Editing Isaac Newton (section)

=== Gravity ===
[[File:NewtonsPrincipia.jpg|thumb|upright=1.25|Newton's own copy of ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'' with Newton's hand-written corrections for the second edition, now housed in the [[Wren Library]] at [[Trinity College, Cambridge]]]]

Newton had been developing his theory of gravitation as far back as 1665.<ref name=":4">{{Cite book |last=Struik |first=Dirk J. |author-link=Dirk Jan Struik |url=https://archive.org/details/concisehistoryof02stru/page/151 |title=A Concise History of Mathematics |publisher=Dover Publications |year=1948 |pages=151, 154}}</ref> In 1679, he returned to his work on [[celestial mechanics]] by considering gravitation and its effect on the orbits of [[planet]]s with reference to [[Kepler's laws]] of planetary motion. Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with [[John Flamsteed]].{{sfn|Westfall|1980|pp=391–392}} After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. He shared his results with [[Edmond Halley]] and the Royal Society in {{lang|la|[[De motu corporum in gyrum]]}}, a tract written on about nine sheets which was copied into the Royal Society's Register Book in December 1684.<ref>Whiteside, D.T., ed. (1974). ''Mathematical Papers of Isaac Newton, 1684–1691''. '''6'''. Cambridge University Press. p.&nbsp;30.</ref> This tract contained the nucleus that Newton developed and expanded to form the ''Principia''.

The {{lang|la|[[Philosophiæ Naturalis Principia Mathematica|Principia]]}} was published on 5 July 1687 with encouragement and financial help from Halley. In this work, Newton stated the [[Newton's laws of motion|three universal laws of motion]]. Together, these laws describe the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for [[classical mechanics]]. They contributed to numerous advances during the [[Industrial Revolution]] and were not improved upon for more than 200 years. Many of these advances still underpin non-relativistic technologies today. Newton used the Latin word ''gravitas'' (weight) for the effect that would become known as [[gravity]], and defined the law of [[Newton's law of universal gravitation|universal gravitation]].<ref name="Schmitz2018">{{Cite book |last=Schmitz |first=Kenneth&nbsp;S. |url=https://books.google.com/books?id=4WGdBgAAQBAJ&pg=PA251 |title=Physical Chemistry: Multidisciplinary Applications in Society |publisher=Elsevier |year=2018 |isbn=978-0-12-800599-6 |location=Amsterdam |page=251 |access-date=1 March 2020 |archive-url=https://web.archive.org/web/20200310132426/https://books.google.com/books?id=4WGdBgAAQBAJ&pg=PA251 |archive-date=10 March 2020 |url-status=live}}</ref> His work achieved the [[Unification of theories in physics#Unification of gravity and astronomy|first great unification in physics]].<ref name=":15" /> He solved the [[two-body problem]], and introduced the [[three-body problem]].<ref name=":14">{{Cite book |last1=Musielak |first1=Zdzislaw |url=https://books.google.com/books?id=D90tDwAAQBAJ&pg=PA3 |title=Three Body Dynamics and Its Applications to Exoplanets |last2=Quarles |first2=Billy |date=2017 |publisher=Springer International Publishing |isbn=978-3-319-58225-2 |series= |location= |pages=3 |language=en |bibcode=2017tbdi.book.....M |doi=10.1007/978-3-319-58226-9}}</ref>

In the same work, Newton presented a calculus-like method of geometrical analysis using 'first and last ratios', gave the first analytical determination (based on [[Boyle's law]]) of the speed of sound in air, inferred the oblateness of Earth's spheroidal figure, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the [[Lunar theory#Newton|irregularities in the motion of the Moon]], provided a theory for the determination of the orbits of comets, and much more.<ref name="Schmitz2018" /> Newton's biographer [[David Brewster]] reported that the complexity of applying his theory of gravity to the motion of the moon was so great it affected Newton's health: "[H]e was deprived of his appetite and sleep" during his work on the problem in 1692–93, and told the astronomer [[John Machin]] that "his head never ached but when he was studying the subject". According to Brewster, Halley also told [[John Conduitt]] that when pressed to complete his analysis Newton "always replied that it made his head ache, and ''kept him awake so often, that he would think of it no more''". [Emphasis in original]<ref>{{Cite book |last=Brewster |first=David |url=https://books.google.com/books?id=acBV7QHgMIAC&pg=108 |title=Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton |publisher=Edmonston and Douglas |year=1860 |pages=108}}</ref> He provided the first calculation of the [[age of Earth]] by experiment,<ref name=":19">{{Cite journal |last=Simms |first=D. L. |date=2004 |title=Newton's Contribution to the Science of Heat |url=https://www.tandfonline.com/doi/full/10.1080/00033790210123810 |journal=Annals of Science |language=en |volume=61 |issue=1 |pages=33–77 |doi=10.1080/00033790210123810 |issn=0003-3790}}</ref> and described a precursor to the modern [[wind tunnel]].<ref name=":21">{{Cite book |last=Rowlands |first=Peter |url=https://books.google.com/books?id=u0NBDwAAQBAJ&pg=PA152 |title=Newton – Innovation And Controversy |publisher=[[World Scientific Publishing]] |year=2017 |isbn=9781786344045 |pages=152–153}}</ref>

Newton made clear his [[heliocentric]] view of the Solar System—developed in a somewhat modern way because already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the Solar System.<ref>See Curtis Wilson, "The Newtonian achievement in astronomy", pp. 233–274 in R Taton & C Wilson (eds) (1989) ''The General History of Astronomy'', Volume, 2A', [https://books.google.com/books?id=rkQKU-wfPYMC&pg=PA233 at p. 233] {{Webarchive|url=https://web.archive.org/web/20151003121307/https://books.google.com/books?id=rkQKU-wfPYMC&pg=PA233 |date=3 October 2015 }}.</ref> For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line". (Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest.)<ref>Text quotations are from 1729 translation of Newton's ''Principia'', Book 3 (1729 vol.2) [https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n257 at pp. 232–33 &#91;233&#93;].</ref>

Newton was criticised for introducing "[[occult]] agencies" into science because of his postulate of an invisible [[action at a distance (physics)|force able to act over vast distances]].<ref>Edelglass et al., ''Matter and Mind'', {{isbn|0-940262-45-2}}. p. 54</ref> Later, in the second edition of the ''Principia'' (1713), Newton firmly rejected such criticisms in a concluding [[General Scholium]], writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here he used what became his famous expression {{lang|la|"[[Hypotheses non fingo]]"}}.<ref>On the meaning and origins of this expression, see Kirsten Walsh, [https://blogs.otago.ac.nz/emxphi/2010/10/does-newton-feign-an-hypothesis/ Does Newton feign an hypothesis?] {{Webarchive|url=https://web.archive.org/web/20140714120054/https://blogs.otago.ac.nz/emxphi/2010/10/does-newton-feign-an-hypothesis/ |date=14 July 2014 }}, [https://blogs.otago.ac.nz/emxphi/ Early Modern Experimental Philosophy] {{Webarchive|url=https://web.archive.org/web/20110721051523/https://blogs.otago.ac.nz/emxphi/ |date=21 July 2011 }}, 18 October 2010.</ref>)

With the {{lang|la|Principia}}, Newton became internationally recognised.{{sfn|Westfall|1980|loc=Chapter 11}} He acquired a circle of admirers, including the Swiss-born mathematician [[Nicolas Fatio de Duillier]].<ref name="Hatch">{{Cite web |last=Hatch |first=Professor Robert&nbsp;A. |title=Newton Timeline |url=http://web.clas.ufl.edu/users/ufhatch/pages/13-NDFE/newton/05-newton-timeline-m.htm |url-status=dead |archive-url=https://web.archive.org/web/20120802071026/http://web.clas.ufl.edu/users/ufhatch/pages/13-NDFE/newton/05-newton-timeline-m.htm |archive-date=2 August 2012 |access-date=13 August 2012}}</ref>

In the 1660s and 1670s, Newton found 72 of the 78 "species" of cubic curves and categorised them into four types, systemizing his results in later publications. However, a 1690s manuscript later analyzed showed that Newton had identified all 78 cubic curves, but chose not to publish the remaining six for unknown reasons.<ref name=":20">{{Cite journal |last1=Bloye |first1=Nicole |last2=Huggett |first2=Stephen |year=2011 |title=Newton, the geometer |url=https://stephenhuggett.com/Newton.pdf |url-status=dead |journal=Newsletter of the European Mathematical Society |issue=82 |pages=19–27 |mr=2896438 |archive-url=https://web.archive.org/web/20230308041757/http://stephenhuggett.com/Newton.pdf |archive-date=8 March 2023 |access-date=19 February 2023}}</ref>{{Sfn|Iliffe|Smith|2016|pp=382–394, 411}} In 1717, and probably with Newton's help, [[James Stirling (mathematician)|James Stirling]] proved that every cubic was one of these four types. He claimed that the four types could be obtained by [[Projective plane|plane projection]] from one of them, and this was proved in 1731, four years after his death.<ref>{{Cite book |last=Bix |first=Robert |url=https://books.google.com/books?id=nlsyqix3FWcC&pg=129 |title=Conics and Cubics: A Concrete Introduction to Algebraic Curves |date=2006 |publisher=Springer |isbn=978-0-387-31802-8 |edition=2nd |series= |location= |pages=129}}</ref>