/web/20220521182328/https://phys.org/news/2015-11-einstein-decades-longer-gravity.html#:~:text=In%201907%2C%20Einstein%20had%20the,not%20feel%20his%20own%20weight. |url-status=live }}</ref> Every description of gravity in any other coordinate system must transform to give no field in the free-fall case, a powerful [[Invariant (physics)|invariance]] constraint on all theories of gravity.<ref name=Weinberg-1972/>{{rp|20}}

Einstein's description of gravity was accepted by the majority of physicists for two reasons. First, by 1910 his special relativity was accepted in German physics and was spreading to other countries. Second, his theory explained experimental results like the perihelion of Mercury and the bending of light around the Sun better than Newton's theory.<ref>{{Cite journal |last=Brush |first=S. G. |date=1 January 1999 |title=Why was Relativity Accepted? |url=https://ui.adsabs.harvard.edu/abs/1999PhP.....1..184B |journal=Physics in Perspective |volume=1 |issue=2 |pages=184–214 |doi=10.1007/s000160050015 |bibcode=1999PhP.....1..184B |s2cid=51825180 |issn=1422-6944 |access-date=22 May 2022 |archive-date=8 April 2023 |archive-url=https://web.archive.org/web/20230408021700/https://ui.adsabs.harvard.edu/abs/1999PhP.....1..184B |url-status=live }}</ref>

In 1919, the British astrophysicist [[Arthur Eddington]] was able to confirm the predicted deflection of light during [[Solar eclipse of May 29, 1919|that year's solar eclipse]].<ref>{{cite journal |last1=Dyson |first1=F. W. |author-link1=Frank Watson Dyson |last2=Eddington |first2=A. S. |author-link2=Arthur Eddington |last3=Davidson |first3=C. R. |date=1920 |title=A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919 |url=https://zenodo.org/record/1432106 |url-status=live |journal=[[Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|Phil. Trans. Roy. Soc. A]] |volume=220 |issue=571–581 |pages=291–333 |bibcode=1920RSPTA.220..291D |doi=10.1098/rsta.1920.0009 |archive-url=https://web.archive.org/web/20200515065314/https://zenodo.org/record/1432106 |archive-date=15 May 2020 |access-date=1 July 2019 |doi-access=free}}. Quote, p. 332: "Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein's generalised theory of relativity, as attributable to the sun's gravitational field."</ref><ref>{{cite book |last=Weinberg |first=Steven |url=https://archive.org/details/gravitationcosmo00stev_0 |title=Gravitation and cosmology |date=1972 |publisher=John Wiley & Sons |isbn=978-0-471-92567-5 |author-link=Steven Weinberg |url-access=registration}}. Quote, p. 192: "About a dozen stars in all were studied, and yielded values 1.98 ± 0.11" and 1.61 ± 0.31", in substantial agreement with Einstein's prediction θ<sub>☉</sub> = 1.75"."</ref> Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. Although Eddington's analysis was later disputed, this experiment made Einstein famous almost overnight and caused general relativity to become widely accepted in the scientific community.<ref>{{Cite journal |last1=Gilmore |first1=Gerard |last2=Tausch-Pebody |first2=Gudrun |date=20 March 2022 |title=The 1919 eclipse results that verified general relativity and their later detractors: a story re-told |journal=Notes and Records: The Royal Society Journal of the History of Science |volume=76 |issue=1 |pages=155–180 |doi=10.1098/rsnr.2020.0040|s2cid=225075861 |doi-access=free |arxiv=2010.13744 }}</ref>

In 1959, American physicists [[Robert Pound]] and [[Glen Rebka]] performed [[Pound–Rebka experiment|an experiment]] in which they used [[gamma ray]]s to confirm the prediction of [[gravitational time dilation]]. By sending the rays down a 74-foot tower and measuring their frequency at the bottom, the scientists confirmed that light is [[Doppler shift]]ed as it moves towards a source of gravity. The observed shift also supports the idea that time runs more slowly in the presence of a gravitational field (many more wave crests pass in a given interval). If light moves outward from a strong source of gravity it will be observed with a [[redshift]].<ref>{{Cite web |title=General Astronomy Addendum 10: Graviational Redshift and time dilation |url=https://homepage.physics.uiowa.edu/~rlm/mathcad/addendum%2010%20gravitational%20redshift%20and%20time%20dilation.htm |access-date=29 May 2022 |website=homepage.physics.uiowa.edu |archive-date=14 May 2022 |archive-url=https://web.archive.org/web/20220514063358/https://homepage.physics.uiowa.edu/~rlm/mathcad/addendum%2010%20gravitational%20redshift%20and%20time%20dilation.htm |url-status=live }}</ref> The [[time delay of light]] passing close to a massive object was first identified by [[Irwin I. Shapiro]] in 1964 in interplanetary spacecraft signals.<ref>{{Cite journal |last=Asada |first=Hideki |date=20 March 2008 |title=Gravitational time delay of light for various models of modified gravity |url=https://www.sciencedirect.com/science/article/pii/S0370269308001810 |journal=Physics Letters B |volume=661 |issue=2–3 |pages=78–81 |doi=10.1016/j.physletb.2008.02.006 |arxiv=0710.0477 |bibcode=2008PhLB..661...78A |s2cid=118365884 |language=en |access-date=29 May 2022 |archive-date=29 May 2022 |archive-url=https://web.archive.org/web/20220529140019/https://www.sciencedirect.com/science/article/pii/S0370269308001810 |url-status=live }}</ref>

In 1971, scientists discovered the first-ever black hole in the galaxy [[Cygnus A|Cygnus]]. The black hole was detected because it was emitting bursts of [[x-rays]] as it consumed a smaller star, and it came to be known as [[Cygnus X-1]].<ref>{{Cite web |title=The Fate of the First Black Hole |url=https://www.science.org/content/article/fate-first-black-hole |access-date=30 May 2022 |website=www.science.org |language=en |archive-date=31 May 2022 |archive-url=https://web.archive.org/web/20220531125138/https://www.science.org/content/article/fate-first-black-hole |url-status=live }}</ref> This discovery confirmed yet another prediction of general relativity, because Einstein's equations implied that light could not escape from a sufficiently large and compact object.<ref>{{Cite web |title=Black Holes Science Mission Directorate |url=https://webarchive.library.unt.edu/web/20170124200640/https://science.nasa.gov/astrophysics/focus-areas/black-holes |access-date=30 May 2022 |website=webarchive.library.unt.edu |archive-date=8 April 2023 |archive-url=https://web.archive.org/web/20230408021657/https://webarchive.library.unt.edu/web/20170124200640/https://science.nasa.gov/astrophysics/focus-areas/black-holes |url-status=live }}</ref>

[[Frame dragging]], the idea that a rotating massive object should twist spacetime around it, was confirmed by [[Gravity Probe B]] results in 2011.<ref>{{cite web |url=http://www.nasa.gov/home/hqnews/2011/may/HQ_11-134_Gravity_Probe_B.html |title=NASA's Gravity Probe B Confirms Two Einstein Space-Time Theories |publisher=Nasa.gov |access-date=23 July 2013 |archive-date=22 May 2013 |archive-url=https://web.archive.org/web/20130522024606/http://www.nasa.gov/home/hqnews/2011/may/HQ_11-134_Gravity_Probe_B.html |url-status=live }}</ref><ref>{{Cite web |title="Frame-Dragging" in Local Spacetime |url=https://einstein.stanford.edu/content/education/lithos/litho-fd.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://einstein.stanford.edu/content/education/lithos/litho-fd.pdf |archive-date=9 October 2022 |url-status=live |website=Stanford University}}</ref> In 2015, the [[LIGO]] observatory detected faint [[gravitational waves]], the existence of which had been predicted by general relativity. Scientists believe that the waves emanated from a [[black hole merger]] that occurred 1.5 billion [[light-years]] away.<ref>{{Cite news |title=Gravitational Waves Detected 100 Years After Einstein's Prediction |url=https://www.ligo.caltech.edu/news/ligo20160211 |access-date=30 May 2022 |newspaper=Ligo Lab &#124; Caltech |archive-date=27 May 2019 |archive-url=https://web.archive.org/web/20190527101043/https://www.ligo.caltech.edu/news/ligo20160211 |url-status=live }}</ref>

==On Earth==
[[File:Falling ball.jpg|thumb|upright=0.45|An initially-stationary object that is allowed to fall freely under gravity drops a distance that is proportional to the square of the elapsed time. This image spans half a second and was captured at 20 flashes per second.]]
{{main|Gravity of Earth}}
Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.
[[File:Gravity action-reaction.gif|thumb|left|If an object with comparable mass to that of the Earth were to fall towards it, then the corresponding acceleration of the Earth would be observable.]]
The strength of the gravitational field is numerically equal to the acceleration of objects under its influence.<ref>{{cite book |title=Companion to the History of Modern Science |first1=G.N. |last1=Cantor |first2=J.R.R. |last2=Christie |first3=M.J.S. |last3=Hodge |first4=R.C. |last4=Olby |publisher=Routledge |year=2006 |isbn=978-1-134-97751-2 |page=448 |url=https://books.google.com/books?id=gkJn6ciwYZsC&pg=PA448 |access-date=22 October 2017 |archive-date=17 January 2020 |archive-url=https://web.archive.org/web/20200117131121/https://books.google.com/books?id=gkJn6ciwYZsC&pg=PA448 |url-status=live }}</ref> The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities.<ref>{{Cite APOD|date = 15 December 2014|title = The Potsdam Gravity Potato|access-date = }}</ref> For purposes of weights and measures, a [[standard gravity]] value is defined by the [[International Bureau of Weights and Measures]], under the [[International System of Units]] (SI).

The force of gravity experienced by objects on Earth's surface is the [[Euclidean vector|vector sum]] of two forces:<ref name=HWM>{{cite book
|last1 = Hofmann-Wellenhof |first1 = B.
|last2 = Moritz |first2 = H.
|title = Physical Geodesy
|publisher = Springer
|edition = 2nd
|isbn = 978-3-211-33544-4
|year = 2006
|quote = § 2.1: "The total force acting on a body at rest on the earth's surface is the resultant of gravitational force and the centrifugal force of the earth's rotation and is called gravity.
}}</ref> (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the [[centrifugal force]] caused by the Earth's rotation and because points on the equator are farthest from the center of the Earth. The force of gravity varies with latitude, and the resultant acceleration increases from about 9.780&nbsp;m/s<sup>2</sup> at the Equator to about 9.832&nbsp;m/s<sup>2</sup> at the poles.<ref name="Boynton">{{cite conference |last=Boynton |first=Richard |date=2001 |title=''Precise Measurement of Mass'' |book-title=Sawe Paper No. 3147 |publisher=S.A.W.E., Inc. |location=Arlington, Texas |url=http://www.space-electronics.com/Literature/Precise_Measurement_of_Mass.PDF |access-date=22 December 2023 |archive-date=27 February 2007 |archive-url=https://web.archive.org/web/20070227132140/http://www.space-electronics.com/Literature/Precise_Measurement_of_Mass.PDF }}</ref><ref>{{cite web |url=https://curious.astro.cornell.edu/question.php?number=310 |title=Curious About Astronomy? |website= Cornell University |access-date=22 December 2023 |archive-date=28 July 2013 |archive-url=https://web.archive.org/web/20130728125707/http://curious.astro.cornell.edu/question.php?number=310}}</ref>

=== Gravity wave ===
{{main|Gravity wave}}
Waves on oceans, lakes, and other bodies of water occur when the gravitational equilibrium at the surface of the water is disturbed by for example wind.<ref>{{Cite book |last=Young |first=I. R. |title=Wind generated ocean waves |date=1999 |publisher=Elsevier |isbn=978-0-08-043317-2 |edition=1st |series=Elsevier ocean engineering book series |location=Amsterdam ; New York}}</ref> Similar effects occur in the [[Atmospheric wave|atmosphere]] where equilibrium is disturbed by thermal [[weather fronts]] or mountain ranges.<ref>{{Cite journal |last1=Fritts |first1=David C. |last2=Alexander |first2=M. Joan |date=March 2003 |title=Gravity wave dynamics and effects in the middle atmosphere |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2001RG000106 |journal=Reviews of Geophysics |language=en |volume=41 |issue=1 |page=1003 |doi=10.1029/2001RG000106 |bibcode=2003RvGeo..41.1003F |issn=8755-1209}}</ref>

== Orbits ==
{{main|Orbit}}
[[Planets]] orbit the [[Sun]] in an [[ellipse]] as a consequence of the law of gravity. Similarly the [[Moon]] and artificial [[satellites]] orbit the Earth. Conceptually two objects in orbit are both falling off of the curve they would travel in if the force of gravity were not pulling them together. Since the force of gravity is universal, all planets attract each other with the most massive and closest pair have the most mutual affect. This means orbits are more complex than simple ellipses.<ref name=Feynman-7/>

==Astrophysics==

=== Stars and black holes ===
{{main|Star formation}}
During star formation, gravitational attraction in a cloud of hydrogen gas competes with thermal gas pressure. As the gas density increases, the temperature rises, then the gas radiates energy, allowing additional gravitational condensation. If the mass of gas in the region is low, the process continues until a [[brown dwarf]] or [[gas-giant planet]] is produced. If more mass is available, the additional gravitational energy allows the central region to reach pressures sufficient for [[nuclear fusion]], forming a [[star]]. In a star, again the gravitational attraction competes, with thermal and radiation pressure in [[hydrostatic equilibrium]] until the star's atomic fuel runs out. The next phase depends upon the total mass of the star. Very low mass stars slowly cool as [[white dwarf]] stars with a small core balancing gravitational attraction with [[electron degeneracy pressure]]. Stars with masses similar to the Sun go through a [[red giant]] phase before becoming white dwarf stars. Higher mass stars have complex core structures that burn helium and high atomic number elements ultimately producing an [[iron]] core. As their fuel runs out, these stars become unstable producing a [[supernova]]. The result can be a [[neutron star]] where gravitational attraction balances [[neutron degeneracy pressure]] or, for even higher masses, a [[black hole]] where gravity operates alone with such intensity that even light cannot escape.<ref>{{Cite book |last=Demtröder |first=Wolfgang |title=Astrophysics |date=2024 |chapter=Birth, Lifetime and Death of Stars |series=Undergraduate Lecture Notes in Physics |chapter-url=https://link.springer.com/10.1007/978-3-031-22135-4_5 |access-date=2025-05-04 |publisher=Springer Nature Switzerland |pages=121–175 |language=en |doi=10.1007/978-3-031-22135-4_5|isbn=978-3-031-22133-0 }}</ref>{{rp|121}}

===Gravitational radiation===
{{Main|Gravitational wave}}
[[File:LIGO Hanford aerial 05.jpg|alt=LIGO Hanford Observatory|thumb|upright=1.2|The [[LIGO]] Hanford Observatory located in Washington (state), United States, where gravitational waves were first observed in September 2015]]
General relativity predicts that energy can be transported out of a system through gravitational radiation also known as gravitational waves. The first indirect evidence for gravitational radiation was through measurements of the [[Hulse–Taylor binary]] in 1973. This system consists of a [[pulsar]] and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the [[Nobel Prize in Physics]] in 1993.<ref name="npp1993">{{cite web |title=The Nobel Prize in Physics 1993 |publisher=[[Nobel Foundation]] |url=https://www.nobelprize.org/prizes/physics/1993/press-release/ |date=13 October 1993 |quote=for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation |access-date=22 December 2023 |archive-date=10 August 2018 |archive-url=https://web.archive.org/web/20180810182047/https://www.nobelprize.org/nobel_prizes/physics/laureates/1993/press.html |url-status=live }}</ref>

The first direct evidence for gravitational radiation was measured on 14 September 2015 by the [[LIGO]] detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion light years from Earth were measured.<ref name='Clark 2016'>{{Cite web|title = Gravitational waves: scientists announce 'we did it!'{{snd}}live|url = https://www.theguardian.com/science/across-the-universe/live/2016/feb/11/gravitational-wave-announcement-latest-physics-einstein-ligo-black-holes-live|website = the Guardian|date = 11 February 2016|access-date = 11 February 2016|first = Stuart|last = Clark|archive-date = 22 June 2018|archive-url = https://web.archive.org/web/20180622055957/https://www.theguardian.com/science/across-the-universe/live/2016/feb/11/gravitational-wave-announcement-latest-physics-einstein-ligo-black-holes-live|url-status = live}}</ref><ref name="Discovery 2016">{{cite journal |title=Einstein's gravitational waves found at last |journal=Nature News |url=http://www.nature.com/news/einstein-s-gravitational-waves-found-at-last-1.19361 |date=11 February 2016 |last1=Castelvecchi |first1=Davide |last2=Witze |first2=Witze |doi=10.1038/nature.2016.19361 |s2cid=182916902 |access-date=11 February 2016 |archive-date=12 February 2016 |archive-url=https://web.archive.org/web/20160212082216/http://www.nature.com/news/einstein-s-gravitational-waves-found-at-last-1.19361 |url-status=live |doi-access=free }}</ref> This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang.<ref>{{cite web|title=WHAT ARE GRAVITATIONAL WAVES AND WHY DO THEY MATTER?|date=13 January 2016 |url=http://www.popsci.com/whats-so-important-about-gravitational-waves|publisher=popsci.com|access-date=12 February 2016|archive-date=3 February 2016|archive-url=https://web.archive.org/web/20160203130600/http://www.popsci.com/whats-so-important-about-gravitational-waves|url-status=live}}</ref> [[Neutron star]] and [[black hole]] formation also create detectable amounts of gravitational radiation.<ref name="PhysRev2017">{{cite journal |last1=Abbott |first1=B. P. |display-authors=etal. |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral |journal=[[Physical Review Letters]] |date=October 2017 |volume=119 |issue=16 |article-number=161101 |doi=10.1103/PhysRevLett.119.161101 |pmid=29099225 |doi-access=free |arxiv=1710.05832 |url=http://www.ligo.org/detections/GW170817/paper/GW170817-PRLpublished.pdf |bibcode=2017PhRvL.119p1101A |access-date=28 September 2019 |archive-date=8 August 2018 |archive-url=https://web.archive.org/web/20180808012441/https://www.ligo.org/detections/GW170817/paper/GW170817-PRLpublished.pdf |url-status=live }}</ref> This research was awarded the Nobel Prize in Physics in 2017.<ref>{{cite web|title=Nobel prize in physics awarded for discovery of gravitational waves|url=https://www.theguardian.com/science/2017/oct/03/nobel-prize-physics-discovery-gravitational-waves-ligo|website=the Guardian|date=3 October 2017|access-date=3 October 2017|last1=Devlin|first1=Hanna|archive-date=3 October 2017|archive-url=https://web.archive.org/web/20171003102211/https://www.theguardian.com/science/2017/oct/03/nobel-prize-physics-discovery-gravitational-waves-ligo|url-status=live}}</ref>

=== Dark matter ===
{{main|Dark matter}}
At the cosmological scale, gravity is a dominant player. About 5/6 of the total mass in the universe consists of dark matter which interacts through gravity but not through electromagnetic interactions. The gravitation of clumps of dark matter known as [[dark matter halo]]s attract hydrogen gas leading to stars and galaxies.<ref>{{Cite journal |last1=Wechsler |first1=Risa H. |last2=Tinker |first2=Jeremy L. |date=2018-09-14 |title=The Connection Between Galaxies and Their Dark Matter Halos |url=https://www.annualreviews.org/doi/10.1146/annurev-astro-081817-051756 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=56 |issue=1 |pages=435–487 |doi=10.1146/annurev-astro-081817-051756 |issn=0066-4146|arxiv=1804.03097 }}</ref>

===Gravitational lensing===
{{main|Gravitational lensing}}
[[File:Einstein cross.jpg|thumb|upright=1|[[Einstein's Cross]], four images of the same distant [[quasar]] around a foreground galaxy due to gravitational lensing – a single quasar is actually hidden behind a massive foreground object (a galaxy in this case)]]
Gravity acts on light and matter equally, meaning that a sufficiently massive object could warp light around it and create a gravitational lens. This phenomenon was first confirmed by observation in 1979 using the 2.1 meter telescope at [[Kitt Peak National Observatory]] in Arizona, which saw two mirror images of the same quasar whose light had been bent around the galaxy [[YGKOW G1]].<ref>{{cite book |author1=Kar |first=Subal |url=https://books.google.com/books?id=IWFkEAAAQBAJ |title=Physics and Astrophysics: Glimpses of the Progress |publisher=CRC Press |year=2022 |isbn=978-1-000-55926-2 |edition=illustrated |page=106}} [https://books.google.com/books?id=IWFkEAAAQBAJ&pg=PT106 Extract of page 106].</ref><ref>{{Cite web |title=Hubble, Hubble, Seeing Double! |url=https://www.nasa.gov/content/goddard/hubble-hubble-seeing-double/#.YpZyvYOZrRl |access-date=31 May 2022 |website=NASA |date=24 January 2014 |archive-date=25 May 2022 |archive-url=https://web.archive.org/web/20220525041837/https://www.nasa.gov/content/goddard/hubble-hubble-seeing-double/#.YpZyvYOZrRl |url-status=live }}</ref>
Many subsequent observations of gravitational lensing provide additional evidence for substantial amounts of dark matter around galaxies. Gravitational lenses do not focus like [[eyeglass]] lenses, but rather lead to annular shapes called [[Einstein rings]].<ref name="Zee-2013"/>{{rp|370}}

=== Speed of gravity ===
{{Main|Speed of gravity}}

In October 2017, the [[LIGO]] and [[Virgo interferometer]] detectors received gravitational wave signals 2 seconds before [[gamma ray]] satellites and optical telescopes seeing signals from the same direction, from a source about 130 million light-years away. This confirmed that the speed of gravitational waves was the same as the speed of light.<ref>{{cite web |url=https://www.ligo.caltech.edu/page/press-release-gw170817 |title=GW170817 Press Release |website=LIGO Lab – Caltech |access-date=24 October 2017 |archive-date=17 October 2017 |archive-url=https://web.archive.org/web/20171017010137/https://www.ligo.caltech.edu/page/press-release-gw170817 |url-status=live }}</ref>

===Anomalies and discrepancies===
{{distinguish|Gravity anomaly}}

There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.
[[File:GalacticRotation2.svg|thumb|Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The discrepancy between the curves is attributed to [[dark matter]].]]
* '''[[Galaxy rotation curve]]s''': Stars in galaxies follow a distribution of velocities where stars on the outskirts are moving faster than they should according to the observed distributions of luminous matter. Galaxies within [[Galaxy groups and clusters|galaxy clusters]] show a similar pattern. The pattern is considered strong evidence for [[dark matter]], which would interact through gravitation but not electromagnetically; various [[Modified Newtonian dynamics|modifications to Newtonian dynamics]] have also been proposed.<ref>{{Cite journal |last1=Sofue |first1=Yoshiaki |last2=Rubin |first2=Vera |date=2001-09-01 |title=Rotation Curves of Spiral Galaxies |url=https://www.annualreviews.org/content/journals/10.1146/annurev.astro.39.1.137 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=39 |pages=137–174 |doi=10.1146/annurev.astro.39.1.137 |issn=0066-4146|arxiv=astro-ph/0010594 |bibcode=2001ARA&A..39..137S }}</ref>
* '''[[Accelerated expansion]]''': The [[expansion of the universe]] seems to be accelerating.<ref>{{Cite web |title=The Nobel Prize in Physics 2011: Adam G. Riess Facts |url=https://www.nobelprize.org/prizes/physics/2011/riess/facts/ |access-date=19 March 2024 |website=NobelPrize.org |language=en-US |archive-date=28 May 2020 |archive-url=https://web.archive.org/web/20200528014511/https://www.nobelprize.org/prizes/physics/2011/riess/facts/ |url-status=live }}</ref> [[Dark energy]] has been proposed to explain this.<ref>{{Cite web |title=What is Dark Energy? Inside our accelerating, expanding Universe |url=https://science.nasa.gov/universe/the-universe-is-expanding-faster-these-days-and-dark-energy-is-responsible-so-what-is-dark-energy/ |access-date=19 March 2024 |website=science.nasa.gov |date=5 February 2024 |language=en |archive-date=19 March 2024 |archive-url=https://web.archive.org/web/20240319153930/https://science.nasa.gov/universe/the-universe-is-expanding-faster-these-days-and-dark-energy-is-responsible-so-what-is-dark-energy/ |url-status=live }}</ref>
* '''[[Flyby anomaly]]''': Various spacecraft have experienced greater acceleration than expected during [[gravity assist]] maneuvers.<ref>{{Cite journal |last1=Anderson |first1=John D. |last2=Campbell |first2=James K. |last3=Ekelund |first3=John E. |last4=Ellis |first4=Jordan |last5=Jordan |first5=James F. |date=3 March 2008 |title=Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth |url=https://link.aps.org/doi/10.1103/PhysRevLett.100.091102 |journal=Physical Review Letters |language=en |volume=100 |issue=9 |article-number=091102 |doi=10.1103/PhysRevLett.100.091102 |pmid=18352689 |bibcode=2008PhRvL.100i1102A |issn=0031-9007|url-access=subscription }}</ref> The [[Pioneer anomaly]] has been shown to be explained by thermal recoil due to the distant sun radiation on one side of the space craft.<ref>{{Cite journal |last1=Turyshev |first1=Slava G. |last2=Toth |first2=Viktor T. |last3=Kinsella |first3=Gary |last4=Lee |first4=Siu-Chun |last5=Lok |first5=Shing M. |last6=Ellis |first6=Jordan |date=12 June 2012 |title=Support for the Thermal Origin of the Pioneer Anomaly |url=https://link.aps.org/doi/10.1103/PhysRevLett.108.241101 |journal=Physical Review Letters |volume=108 |issue=24 |article-number=241101 |doi=10.1103/PhysRevLett.108.241101|pmid=23004253 |arxiv=1204.2507 |bibcode=2012PhRvL.108x1101T }}</ref><ref>{{Cite journal |last=Iorio |first=Lorenzo |date=May 2015 |title=Gravitational anomalies in the solar system? |url=https://www.worldscientific.com/doi/abs/10.1142/S0218271815300153 |journal=International Journal of Modern Physics D |language=en |volume=24 |issue=6 |pages=1530015–1530343 |doi=10.1142/S0218271815300153 |issn=0218-2718|arxiv=1412.7673 |bibcode=2015IJMPD..2430015I }}</ref>

== Models ==
The physical models of gravity, like all physical models, are expressed mathematically. Physicists use several different models, depending on the problem to be solved or for the purpose of gaining physical intuition.<ref name=FeynmanLaw/>{{rp|44}}

=== Newtonian action-at-a-distance ===
[[Newton's law of universal gravitation|Newton's inverse square law]] models gravity as a force {{mvar|F}} between two objects proportional to their mass, {{mvar|m}}:
<math display="block">F_{12} = G \frac{m_1 m_2}{{r_{12}}^2}</math>
This gravitational force causes the objects to accelerate towards each other unless balanced by other forces. The force is "nonlocal": it depends on the mass of an object at a distance.<ref name=FeynmanLaw>{{cite book |last=Feynman |first=Richard P. |title=The character of physical law |date=1990 |publisher=MIT Press |isbn=978-0-262-56003-0 |edition=16. pr |location=Cambridge, Mass. }}</ref>{{rp|44}} Scientists from Newton onwards recognized that this [[action at a distance]] does not explain the root cause of the force, but nevertheless the model explains a vast number of physical effects including cannon ball trajectories, tidal motion and planetary orbits.<ref name=FeynmanLaw/>{{rp|4}} However, combining the concept of [[Principle of relativity|relativity]] with gravity is enormously complex using this Newtonian model.<ref name=FeynmanLaw/>{{rp|48}}

=== Gravitational field ===
{{main|Gravitational field}}
A second equivalent approach to model gravity uses fields.<ref name=FeynmanLaw/>{{rp|44}} In physics, a field represents a physical phenomenon using a mathematical entity associated with each point in a space. Different field theories use different entities and concepts of space. For classical field theories of gravity, the entities can be vectors associated with points in a 3-dimensional space. Each vector gives the force experienced by an insignificantly small test mass at that point in space. The force vector at each point can be computed as the direction of the highest rate of change in the gravitational potential, a single number at each point in space. The three-dimensional map of the potential or of the gravitational field provides a visual representation of the effect of the gravitational effect of all surrounding objects.{{dubious|reason=GR is a "classical theory", but does not fit this description.  Presumably the field theory that is equivalent to Newtonian theory is meant?  Also, not all historical classical field theories fit this description (for example, that of Heaviside).|date=July 2025}} Field models are local: the field values on a sphere completely determine the effects of gravity with the sphere.<ref name=FeynmanLaw/>{{rp|45}}

Fields are also used in general relativity, but rather than vectors over [[Euclidean space]], the entities are [[tensors]] over [[spacetime]]. The [[Einstein field equations]] relate the 10 independent values in the tensors to the distribution of mass and energy in space.{{dubious|reason=Not "mass and energy in space, but rather "mass (or equivalently energy), momentum and stress in spacetime".|date=July 2025}}

=== Action principles ===
{{main|Action principles}}
A third completely different way to derive a model of gravity is based on [[action principles]]. This formulation represents the effects of gravity on a system in a mathematically abstract way. The state of the system, for example the position and velocity of every particle, is expressed as a single mathematical entity. Each state has an associated energy property called the [[Lagrangian (mechanics)|Lagrangian]]; the physically allowed changes to the state of the system minimize the value of this property. The path of the state is not a path in physical space, but rather in a high-dimensional state space: each point along the path corresponds to a different position and or velocity collectively for all particles in the system. This formulation does not express the forces or fields of the individual particles.<ref name=FeynmanLaw/>{{rp|46}} Modern theories of physics rely on these action principles.<ref name="ZeeEnstein">{{cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1st |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|396}} The [[Einstein field equation]] for gravitation can be derived from the [[Einstein–Hilbert action]].<ref name="ZeeEnstein"/>{{rp|388}}

== General relativity ==
{{see also | Introduction to general relativity}}
In [[modern physics]], general relativity is considered the most successful theory of gravitation.<ref>{{Cite book |last=Stephani |first=Hans |title=Exact Solutions to Einstein's Field Equations |year=2003 |isbn=978-0-521-46136-8 |page=1 |publisher=Cambridge University Press |language=en}}</ref> Physicists continue to work to find [[Solutions of the Einstein field equations|solutions]] to the [[Einstein field equations]] that form the basis of general relativity and continue to test the theory, finding excellent agreement in all cases.<ref name="ScienceNews2019">{{cite web
  | title = Einstein's general relativity theory is questioned but still stands for now
  | work = Science News
  | publisher = Science Daily
  | date = 25 July 2019
| url = https://www.sciencedaily.com/releases/2019/07/190725150408.htm
  | doi = 
  | access-date = 11 August 2024}}</ref><ref name="Lea">{{cite web
  | last = Lea
  | first = Robert 
  | title = Einstein's greatest theory just passed its most rigorous test yet
  | website = Scientific American
  | publisher = Springer Nature America, Inc.
  | date = 15 September 2022
| url = https://www.scientificamerican.com/article/einsteins-greatest-theory-just-passed-its-most-rigorous-test-yet/
  | format = 
  | doi = 
  | access-date = 11 August 2024}}</ref><ref name="Will"/>{{rp|p.9}}

=== Constraints ===
Any theory of gravity must conform to the requirements of special relativity and experimental observations. Newton's theory of gravity assumes [[action at a distance]] and therefore cannot be reconciled with special relativity. The simplest generalization of Newton's approach would be a [[scalar field]] theory with the gravitational potential represented by a single number in a 4-dimensional spacetime. However, this type of theory fails to predict gravitational redshift or the deviation of light by matter and gives values for the precession of Mercury which are incorrect. A [[vector field]] theory predicts negative energy gravitational waves so it also fails. Furthermore, no theory without curvature in spacetime can be consistent with special relativity. The simplest theory consistent with special relativity and the well-studied observations is general relativity.<ref>{{cite journal |last1=Debono |first1=Ivan |last2=Smoot |first2=George |date=2016-09-28 |title=General Relativity and Cosmology: Unsolved Questions and Future Directions |journal=Universe |language=en |volume=2 |issue=4 |page=23 |doi=10.3390/universe2040023 |doi-access=free |arxiv=1609.09781 |bibcode=2016Univ....2...23D |issn=2218-1997}}</ref>

=== General characteristics ===
Unlike Newton's formula with one parameter, {{math|''G''}}, force in general relativity is terms of 10 numbers formed in to a [[metric tensor]].<ref name=Weinberg-1972/>{{rp|70}}In general relativity the effects of gravitation are described in different ways in different frames of reference. In a free-falling or co-moving [[coordinate system]], an object travels in a straight line. In other coordinate systems, the object accelerates and thus is seen to move under a force. The path in [[spacetime]] (not 3D space) taken by a free-falling object is called a [[geodesic]] and the length of that path as measured by time in the objects frame is the shortest (or rarely the longest) one. Consequently the effect of gravity can be described as curving spacetime. In a weak stationary gravitational field, general relativity reduces to Newton's equations. The corrections introduced by general relativity on Earth are on the order of 1 part in a billion.<ref name=Weinberg-1972/>{{rp|77}}

=== Einstein field equations ===
{{main| Einstein field equations}}
The Einstein field equations are a [[System of equations|system]] of 10 [[partial differential equation]]s which describe how matter affects the curvature of spacetime. The system is may be expressed in the form
<math display="block">G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu},</math>
where {{mvar|G{{sub|μν}}}} is the [[Einstein tensor]], {{mvar|g{{sub|μν}}}} is the [[metric tensor (general relativity)|metric tensor]], {{mvar|T{{sub|μν}}}} is the [[stress–energy tensor]], {{math|Λ}} is the [[cosmological constant]], <math>G</math> is the Newtonian constant of gravitation and <math>c</math> is the [[speed of light]].<ref>{{Cite web |title=Einstein Field Equations (General Relativity) |url=https://warwick.ac.uk/fac/sci/physics/intranet/pendulum/generalrelativity/ |access-date=24 May 2022 |website=University of Warwick |language=en |archive-date=25 May 2022 |archive-url=https://web.archive.org/web/20220525140036/https://warwick.ac.uk/fac/sci/physics/intranet/pendulum/generalrelativity/ |url-status=live }}</ref> The constant <math>\kappa = \frac{8\pi G}{c^4}</math> is referred to as the Einstein gravitational constant.<ref>{{Cite web |title=How to understand Einstein's equation for general relativity |url=https://bigthink.com/starts-with-a-bang/einstein-general-theory-relativity-equation/ |access-date=24 May 2022 |website=Big Think |date=15 September 2021 |language=en-US |archive-date=26 May 2022 |archive-url=https://web.archive.org/web/20220526023430/https://bigthink.com/starts-with-a-bang/einstein-general-theory-relativity-equation/ |url-status=live }}</ref>

=== Solutions ===
{{main|Solutions of the Einstein field equations}}
The non-linear second-order Einstein field equations are extremely complex and have been solved in only a few special cases.<ref>{{Cite web |last=Siegel |first=Ethan |title=This Is Why Scientists Will Never Exactly Solve General Relativity |url=https://www.forbes.com/sites/startswithabang/2019/12/04/this-is-why-scientists-will-never-exactly-solve-general-relativity/ |access-date=27 May 2022 |website=Forbes |language=en |archive-date=27 May 2022 |archive-url=https://web.archive.org/web/20220527212804/https://www.forbes.com/sites/startswithabang/2019/12/04/this-is-why-scientists-will-never-exactly-solve-general-relativity/ |url-status=live }}</ref> These cases however have been transformational in our understanding of the cosmos. Several solutions are the basis for understanding [[black holes]] and for our modern model of the evolution of the universe since the [[Big Bang]].<ref name="Longair-2009">{{Cite book |author=Longair |first=Malcolm S. |author-link=Malcolm Longair |url=http://link.springer.com/10.1007/978-3-540-73478-9 |title=Galaxy Formation |date=2008 |publisher=Springer Berlin Heidelberg |isbn=978-3-540-73477-2 |series=Astronomy and Astrophysics Library |location=Berlin, Heidelberg |language=en |doi=10.1007/978-3-540-73478-9}}</ref>{{rp|227}}

=== Tests of general relativity ===
{{main | Tests of general relativity}}
[[File:1919 eclipse positive.jpg|thumb|upright=0.8|The 1919 [[total solar eclipse]] provided one of the first opportunities to test the predictions of general relativity.]]

Testing the predictions of general relativity has historically been difficult, because they are almost identical to the predictions of Newtonian gravity for small energies and masses.<ref name="NASA-2022">{{cite web |title=Testing General Relativity |url=https://asd.gsfc.nasa.gov/blueshift/index.php/2015/11/27/testing-general-relativity/ |access-date=29 May 2022 |website=NASA Blueshift |language=en-US |archive-date=16 May 2022 |archive-url=https://web.archive.org/web/20220516115115/https://asd.gsfc.nasa.gov/blueshift/index.php/2015/11/27/testing-general-relativity/ |url-status=live }}</ref> A wide range of experiments provided support of general relativity.<ref name="Will">
{{cite book
  | last = Will | first = Clifford M.
  | title = Theory and Experiment in Gravitational Physics
  | publisher = Cambridge Univ. Press
  | date = 2018
  | location = 
  | language = 
  | url = https://books.google.com/books?id=gf1uDwAAQBAJ
  | doi = 
  | id = 
  | isbn = 978-1-107-11744-0
  | mr = 
  | zbl = 
  | jfm =
}}</ref>{{rp|pp=1–9}}<ref>{{cite journal |last=Lindley |first=David |date=12 July 2005 |title=The Weight of Light |url=https://physics.aps.org/story/v16/st1 |journal=Physics |language=en |volume=16 |access-date=22 May 2022 |archive-date=25 May 2022 |archive-url=https://web.archive.org/web/20220525201415/https://physics.aps.org/story/v16/st1 |url-status=live }}</ref><ref>{{cite web |title=Hafele-Keating Experiment |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/airtim.html |access-date=22 May 2022 |website=hyperphysics.phy-astr.gsu.edu |archive-date=18 April 2017 |archive-url=https://web.archive.org/web/20170418005731/http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/airtim.html |url-status=live }}</ref><ref>{{Cite web |title=How the 1919 Solar Eclipse Made Einstein the World's Most Famous Scientist |url=https://www.discovermagazine.com/the-sciences/how-the-1919-solar-eclipse-made-einstein-the-worlds-most-famous-scientist |access-date=22 May 2022 |website=Discover Magazine |language=en |archive-date=22 May 2022 |archive-url=https://web.archive.org/web/20220522141013/https://www.discovermagazine.com/the-sciences/how-the-1919-solar-eclipse-made-einstein-the-worlds-most-famous-scientist |url-status=live }}</ref><ref>{{cite web |title=At Long Last, Gravity Probe B Satellite Proves Einstein Right |url=https://www.science.org/content/article/long-last-gravity-probe-b-satellite-proves-einstein-right |access-date=22 May 2022 |website=www.science.org |language=en |archive-date=22 May 2022 |archive-url=https://web.archive.org/web/20220522141013/https://www.science.org/content/article/long-last-gravity-probe-b-satellite-proves-einstein-right |url-status=live }}</ref> Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law is accurate enough for virtually all ordinary calculations.<ref name="Will" />{{rp|79}}<ref name="Hassani">
{{cite book
  | last = Hassani
  | first = Sadri
  | title = From Atoms to Galaxies: A conceptual physics approach to scientific awareness
  | publisher = CRC Press
  | date = 2010
  | location = 
  | page = 131
  | language = 
  | url = https://books.google.com/books?id=oypZ_a9pqdsC&pg=PA131
  | doi = 
  | id = 
  | isbn = 978-1-4398-0850-4
  | mr = 
  | zbl = 
  | jfm =
}}</ref>

===Gravity and quantum mechanics===
{{Main|Graviton|Quantum gravity}}

Despite its success in predicting the effects of gravity at large scales, general relativity is ultimately incompatible with [[quantum mechanics]]. This is because general relativity describes gravity as a smooth, continuous distortion of spacetime, while quantum mechanics holds that all forces arise from the exchange of discrete particles known as [[quantum|quanta]]. This contradiction is especially vexing to physicists because the other three fundamental forces (strong force, weak force and electromagnetism) were reconciled with a quantum framework decades ago.<ref>{{Cite web |title=Gravity Probe B – Special & General Relativity Questions and Answers |url=https://einstein.stanford.edu/content/relativity/a11758.html#:~:text=Quantum%20mechanics%20is%20incompatible%20with,exchange%20of%20well-defined%20quanta. |access-date=1 August 2022 |website=einstein.stanford.edu |archive-date=6 June 2022 |archive-url=https://web.archive.org/web/20220606161408/https://einstein.stanford.edu/content/relativity/a11758.html#:~:text=Quantum%20mechanics%20is%20incompatible%20with,exchange%20of%20well-defined%20quanta. |url-status=live }}</ref> As a result, researchers have begun to search for a theory that could unite both gravity and quantum mechanics under a more general framework.<ref>{{Cite book |last1=Huggett |first1=Nick |title=Beyond Spacetime: The Foundations of Quantum Gravity |last2=Matsubara |first2=Keizo |last3=Wüthrich |first3=Christian |publisher=[[Cambridge University Press]] |year=2020 |isbn=978-1-108-65570-5 |page=6 |language=en}}</ref>

One path is to describe gravity in the framework of [[quantum field theory]] (QFT), which has been successful to accurately describe the other [[fundamental interaction]]s. The electromagnetic force arises from an exchange of virtual [[photon]]s, where the QFT description of gravity is that there is an exchange of [[virtual particle|virtual]] [[graviton]]s.<ref>{{cite book |last1=Feynman |first1=R. P. |url=https://archive.org/details/feynmanlectureso0000feyn_g4q1 |title=Feynman lectures on gravitation |last2=Morinigo |first2=F. B. |last3=Wagner |first3=W. G. |last4=Hatfield |first4=B. |date=1995 |publisher=Addison-Wesley |isbn=978-0-201-62734-3 |url-access=registration}}</ref><ref>{{cite book | author=Zee, A. |title=Quantum Field Theory in a Nutshell | publisher = Princeton University Press | date=2003 | isbn=978-0-691-01019-9}}</ref> This description reproduces general relativity in the [[classical limit]]. However, this approach fails at short distances of the order of the [[Planck length]],<ref name="Randall, Lisa 2005">{{cite book | author=Randall, Lisa | title=Warped Passages: Unraveling the Universe's Hidden Dimensions | publisher=Ecco | date=2005 | isbn=978-0-06-053108-9 | url=https://archive.org/details/warpedpassagesun00rand_1 }}</ref> where a more complete theory of [[quantum gravity]] (or a new approach to quantum mechanics) is required.

===Alternative theories===
{{Main|Alternatives to general relativity}}
General relativity has withstood many [[tests of general relativity|tests]] over a large range of mass and size scales.<ref name=WillReview2014>{{cite journal | last=Will | first=Clifford M. | title=The Confrontation between General Relativity and Experiment | journal=Living Reviews in Relativity | volume=17 | issue=1 | date=2014-12-01 | issn=2367-3613 | doi=10.12942/lrr-2014-4 | article-number=4 | pmid=28179848 | pmc=5255900 | arxiv=1403.7377 | bibcode=2014LRR....17....4W | doi-access=free}}</ref><ref>{{cite arXiv |eprint=1705.04397v1|last1= Asmodelle|first1= E.|title= Tests of General Relativity: A Review|class= physics.class-ph|year= 2017}}</ref> When applied to interpret astronomical observations, cosmological models based on general relativity introduce two components to the universe,<ref name="k889">{{cite book | last=Ryden | first=Barbara Sue | title=Introduction to cosmology | publisher=Cambridge University Press | publication-place=Cambridge | date=2017 | isbn=978-1-316-65108-7 | page=}}</ref> [[dark matter]]<ref name="dm">{{cite journal | last1=Garrett | first1=Katherine | last2=Duda | first2=Gintaras | title=Dark Matter: A Primer | journal=Advances in Astronomy | volume=2011 | date=2011 | issn=1687-7969 | doi=10.1155/2011/968283 | doi-access=free | pages=1–22| arxiv=1006.2483 | bibcode=2011AdAst2011E...8G }}</ref> and [[dark energy]],<ref name="de">{{cite journal | last1=Li | first1=Miao | last2=Li | first2=Xiao-Dong | last3=Wang | first3=Shuang | last4=Wang | first4=Yi | title=Dark energy: A brief review | journal=Frontiers of Physics | volume=8 | issue=6 | date=2013 | issn=2095-0462 | doi=10.1007/s11467-013-0300-5 | pages=828–846| arxiv=1209.0922 | bibcode=2013FrPhy...8..828L }}</ref> the nature of which is currently an [[List of unsolved problems in physics#Cosmology and general relativity|unsolved problem in physics]]. The many successful, high precision predictions of the [[Lambda-CDM model|standard model of cosmology]] has led astrophysicists to conclude it and thus general relativity will be the basis for future progress.<ref name=Turner-2022>{{Cite journal |last=Turner |first=Michael S. |date=2022-09-26 |title=The Road to Precision Cosmology |url=https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-111119-041046 |journal=Annual Review of Nuclear and Particle Science |language=en |volume=72 |issue=2022 |pages=1–35 |doi=10.1146/annurev-nucl-111119-041046 |issn=0163-8998|arxiv=2201.04741 |bibcode=2022ARNPS..72....1T }}</ref><ref name=Intertwined-2022>{{Cite journal |last1=Abdalla |first1=Elcio |last2=Abellán |first2=Guillermo Franco |last3=Aboubrahim |first3=Amin |last4=Agnello |first4=Adriano |last5=Akarsu |first5=Özgür |last6=Akrami |first6=Yashar |last7=Alestas |first7=George |last8=Aloni |first8=Daniel |last9=Amendola |first9=Luca |last10=Anchordoqui |first10=Luis A. |last11=Anderson |first11=Richard I. |last12=Arendse |first12=Nikki |last13=Asgari |first13=Marika |last14=Ballardini |first14=Mario |last15=Barger |first15=Vernon |date=2022-06-01 |title=Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies |url=https://linkinghub.elsevier.com/retrieve/pii/S2214404822000179 |journal=Journal of High Energy Astrophysics |volume=34 |pages=49–211 |doi=10.1016/j.jheap.2022.04.002 |issn=2214-4048|arxiv=2203.06142 |bibcode=2022JHEAp..34...49A }}</ref> However, dark matter is not supported by the [[Standard Model of particle physics]], physical models for dark energy do not match cosmological data, and some cosmological observations are inconsistent.<ref name=Intertwined-2022/> These issues have led to the study of alternative theories of gravity.<ref name="physicsworld">{{cite web |author=Cooper |first=Keith |date=6 February 2024 |title=Cosmic combat: delving into the battle between dark matter and modified gravity |url=https://physicsworld.com/a/cosmic-combat-delving-into-the-battle-between-dark-matter-and-modified-gravity |publisher=physicsworld}}</ref>

==See also==
{{cols|colwidth=30em}}
* {{Annotated link |Anti-gravity}}
* {{Annotated link |Artificial gravity}}
* {{Annotated link |Equations for a falling body}}
* {{Annotated link |Escape velocity}}
* {{Annotated link |Atmospheric escape}}
* {{Annotated link |Gauss's law for gravity}}
* {{Annotated link |Gravitational potential}}
* {{Annotated link |Gravitational biology}}
* {{Annotated link |Newton's laws of motion}}
* {{Annotated link |Standard gravitational parameter}}
* {{Annotated link |Weightlessness}}
{{colend}}
{{clear}}

==References==
{{Reflist|30em}}

==Further reading==
* {{cite book |last1=Halliday |first1=David |author-link1=David Halliday (physicist) |last2=Resnick |first2=Robert |last3=Krane |first3=Kenneth S. |title=Physics v. 1 |location=New York |publisher=John Wiley & Sons |date=2001 |isbn=978-0-471-32057-9}}
* {{cite book | last = Serway | first = Raymond A. | author2 = Jewett, John W. | title = Physics for Scientists and Engineers | edition = 6th | publisher = Brooks/Cole | date = 2004 | isbn = 978-0-534-40842-8 | url = https://archive.org/details/physicssciengv2p00serw }}
* {{cite book | last = Tipler | first = Paul | title = Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition = 5th | publisher = W.H. Freeman | date = 2004 | isbn = 978-0-7167-0809-4 }}
* {{cite book |author=Thorne |first1=Kip S. |author-link1=Kip Thorne |last2=Misner |first2=Charles W. |author-link2=Charles W. Misner |last3=Wheeler |first3=John Archibald |author-link3=John Archibald Wheeler |title=Gravitation |publisher=W.H. Freeman |date=1973 |isbn=978-0-7167-0344-0}}

==External links==
{{sister project links|d=y|wikt=gravity|v=Gravitation|b=Physics Study Guide/Gravity|s=1911 Encyclopædia Britannica/Gravitation|c=category:Gravitation|n=no|q=Gravity|m=no|mw=no|species=no}}
* {{springer|title=Gravitation|id=p/g045040}}
* {{springer|title=Gravitation, theory of|id=p/g045050}}

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