Editing Gravity (section)

==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 |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=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><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 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|authorlink=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 |url=https://www.worldcat.org/title/141385334 |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=9780471925675 |author-link=Steven Weinberg |url-access=registration}}</ref>{{rp|17}}

[[Johannes Kepler]], in his 1609 book [[Astronomia nova]] 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 since he was unable to convert them in to 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 where 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, lead 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 [[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=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 [[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>