View source for Gravity

{{Short description|Attraction of masses and energy}}
{{Other uses}}
{{pp-semi-indef}}
{{pp-move}}
{{redirect-multi|2|Gravitation|Law of Gravity}}
{{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 [[galaxy|galaxies]] in the photo are distorted due to 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>) is a [[fundamental interaction]] primarily observed as mutual attraction between all things that have [[mass]]. Gravity is, by far, the weakest of the four fundamental interactions, approximately 10<sup>38</sup> times weaker than the [[strong interaction]], 10<sup>36</sup> times weaker than the [[electromagnetic force]] and 10<sup>29</sup> times weaker than the [[weak interaction]]. As a result, it has no significant influence 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> However, gravity is the most significant interaction between objects at the [[macroscopic scale]], and it determines the motion of [[planet]]s, [[star]]s, [[Galaxy|galaxies]], and even [[Electromagnetic radiation|light]].

[[Gravity of Earth|On Earth]], gravity gives [[weight]] to [[physical object]]s, and the [[gravitation of the Moon|Moon's gravity]] is responsible for sublunar [[tide]]s in the oceans. The corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another. Gravity 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.

The gravitational attraction between the original gaseous matter in the [[universe]] caused it to [[coalescence (physics)|coalesce]] and [[star formation|form stars]] which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.

Gravity is most accurately described by the [[general relativity|general theory of relativity]], proposed by [[Albert Einstein]] in 1915, which describes gravity not as a force, but as the [[curvature]] of [[spacetime]], caused by the uneven distribution of mass, and causing masses to move along [[geodesic]] lines. 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 well approximated by [[Newton's law of universal gravitation]], which describes gravity as a [[force]] causing any two bodies to be attracted toward each other, with magnitude [[proportionality (mathematics)|proportional]] to the product of their masses and [[inversely proportional]] to the [[square (algebra)|square]] of the [[distance]] between them.

Current models of [[particle physics]] imply that the earliest instance of gravity in the universe, possibly in the form of [[quantum gravity]], [[supergravity]] or a [[gravitational singularity]], along with ordinary [[space]] and [[time]], developed during the [[Chronology of the universe#Planck epoch|Planck epoch]] (up to 10<sup>−43</sup> seconds after the [[Big Bang|birth]] of the universe), possibly from a primeval state, such as a [[false vacuum]], [[quantum vacuum]] or [[virtual particle]], in a currently unknown manner.<ref name="Planck-UOregon">{{cite web |author=Staff |title=Birth of the Universe |url=http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html |website=[[University of Oregon]] |access-date=24 September 2016 |archive-date=28 November 2018 |archive-url=https://web.archive.org/web/20181128045313/http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html |url-status=live }} – discusses "[[Planck time]]" and "[[Planck era]]" at the [[Big Bang|very beginning]] of the Universe</ref> Scientists are currently working to develop a theory of gravity consistent with [[quantum mechanics]], a quantum gravity theory,<ref name="NYT-20221010">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |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 |date=10 October 2022 |work=[[The New York Times]] |accessdate=10 October 2022 |archive-date=16 November 2022 |archive-url=https://web.archive.org/web/20221116151210/https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html |url-status=live }}</ref> which would allow gravity to be united in a common mathematical framework (a [[theory of everything]]) with the other three fundamental interactions of physics.

==Definitions==
{{Dfn|Gravitation}}, also known as gravitational attraction, is the mutual attraction between all masses in the universe. Gravity is the gravitational attraction at the surface of a planet or other celestial body;<ref>{{harvtxt|McGraw-Hill Dict|1989}}</ref> gravity may also include, in addition to gravitation, the [[centrifugal force]] resulting from the planet's rotation {{Xref|text=(see {{slink||Earth's gravity}})|printworthy=1}}.<ref name=HWM/>

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

===Ancient world===
The nature and mechanism of gravity were explored by a wide range of ancient scholars. In [[Greece]], [[Aristotle]] believed that objects fell towards the Earth because the Earth was the center of the Universe and attracted all of the mass in the Universe towards it. 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 }}</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 |author1=Reviel Neitz |author2=William Noel |url=https://books.google.com/books?id=ZC1MOaAkKnsC&pg=PT125 |title=The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest |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=CJ Tuplin, Lewis Wolpert |url=https://books.google.com/books?id=ajGkvOo0egwC&pg=PR11 |title=Science and Mathematics in Ancient Greek Culture |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 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|Indian]] 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=9780199792689 |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=9780691165851 |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=9780415124119|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-year=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=9780674971660|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> 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 1604, Galileo correctly hypothesized that the distance of a falling object is proportional to the [[Square (algebra)|square]] of the time elapsed.<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|authorlink=Charles Coulston Gillispie}}</ref> 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: University of California Press, 1979), 180.</ref>

===Newton's theory of gravitation===
{{main|Newton's law of universal gravitation|Newton-Hooke priority controversy for the inverse square law}}
In 1657, [[Robert Hooke]] published his ''[[Micrographia]]'', in which he hypothesized that the Moon must have its own gravity.{{sfnp|Gribbin|Gribbin|2017|p=57}} In 1666, he added two further principles: that all bodies move in straight lines until deflected by some force and that the attractive force is stronger for closer bodies. In a communication to the Royal Society in 1666, Hooke wrote<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>
{{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....}}
Hooke's 1674 Gresham lecture, ''An Attempt to prove the Annual Motion of the Earth'', explained that gravitation applied to "all celestial bodies"{{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]}} 

[[File:Portrait of Sir Isaac Newton, 1689.jpg|thumb|upright|English physicist and mathematician, Sir [[Isaac Newton]] (1642–1727)]]
In 1684, 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''). In this book, Newton described gravitation as a universal force, and claimed that "the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve." This statement was later condensed into the following 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}}

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>

===General relativity===
{{see also|Introduction to 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>

In general relativity, the effects of gravitation are ascribed to spacetime [[curvature]] instead of a force. Einstein began to toy with this idea in the form of the [[equivalence principle]], a discovery which he later described as "the happiest thought of my life."<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> In this theory, free fall is considered to be equivalent to inertial motion, meaning that free-falling inertial objects are accelerated relative to non-inertial observers on the ground.<ref>{{cite web|url=http://www.black-holes.org/relativity6.html |title=Gravity and Warped Spacetime |publisher=black-holes.org |access-date=16 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20110621005940/http://www.black-holes.org/relativity6.html |archive-date=21 June 2011 }}</ref><ref>{{cite web |title=Lecture 20: Black Holes – The Einstein Equivalence Principle |author=Dmitri Pogosyan |url=https://www.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect20/lecture20.html |publisher=University of Alberta |access-date=14 October 2011 |archive-date=8 September 2013 |archive-url=https://web.archive.org/web/20130908024651/http://www.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect20/lecture20.html |url-status=live }}</ref> In contrast to [[Classical mechanics|Newtonian physics]], Einstein believed that it was possible for this acceleration to occur without any force being applied to the object.

Einstein proposed that [[spacetime]] is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called [[geodesic (general relativity)|geodesics]]. As in Newton's first law of motion, Einstein believed that a force applied to an object would cause it to deviate from a geodesic. For instance, people standing on the surface of the Earth are prevented from following a geodesic path because the mechanical resistance of the Earth exerts an upward force on them. This explains why moving along the geodesics in spacetime is considered inertial.

Einstein's description of gravity was quickly accepted by the majority of physicists, as it was able to explain a wide variety of previously baffling experimental results.<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 the coming years, a wide range of experiments provided additional support for the idea 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&dq=%22newton%27s+theory+of+gravity%22+adequate+for+all+ordinary+uses&pg=PA79
  | archive-url= 
  | archive-date=
  | doi = 
  | id = 
  | isbn = 9781107117440
  | mr = 
  | zbl = 
  | jfm =}}</ref>{{rp|p.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|p.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 = 
  | pages = 131
  | language = 
  | url = https://books.google.com/books?id=oypZ_a9pqdsC&pg=PA131
  | archive-url= 
  | archive-date=
  | doi = 
  | id = 
  | isbn = 9781439808504
  | mr = 
  | zbl = 
  | jfm =}}</ref>

== Modern research ==
In [[modern physics]], general relativity remains the framework for the understanding of gravity.<ref>{{Cite book |last=Stephani |first=Hans |title=Exact Solutions to Einstein's Field Equations |year=2003 |isbn=978-0-521-46136-8 |pages=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
  | format = 
  | doi = 
  | accessdate = 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 = 
  | accessdate = 11 August 2024}}</ref><ref name="Will"/>{{rp|p.9}}

=== 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 often 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>

[[File:Schwarzchild-metric.jpg|thumb|An illustration of the [[Schwarzschild solution|Schwarzschild metric]], which describes spacetime around a spherical, uncharged, and nonrotating object with mass]]
A major area of research is the discovery of [[Exact solutions in general relativity|exact solutions]] to the Einstein field equations. Solving these equations amounts to calculating a precise value for the metric tensor (which defines the curvature and geometry of spacetime) under certain physical conditions. There is no formal definition for what constitutes such solutions, but most scientists agree that they should be expressable using [[elementary functions]] or [[linear differential equations]].<ref>{{Cite web |last=Ishak |first=Mustafa |title=Exact Solutions to Einstein's Equations in Astrophysics |url=https://personal.utdallas.edu/~mishak/ExactSolutionsInAstrophysics_Ishak_Final.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://personal.utdallas.edu/~mishak/ExactSolutionsInAstrophysics_Ishak_Final.pdf |archive-date=9 October 2022 |url-status=live |access-date=25 May 2022 |website=University of Texas at Dallas}}</ref> Some of the most notable solutions of the equations include: 
* The [[Schwarzschild solution]], which describes spacetime surrounding a [[Circular symmetry|spherically symmetric]] non-[[rotation|rotating]] uncharged massive object. For compact enough objects, this solution generated a [[black hole]] with a central [[gravitational singularity|singularity]].<ref>{{Cite web |title=The Schwarzchild Metric and Applications |url=http://physics.gmu.edu/~joe/PHYS428/Topic10.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://physics.gmu.edu/~joe/PHYS428/Topic10.pdf |archive-date=9 October 2022 |url-status=live |access-date=26 May 2022 |page=36}}</ref> At points far away from the central mass, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.<ref>{{Cite journal |last=Ehlers |first=Jurgen |title=Examples of Newtonian limits of relativistic spacetimes |url=https://pure.mpg.de/rest/items/item_153004_1/component/file_153003/content |journal=Classical Quantum Gravity |year=1997 |volume=14 |issue=1A |pages=122–123 |doi=10.1088/0264-9381/14/1A/010 |bibcode=1997CQGra..14A.119E |hdl=11858/00-001M-0000-0013-5AC5-F |s2cid=250804865 |hdl-access=free |access-date=27 May 2022 |archive-date=6 December 2022 |archive-url=https://web.archive.org/web/20221206081653/https://pure.mpg.de/rest/items/item_153004_1/component/file_153003/content |url-status=live }}</ref>
* The [[Reissner–Nordström metric|Reissner–Nordström solution]], which analyzes a non-rotating spherically symmetric object with charge and was independently discovered by several different researchers between 1916 and 1921.<ref>{{Cite web |title=Surprise: the Big Bang isn't the beginning of the universe anymore |url=https://bigthink.com/starts-with-a-bang/big-bang-beginning-universe/ |access-date=26 May 2022 |website=Big Think |date=13 October 2021 |language=en-US |archive-date=26 May 2022 |archive-url=https://web.archive.org/web/20220526110921/https://bigthink.com/starts-with-a-bang/big-bang-beginning-universe/ |url-status=live }}</ref> In some cases, this solution can predict the existence of black holes with double [[event horizon]]s.<ref>{{Cite web |last=Norebo |first=Jonatan |date=16 March 2016 |title=The Reissner-Nordström metric |url=https://www.diva-portal.org/smash/get/diva2:912393/FULLTEXT01.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.diva-portal.org/smash/get/diva2:912393/FULLTEXT01.pdf |archive-date=9 October 2022 |url-status=live |language=en}}</ref>
* The [[Kerr metric|Kerr solution]], which generalizes the Schwarzchild solution to rotating massive objects. Because of the difficulty of factoring in the effects of rotation into the Einstein field equations, this solution was not discovered until 1963.<ref>{{Cite journal |last=Teukolsky |first=Saul |date=1 June 2015 |title=The Kerr metric |url=http://www.shao.ac.cn/grefa/journalClub/201811/W020181112777812239088.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.shao.ac.cn/grefa/journalClub/201811/W020181112777812239088.pdf |archive-date=9 October 2022 |url-status=live |journal=Classical and Quantum Gravity |volume=32 |issue=12 |page=124006 |doi=10.1088/0264-9381/32/12/124006 |arxiv=1410.2130 |bibcode=2015CQGra..32l4006T |s2cid=119219499 |language=en}}</ref>
* The [[Kerr–Newman metric|Kerr–Newman solution]] for charged, rotating massive objects. This solution was derived in 1964, using the same technique of complex coordinate transformation that was used for the Kerr solution.<ref>{{Cite journal |last1=Newman |first1=E. T. |last2=Couch |first2=E. |last3=Chinnapared |first3=K. |last4=Exton |first4=A. |last5=Prakash |first5=A. |last6=Torrence |first6=R. |date=June 1965 |title=Metric of a Rotating, Charged Mass |journal=Journal of Mathematical Physics |volume=6 |issue=6 |pages=918–919 |doi=10.1063/1.1704351 |bibcode=1965JMP.....6..918N |s2cid=122962090 |issn=0022-2488}}</ref> 
* The [[physical cosmology|cosmological]] [[Friedmann–Lemaître–Robertson–Walker metric|Friedmann–Lemaître–Robertson–Walker solution]], discovered in 1922 by [[Alexander Friedmann]] and then confirmed in 1927 by [[Georges Lemaître]]. This solution was revolutionary for predicting the [[expansion of the Universe]], which was confirmed seven years later after a series of measurements by [[Edwin Hubble]].<ref>{{Cite web |last=Pettini |first=M. |title=RELATIVISTIC COSMOLOGY |url=https://people.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture03.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://people.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture03.pdf |archive-date=9 October 2022 |url-status=live |access-date=27 May 2022 |language=en}}</ref> It even showed that general relativity was incompatible with a [[static universe]], and Einstein later conceded that he had been wrong to design his field equations to account for a Universe that was not expanding.<ref>{{Cite journal |last1=O’Raifeartaigh |first1=Cormac |last2=O’Keeffe |first2=Michael |title=Einstein's 1917 Static Model of the Universe: A Centennial Review |url=https://link.springer.com/article/10.1140/epjh/e2017-80002-5 |journal=The European Physical Journal H |year=2017 |volume=42 |issue=3 |language=en |page=41 |doi=10.1140/epjh/e2017-80002-5 |arxiv=1701.07261 |bibcode=2017EPJH...42..431O |s2cid=119461771 |access-date=29 May 2022 |archive-date=29 May 2022 |archive-url=https://web.archive.org/web/20220529140023/https://link.springer.com/article/10.1140/epjh/e2017-80002-5 |url-status=live }}</ref>

Today, there remain many important situations in which the Einstein field equations have not been solved. Chief among these is the [[two-body problem]], which concerns the geometry of spacetime around two mutually interacting massive objects, such as the Sun and the Earth, or the two stars in a [[binary star system]]. The situation gets even more complicated when considering the interactions of three or more massive bodies (the "''n''-body problem"), and some scientists suspect that the Einstein field equations will never be solved in this context.<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> However, it is still possible to construct an approximate solution to the field equations in the ''n''-body problem by using the technique of [[post-Newtonian expansion]].<ref>{{Cite journal |last=Spyrou |first=N. |date=1 May 1975 |title=The ''N''-body problem in general relativity. |journal=The Astrophysical Journal |volume=197 |pages=725–743 |doi=10.1086/153562 |bibcode=1975ApJ...197..725S |issn=0004-637X|doi-access=free }}</ref> In general, the extreme nonlinearity of the Einstein field equations makes it difficult to solve them in all but the most specific cases.<ref>{{Cite web |last=Sleator |first=Daniel |date=6 June 1996 |title=Hermeneutics of Classical General Relativity |url=https://physics.nyu.edu/sokal/transgress_v2/node2.html |access-date=23 May 2022}}</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, modern 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=9781108655705 |pages=6 |language=en}}</ref>

One path is to describe gravity in the framework of [[quantum field theory]], 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 |last= Feynman |first= R.P. |author2=Morinigo, F.B. |author3=Wagner, W.G. |author4=Hatfield, B.  |title= Feynman lectures on gravitation |url= https://archive.org/details/feynmanlectureso0000feyn_g4q1 |url-access= registration |publisher= Addison-Wesley |date= 1995 |isbn=978-0-201-62734-3 }}</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.

=== Tests of general relativity ===
{{main | Tests of general relativity}}
[[File:1919 eclipse positive.jpg|thumb|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> Still, since its development, an ongoing series of experimental results have provided support for the theory:<ref name="NASA-2022"/> In 1919, the British astrophysicist [[Arthur Eddington]] was able to confirm the predicted [[gravitational lens]]ing 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=9780471925675 |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 [[redshift]]ed as it moves towards a source of gravity. The observed redshift also supported the idea that time runs more slowly in the presence of a gravitational field.<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>

General relativity states that gravity acts on light and matter equally, meaning that a sufficiently massive object could warp light around it and create a [[gravitational lensing|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 |title=Physics and Astrophysics: Glimpses of the Progress |author1=Subal Kar |edition=illustrated |publisher=CRC Press |year=2022 |isbn=978-1-000-55926-2 |page=106 |url=https://books.google.com/books?id=IWFkEAAAQBAJ}} [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>

[[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>

==Specifics==

===Earth's gravity===
[[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 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 furthest from the center of the Earth. The force of gravity varies with latitude and 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 |url-status=dead }}</ref><ref>{{cite web |url=http://curious.astro.cornell.edu/question.php?number=310 |title=Curious About Astronomy? |website= Cornell University |accessdate=22 December 2023 |archive-date=28 July 2013 |archiveurl=https://web.archive.org/web/20130728125707/http://curious.astro.cornell.edu/question.php?number=310}} </ref>

===Gravitational radiation===
[[File:LIGO Hanford aerial 05.jpg|alt=LIGO Hanford Observatory|thumb|The [[LIGO]] Hanford Observatory located in Washington, United States, where gravitational waves were first observed in September 2015]]
{{Main|Gravitational wave}}
General relativity predicts that energy can be transported out of a system through gravitational radiation. 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 }}</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 |pages=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>

===Speed of gravity===
{{Main|Speed of gravity}}
In December 2012, a research team in China announced that it had produced measurements of the phase lag of [[Earth tide]]s during full and new moons which seem to prove that the speed of gravity is equal to the speed of light.<ref>[http://www.astrowatch.net/2012/12/chinese-scientists-find-evidence-for.html Chinese scientists find evidence for speed of gravity] {{Webarchive|url=https://web.archive.org/web/20130108083729/http://www.astrowatch.net/2012/12/chinese-scientists-find-evidence-for.html |date=8 January 2013 }}, astrowatch.com, 12/28/12.</ref> This means that if the Sun suddenly disappeared, the Earth would keep orbiting the vacant point normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in ''[[Science Bulletin]]'' in February 2013.<ref>{{cite journal|last=TANG|first=Ke Yun|author2=HUA ChangCai |author3=WEN Wu |author4=CHI ShunLiang |author5=YOU QingYu |author6=YU Dan |title=Observational evidences for the speed of the gravity based on the Earth tide|journal=Chinese Science Bulletin|date=February 2013|volume=58|issue=4–5|pages=474–477|doi=10.1007/s11434-012-5603-3|bibcode=2013ChSBu..58..474T|doi-access=free}}</ref>

In October 2017, the [[LIGO]] and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from the same direction. 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]].]]
* '''Extra-fast stars''': Stars in galaxies follow a [[Galaxy rotation curve|distribution of velocities]] where stars on the outskirts are moving faster than they should according to the observed distributions of normal matter. Galaxies within [[Galaxy groups and clusters|galaxy clusters]] show a similar pattern. [[Dark matter]], which would interact through gravitation but not electromagnetically, would account for the discrepancy. Various [[Modified Newtonian dynamics|modifications to Newtonian dynamics]] have also been proposed.
* '''[[Accelerated expansion]]''': The [[expansion of the universe]] seems to be speeding up.<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 |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 |page=091102 |doi=10.1103/PhysRevLett.100.091102 |pmid=18352689 |bibcode=2008PhRvL.100i1102A |issn=0031-9007}}</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 |pages=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>

==Alternative theories==
{{Main|Alternatives to general relativity}}

===Historical alternative theories===
* [[Aristotelian theory of gravity]]
* [[Le Sage's theory of gravitation]] (1784) also called LeSage gravity but originally proposed by Fatio and further elaborated by [[Georges-Louis Le Sage]], based on a fluid-based explanation where a light gas fills the entire Universe.
* [[Ritz's Equation|Ritz's theory of gravitation]], ''Ann. Chem. Phys.'' 13, 145, (1908) pp.&nbsp;267–271, Weber–Gauss electrodynamics applied to gravitation. Classical advancement of perihelia.
* [[Nordström's theory of gravitation]] (1912, 1913), an early competitor of general relativity.
* [[Kaluza–Klein theory]] (1921)
* [[Whitehead's theory of gravitation]] (1922), another early competitor of general relativity.

===Modern alternative theories===
* [[Brans–Dicke theory]] of gravity (1961)<ref name=2014Schpj...931358B>{{cite journal|author=Brans, C.H. |date=Mar 2014  |title= Jordan–Brans–Dicke Theory|journal=Scholarpedia |volume=9 |issue=4  |page=31358 |doi= 10.4249/scholarpedia.31358|bibcode= 2014SchpJ...931358B|arxiv=gr-qc/0207039|doi-access=free }}</ref>
* [[Induced gravity]] (1967), a proposal by [[Andrei Sakharov]] according to which [[general relativity]] might arise from [[quantum field theory|quantum field theories]] of matter
*[[String theory]] (late 1960s)
* [[F(R) gravity|ƒ(R) gravity]] (1970)
* [[Horndeski's theory|Horndeski theory]] (1974)<ref name=1974IJTP...10..363H>{{cite journal|author=Horndeski, G.W. |date=Sep 1974  |title= Second-Order Scalar–Tensor Field Equations in a Four-Dimensional Space |journal=International Journal of Theoretical Physics |volume=88 |issue= 10 |pages=363–384 |doi= 10.1007/BF01807638|bibcode= 1974IJTP...10..363H|s2cid=122346086 }}</ref>
* [[Supergravity]] (1976)
* In the [[modified Newtonian dynamics]] (MOND) (1981), [[Mordehai Milgrom]] proposes a modification of [[Newton's second law]] of motion for small accelerations<ref name="2014SchpJ...931410M">{{cite journal|author=Milgrom, M. |date=Jun 2014  |title= The MOND paradigm of modified dynamics|journal=Scholarpedia |volume=9 |issue=6  |page=31410 |doi= 10.4249/scholarpedia.31410|bibcode= 2014SchpJ...931410M|doi-access=free}}</ref>
* The [[self-creation cosmology]] theory of gravity (1982) by G.A. Barber in which the Brans–Dicke theory is modified to allow mass creation
* [[Loop quantum gravity]] (1988) by [[Carlo Rovelli]], [[Lee Smolin]], and [[Abhay Ashtekar]]
* [[Nonsymmetric gravitational theory]] (NGT) (1994) by [[John Moffat (physicist)|John Moffat]]
*[[Tensor–vector–scalar gravity]] (TeVeS) (2004), a relativistic modification of MOND by [[Jacob Bekenstein]]
*[[Chameleon particle|Chameleon theory]] (2004) by [[Justin Khoury]] and [[Amanda Weltman]].
* [[Pressuron|Pressuron theory]] (2013) by [[Olivier Minazzoli]] and [[Aurélien Hees]].
*[[Conformal gravity]]<ref>{{Cite arXiv|title=Einstein gravity from conformal gravity|eprint=1105.5632|last1=Haugan|first1=Mark P|last2=Lämmerzahl|first2=C|class=hep-th|year=2011}}</ref>
*[[Gravity as an entropic force]], gravity arising as an emergent phenomenon from the thermodynamic concept of entropy.
*In the [[superfluid vacuum theory]] the gravity and curved spacetime arise as a [[collective excitation]] mode of non-relativistic background [[superfluid]].
*[[Massive gravity]], a theory where gravitons and gravitational waves have a non-zero mass

==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}}

===Sources===
{{refbegin}}
* {{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}}
* {{ citation | title = McGraw-Hill Dictionary of Scientific and Technical Terms | edition = 4th | location = New York | publisher = [[McGraw-Hill]] | year = 1989 | isbn = 0-07-045270-9 | ref = {{harvid|McGraw-Hill Dict|1989}} }}
* {{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/n7/mode/2up}}
{{refend}}

==Further reading==
* {{cite book |first=Isaac |last=Newton |translator=I. Bernard Cohen  |title=The Principia : mathematical principles of natural philosophy |contribution=A Guide to Newton's Principia |contributor=I. Bernard Cohen |publisher=University of California Press |date=1999 |orig-date=1687 |isbn=9780520088160 |oclc=313895715}}
* {{cite book | last = Halliday | first = David | author2 = Robert Resnick | author3 = Kenneth S. Krane | 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, Kip S. |author-link=Kip Thorne |author2=Misner, Charles W. |author3=Wheeler, John Archibald |title=Gravitation |publisher=W.H. Freeman |date=1973 |isbn=978-0-7167-0344-0}}
* {{cite news
|title=Everything you thought you knew about gravity is wrong
|first=Richard
|last=Panek
|date=2 August 2019
|newspaper=[[The Washington Post]]
|url=https://www.washingtonpost.com/outlook/everything-you-thought-you-knew-about-gravity-is-wrong/2019/08/01/627f3696-a723-11e9-a3a6-ab670962db05_story.html}}

==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}}
* [https://feynmanlectures.caltech.edu/I_07.html The Feynman Lectures on Physics Vol. I Ch. 7: The Theory of Gravitation]
* {{springer|title=Gravitation|id=p/g045040}}
* {{springer|title=Gravitation, theory of|id=p/g045050}}

{{Fundamental interactions}}
{{Theories of gravitation}}
{{Portal bar|Physics|Astronomy|Stars|Spaceflight|Outer space|Solar System}}
{{Authority control}}

[[Category:Gravity| ]]
[[Category:Fundamental interactions]]
[[Category:Acceleration]]
[[Category:Articles containing video clips]]
[[Category:Empirical laws]]