Editing Three-body problem (section)

==History==
The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when [[Isaac Newton]] published his ''[[Philosophiæ Naturalis Principia Mathematica]],'' in which Newton attempted to figure out if any long term stability is possible especially for such a system like that of the [[Earth]], the [[Moon]], and [[Sun|the Sun]], after having solved the [[two-body problem]].<ref>{{Cite book |last=Musielak |first=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 |doi=10.1007/978-3-319-58226-9}}</ref> Guided by major [[Renaissance]] astronomers [[Nicolaus Copernicus]], [[Tycho Brahe]] and [[Johannes Kepler]], Newton introduced later generations to the beginning of the gravitational three-body problem.<ref name=":1">{{Cite book |last=Valtonen |first=Mauri |author-link=Mauri Valtonen |url=https://books.google.com/books?id=4-wgDAAAQBAJ&pg=PA4 |title=The Three-body Problem from Pythagoras to Hawking |publisher=Springer |year=2016 |isbn=978-3-319-22726-9 |pages=4 |oclc=1171227640}}</ref> In Proposition 66 of Book 1 of the ''Principia'', and its 22 Corollaries, Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions. In Propositions 25 to 35 of Book 3, Newton also took the first steps in applying his results of Proposition 66 to the [[Lunar theory#Newton|lunar theory]], the motion of the Moon under the gravitational influence of Earth and the Sun.<ref>{{Cite book |last=Newton |first=Isaac |title=Philosophiæ naturalis principia mathematica |location=London |publisher=G. & J. Innys |date=1726 |url=https://lbezone.hkust.edu.hk/bib/b706487 |access-date=2022-10-05 |via=Hong Kong University of Science and Technology |doi=10.14711/spcol/b706487 }}</ref> Later, this problem was also applied to other planets' interactions with the Earth and the Sun.<ref name=":1" />

The physical problem was first addressed by [[Amerigo Vespucci]] and subsequently by [[Galileo Galilei]], as well as [[Simon Stevin]], but they did not realize what they contributed. Though Galileo determined that the speed of fall of all bodies changes uniformly and in the same way, he did not apply it to planetary motions.<ref name=":1" /> Whereas in 1499, Vespucci used knowledge of the position of the Moon to determine his position in Brazil.<ref>{{Cite web |title=Amerigo Vespucci |url=https://www.biography.com/explorer/amerigo-vespucci |access-date=2022-10-05 |website=Biography |date=23 June 2021 |language=en-us}}</ref> It became of technical importance in the 1720s, as an accurate solution would be applicable to navigation, specifically for the [[History of longitude#Problem of longitude|determination of longitude at sea]], solved in practice by [[John Harrison]]'s invention of the [[marine chronometer]]. However the accuracy of the [[lunar theory]] was low, due to the perturbing effect of the Sun and planets on the motion of the Moon around Earth.

[[Jean le Rond d'Alembert]] and [[Alexis Clairaut]], who developed a longstanding rivalry, both attempted to analyze the problem in some degree of generality; they submitted their competing first analyses to the Académie Royale des Sciences in 1747.<ref>The 1747 memoirs of both parties can be read in the volume of ''Histoires'' (including ''Mémoires'') of the Académie Royale des Sciences for 1745 (belatedly published in Paris in 1749) (in French):

: Clairaut: "On the System of the World, according to the principles of Universal Gravitation" (at pp.&nbsp;329–364); and
: d'Alembert: "General method for determining the orbits and the movements of all the planets, taking into account their mutual actions" (at pp.&nbsp;365–390).The peculiar dating is explained by a note printed on page 390 of the "Memoirs" section: "Even though the preceding memoirs, of Messrs. Clairaut and d'Alembert, were only read during the course of 1747, it was judged appropriate to publish them in the volume for this year" (i.e. the volume otherwise dedicated to the proceedings of 1745, but published in 1749).</ref> It was in connection with their research, in Paris during the 1740s, that the name "three-body problem" ({{langx|fr|Problème des trois Corps}}) began to be commonly used. An account published in 1761 by Jean le Rond d'Alembert indicates that the name was first used in 1747.<ref>[[Jean le Rond d'Alembert]], in a paper of 1761 reviewing the mathematical history of the problem, mentions that Euler had given a method for integrating a certain differential equation "in 1740 (seven years before there was question of the Problem of Three Bodies)": see d'Alembert, "Opuscules Mathématiques", vol.&nbsp;2, Paris 1761, Quatorzième Mémoire ("Réflexions sur le Problème des trois Corps, avec de Nouvelles Tables de la Lune ...") pp.&nbsp;329–312, at sec.&nbsp;VI, p.&nbsp;245.</ref>

From the end of the 19th century to early 20th century, the approach to solve the three-body problem with the usage of short-range attractive two-body forces was developed by scientists, which offered P. F. Bedaque, H.-W. Hammer and U. van Kolck an idea to renormalize the short-range three-body problem, providing scientists a rare example of a [[renormalization group]] [[limit cycle]] at the beginning of the 21st century.<ref name=":0">{{Cite journal |last1=Mohr |first1=R.F. |last2=Furnstahl |first2=R.J. |last3=Hammer |first3=H.-W. |last4=Perry |first4=R.J. |last5=Wilson |first5=K.G. |date=January 2006 |title=Precise numerical results for limit cycles in the quantum three-body problem |journal=[[Annals of Physics]] |volume=321 |issue=1 |pages=225–259 |doi=10.1016/j.aop.2005.10.002 |arxiv=nucl-th/0509076 |bibcode=2006AnPhy.321..225M |s2cid=119073191 |issn=0003-4916}}</ref> [[George William Hill]] worked on the restricted problem in the late 19th century with an application of motion of [[Venus]] and [[Mercury (planet)|Mercury]].<ref>[https://babel.hathitrust.org/cgi/pt?id=uc1.32106020676935&view=1up&seq=122&skin=2021 "Coplanar Motion of Two Planets, One Having a Zero Mass"]. [[Annals of Mathematics]], Vol. III, pp. 65–73, 1887.</ref>

At the beginning of the 20th century,  [[Karl F. Sundman|Karl Sundman]] approached the problem mathematically and systematically by providing a functional theoretical proof to the problem valid for all values of time. It was the first time scientists theoretically solved the three-body problem. However, because there was not a qualitative enough solution of this system, and it was too slow for scientists to practically apply it, this solution still left some issues unresolved.<ref>{{Cite book |last=Barrow-Green |first=June |author-link=June Barrow-Green |title=Poincaré and the Three Body Problem |date=1996-10-29 |publisher=American Mathematical Society |isbn=978-0-8218-0367-7 |series=History of Mathematics |volume=11 |location=Providence, Rhode Island|doi=10.1090/hmath/011 |url=http://oro.open.ac.uk/57403/1/335423.pdf }}</ref> In the 1970s, implication to three-body from two-body forces had been discovered by [[Vitaly Efimov|V. Efimov]], which was named the [[Efimov effect]].<ref>{{Cite journal |last=Efimov |first=V. |date=1970-12-21 |title=Energy levels arising from resonant two-body forces in a three-body system |journal=Physics Letters B |language=en |volume=33 |issue=8 |pages=563–564 |doi=10.1016/0370-2693(70)90349-7 |bibcode=1970PhLB...33..563E |issn=0370-2693}}</ref>

In 2017,  [[Liao Shijun|Shijun Liao]] and Xiaoming Li applied a new strategy of numerical simulation for chaotic systems called the clean numerical simulation (CNS), with the use of a national supercomputer, to successfully gain 695 families of periodic solutions of the three-body system with equal mass.<ref>{{Cite journal |last1=Liao |first1=Shijun |last2=Li |first2=Xiaoming |date=2019-11-01 |title=On the periodic solutions of the three-body problem |url=https://academic.oup.com/nsr/article/6/6/1070/5537324 |journal=National Science Review |language=en |volume=6 |issue=6 |pages=1070–1071 |doi=10.1093/nsr/nwz102 |pmid=34691975 |pmc=8291409 |issn=2095-5138}}</ref>

In 2019, Breen et al. announced a fast [[neural network]] solver for the three-body problem, trained using a numerical integrator.<ref>{{cite journal |last1=Breen |first1=Philip G. |last2=Foley |first2=Christopher N. |last3=Boekholt |first3=Tjarda |last4=Portegies Zwart |first4=Simon |title=Newton versus the machine: Solving the chaotic three-body problem using deep neural networks |arxiv=1910.07291 |doi=10.1093/mnras/staa713 |journal=Monthly Notices of the Royal Astronomical Society |volume=494 |issue=2 |date=2020 |pages=2465–2470 |doi-access=free |s2cid=204734498}}</ref>

In September 2023, several possible solutions have been found to the problem according to reports.<ref name="SA-20230923">{{cite news |last=Watson |first=Claire |title=We Just Got 12,000 New Solutions to The Infamous Three-Body Problem |url=https://www.sciencealert.com/we-just-got-12000-new-solutions-to-the-infamous-three-body-problem |date=23 September 2023 |work=[[ScienceAlert]] |url-status=live |archiveurl=https://archive.today/20230924005541/https://www.sciencealert.com/we-just-got-12000-new-solutions-to-the-infamous-three-body-problem |archivedate=24 September 2023 |accessdate=23 September 2023 }}</ref><ref name="ARX-2023">{{cite journal |title=Three-body periodic collisionless equal-mass free-fall orbits revisited |date=2024 |arxiv=2308.16159 |last1=Hristov |first1=Ivan |last2=Hristova |first2=Radoslava |last3=Dmitrašinović |first3=Veljko |last4=Tanikawa |first4=Kiyotaka |journal=Celestial Mechanics and Dynamical Astronomy |volume=136 |issue=1 |doi=10.1007/s10569-023-10177-w |bibcode=2024CeMDA.136....7H }}</ref>