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=== Astronomical concepts === {{Main|History of astronomy|Timeline of astronomy}} [[File:Aristarchus working.jpg|thumb|right|3rd century BCE calculations by [[Aristarchus of Samos|Aristarchus]] on the relative sizes of, from left to right, the Sun, Earth, and Moon, from a 10th-century AD Greek copy]] The earliest written records of identifiable [[history of astronomy|predecessors to modern astronomy]] come from [[Ancient Egypt]] and [[Mesopotamia]] from around 3000 to 1200 [[Common Era|BCE]].<ref name=Lindberg2007a>{{Cite book |last=Lindberg |first=David C. |title=The beginnings of Western science: the European Scientific tradition in philosophical, religious, and institutional context |publisher=University of Chicago Press |year=2007 |isbn=9780226482057 |edition=2nd |page=12}}</ref><ref name="Grant2007a">{{cite book |last=Grant |first=Edward |title=A History of Natural Philosophy: From the Ancient World to the Nineteenth Century |publisher=Cambridge University Press |year=2007 |isbn=978-0-521-68957-1 |edition=|location=New York |pages=1–26 |chapter=Ancient Egypt to Plato |chapter-url=https://archive.org/details/historynaturalph00gran/page/n16 |chapter-url-access=limited}}</ref> [[Babylonian astronomy|Babylonian astronomers]] of the 7th century BCE viewed the world as a [[Flat Earth|flat disk]] surrounded by the ocean.<ref>{{cite journal|first=Wayne |last=Horowitz |journal=Iraq |year=1988 |title=The Babylonian Map of the World |volume=50 |pages=147–165 |doi=10.2307/4200289 |jstor=4200289|s2cid=190703581 }}</ref><ref>{{cite book |last1=Keel |first1=Othmar |title=The Symbolism of the Biblical World |year=1997 |publisher=Eisenbrauns |isbn=978-1-575-06014-9 |url=https://books.google.com/books?id=Fy4B1iMg33YC |pages=20–22 |access-date=February 26, 2023 |archive-date=March 13, 2024 |archive-url=https://web.archive.org/web/20240313184352/https://books.google.com/books?id=Fy4B1iMg33YC |url-status=live }}</ref> Later [[Ancient Greece|Greek]] philosophers, observing the motions of the heavenly bodies, were concerned with developing models of the universe based more profoundly on [[empirical evidence]]. The first coherent model was proposed by [[Eudoxus of Cnidos]], a student of Plato who followed Plato's idea that heavenly motions had to be circular. In order to account for the known complications of the planets' motions, particularly [[Retrograde and prograde motion|retrograde movement]], Eudoxus' model included 27 different [[celestial spheres]]: four for each of the planets visible to the naked eye, three each for the Sun and the Moon, and one for the stars. All of these spheres were centered on the Earth, which remained motionless while they rotated eternally. Aristotle elaborated upon this model, increasing the number of spheres to 55 in order to account for further details of planetary motion. For Aristotle, normal [[classical elements|matter]] was entirely contained within the terrestrial sphere, and it obeyed fundamentally different rules from [[Aether (classical element)|heavenly material]].<ref>{{Cite journal |last=Wright |first=Larry |date=August 1973 |title=The astronomy of Eudoxus: Geometry or physics? |url=https://linkinghub.elsevier.com/retrieve/pii/0039368173900022 |journal=Studies in History and Philosophy of Science |language=en |volume=4 |issue=2 |pages=165–172 |doi=10.1016/0039-3681(73)90002-2 |bibcode=1973SHPSA...4..165W |access-date=February 27, 2023 |archive-date=March 15, 2023 |archive-url=https://web.archive.org/web/20230315164807/https://linkinghub.elsevier.com/retrieve/pii/0039368173900022 |url-status=live }}</ref><ref>{{Citation |last=Dicati |first=Renato |title=The Ancients' Astronomy |date=2013 |url=http://link.springer.com/10.1007/978-88-470-2829-6_2 |work=Stamping Through Astronomy |pages=19–55 |place=Milano |publisher=Springer Milan |language=en |doi=10.1007/978-88-470-2829-6_2 |isbn=978-88-470-2828-9 |access-date=February 27, 2023 |archive-date=March 13, 2024 |archive-url=https://web.archive.org/web/20240313184405/https://link.springer.com/chapter/10.1007/978-88-470-2829-6_2 |url-status=live }}</ref> The post-Aristotle treatise ''[[De Mundo]]'' (of uncertain authorship and date) stated, "Five elements, situated in spheres in five regions, the less being in each case surrounded by the greater—namely, earth surrounded by water, water by air, air by fire, and fire by ether—make up the whole universe".<ref name=1908DeMundo>{{cite book |url=https://archive.org/details/demundoarisrich |title=De Mundo |year=1914 |author=Aristotle |author2=Forster, E. S. |author3=Dobson, J. F. |page=[https://archive.org/details/demundoarisrich/page/2 2] |location=Oxford |publisher=The Clarendon Press}}</ref> This model was also refined by [[Callippus]] and after concentric spheres were abandoned, it was brought into nearly perfect agreement with astronomical observations by [[Ptolemy]].<ref name="almagest">{{cite journal |last=Goldstein |first=Bernard R. |date=1997 |title=Saving the phenomena: the background to Ptolemy's planetary theory |journal=Journal for the History of Astronomy |volume=28 |issue=1 |pages=1–12 |bibcode=1997JHA....28....1G |doi=10.1177/002182869702800101 |s2cid=118875902}}</ref> The success of such a model is largely due to the mathematical fact that any function (such as the position of a planet) can be decomposed into a set of circular functions (the [[Fourier series|Fourier modes]]). Other Greek scientists, such as the [[Pythagoreans|Pythagorean]] philosopher [[Philolaus]], postulated (according to [[Stobaeus]]' account) that at the center of the universe was a "central fire" around which the [[Earth]], [[Sun]], [[Moon]] and [[planet]]s revolved in uniform circular motion.<ref>Boyer, C. (1968) [https://archive.org/details/AHistoryOfMathematics ''A History of Mathematics'']. Wiley, p. 54.</ref> The [[Greek astronomy|Greek astronomer]] [[Aristarchus of Samos]] was the first known individual to propose a [[Heliocentrism|heliocentric]] model of the universe. Though the original text has been lost, a reference in [[Archimedes]]' book ''[[The Sand Reckoner]]'' describes Aristarchus's heliocentric model. Archimedes wrote: <blockquote>You, King Gelon, are aware the universe is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the universe just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.<ref>{{Cite book |last=Heath |first=Thomas |url=https://books.google.com/books?id=rZmHAAAAQBAJ |title=Aristarchus of Samos, the Ancient Copernicus: A History of Greek Astronomy to Aristarchus, Together with Aristarchus's Treatise on the Sizes and Distances of the Sun and Moon |date=2013 |publisher=Cambridge University Press |isbn=978-1-108-06233-6 |pages=302 |language=en |author-link=Thomas Heath (classicist) |access-date=February 26, 2023 |archive-date=March 13, 2024 |archive-url=https://web.archive.org/web/20240313184546/https://books.google.com/books?id=rZmHAAAAQBAJ |url-status=live }}</ref></blockquote> Aristarchus thus believed the stars to be very far away, and saw this as the reason why [[stellar parallax]] had not been observed, that is, the stars had not been observed to move relative each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with precision instruments. The geocentric model, consistent with planetary parallax, was assumed to be the explanation for the unobservability of stellar parallax.<ref>{{Cite book |last=Kolkata |first=James J. |url=http://iopscience.iop.org/book/978-1-6817-4100-0 |title=Elementary Cosmology: From Aristotle's Universe to the Big Bang and Beyond |date=2015 |publisher=IOP Publishing |isbn=978-1-68174-100-0 |doi=10.1088/978-1-6817-4100-0ch4 |access-date=February 27, 2023 |archive-date=June 5, 2018 |archive-url=https://web.archive.org/web/20180605142714/http://iopscience.iop.org/book/978-1-6817-4100-0 |url-status=live }}</ref> [[File:Flammarion.jpg|thumb|right|[[Flammarion engraving]], Paris 1888]] The only other astronomer from antiquity known by name who supported Aristarchus's heliocentric model was [[Seleucus of Seleucia]], a [[Hellenistic astronomer]] who lived a century after Aristarchus.<ref>{{cite journal|author-link=Otto E. Neugebauer|author=Neugebauer, Otto E. |date=1945|title=The History of Ancient Astronomy Problems and Methods|journal=Journal of Near Eastern Studies|volume=4|issue=1|pages= 166–173|quote=the [[Chaldaea]]n Seleucus from Seleucia|jstor=595168|doi=10.1086/370729|s2cid=162347339 }}</ref><ref>{{cite journal |author=Sarton |first=George |author-link=George Sarton |date=1955 |title=Chaldaean Astronomy of the Last Three Centuries B. C. |journal=Journal of the American Oriental Society |volume=75 |issue=3 |pages=166–173 [169] |doi=10.2307/595168 |jstor=595168 |quote=the heliocentrical astronomy invented by Aristarchos of Samos and still defended a century later by Seleucos the [[Babylonia]]n}}</ref><ref>William P. D. Wightman (1951, 1953), ''The Growth of Scientific Ideas'', Yale University Press. p. 38, where Wightman calls him [[Seleucus of Seleucia|Seleukos]] the [[Chaldea]]n.</ref> According to Plutarch, Seleucus was the first to prove the heliocentric system through [[reasoning]], but it is not known what arguments he used. Seleucus' arguments for a heliocentric cosmology were probably related to the phenomenon of [[tide]]s.<ref>[[Lucio Russo]], ''Flussi e riflussi'', Feltrinelli, Milano, Italy, 2003, {{ISBN|88-07-10349-4}}.</ref> According to [[Strabo]] (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun.<ref>{{harvtxt|Van Der Waerden|1987|loc=p. 527}}</ref> Alternatively, he may have proved heliocentricity by determining the constants of a [[Geometry|geometric]] model for it, and by developing methods to compute planetary positions using this model, similar to [[Nicolaus Copernicus]] in the 16th century.<ref>{{harvtxt|Van Der Waerden|1987|loc=pp. 527–529}}</ref> During the [[Middle Ages]], [[Heliocentrism|heliocentric]] models were also proposed by the [[Islamic astronomy|Persian astronomers]] [[Ja'far ibn Muhammad Abu Ma'shar al-Balkhi|Albumasar]]<ref>{{harvtxt|Van Der Waerden|1987 |loc=pp. 534–537}}</ref> and [[Al-Sijzi]].<ref name=Nasr>{{Cite book |last=Nasr |first=Seyyed H. |author-link=Hossein Nasr |orig-year=1964 |date=1993 |title=An Introduction to Islamic Cosmological Doctrines |edition=2nd |publisher=1st edition by [[Harvard University Press]], 2nd edition by [[State University of New York Press]] |isbn=978-0-7914-1515-3 |pages=[https://archive.org/details/introductiontois00nasr/page/135 135–136] |url=https://archive.org/details/introductiontois00nasr/page/135 }}</ref> [[File:ThomasDiggesmap.JPG|thumb|left|upright=1.4|[[Copernican heliocentrism|Model of the Copernican Universe]] by [[Thomas Digges]] in 1576, with the amendment that the stars are no longer confined to a sphere, but spread uniformly throughout the space surrounding the [[planet]]s]] The Aristotelian model was accepted in the [[Western world]] for roughly two millennia, until Copernicus revived Aristarchus's perspective that the astronomical data could be explained more plausibly if the [[Earth]] rotated on its axis and if the [[Sun]] were placed at the center of the universe.<ref name="TMU">{{Cite book |last1=Frautschi |first1=Steven C. |title=The Mechanical Universe: Mechanics and Heat |title-link=The Mechanical Universe |last2=Olenick |first2=Richard P. |last3=Apostol |first3=Tom M. |last4=Goodstein |first4=David L. |date=2007 |publisher=Cambridge University Press |isbn=978-0-521-71590-4 |edition=Advanced |location=Cambridge [Cambridgeshire] |page=58 |oclc=227002144 |author-link=Steven Frautschi |author-link3=Tom M. Apostol |author-link4=David L. Goodstein}}</ref> {{blockquote|In the center rests the Sun. For who would place this lamp of a very beautiful temple in another or better place than this wherefrom it can illuminate everything at the same time?|Nicolaus Copernicus|in Chapter 10, Book 1 of ''De Revolutionibus Orbium Coelestrum'' (1543)}} As noted by Copernicus, the notion that the [[Earth's rotation|Earth rotates]] is very old, dating at least to [[Philolaus]] ({{Circa|450 BC}}), [[Heraclides Ponticus]] ({{Circa|350 BC}}) and [[Ecphantus the Pythagorean]]. Roughly a century before Copernicus, the Christian scholar [[Nicholas of Cusa]] also proposed that the Earth rotates on its axis in his book, ''On Learned Ignorance'' (1440).<ref>[[#Misner|Misner, Thorne and Wheeler]], p. 754.</ref> Al-Sijzi<ref>{{cite book|title=Science in the Quran|volume=1|publisher=Malik Library|first=Ema Ākabara|last=Ālī|page=218}}</ref> also proposed that the Earth rotates on its axis. [[Empirical research|Empirical evidence]] for the Earth's rotation on its axis, using the phenomenon of [[comet]]s, was given by [[Nasīr al-Dīn al-Tūsī|Tusi]] (1201–1274) and [[Ali Qushji]] (1403–1474).<ref>{{Citation |last=Ragep |first=F. Jamil |year=2001 |title=Tusi and Copernicus: The Earth's Motion in Context |journal=Science in Context |volume=14 |issue=1–2 |pages=145–163 |doi=10.1017/s0269889701000060 |s2cid=145372613 }}</ref> This cosmology was accepted by [[Isaac Newton]], [[Christiaan Huygens]] and later scientists.<ref name="Misner-p755">[[#Misner|Misner, Thorne and Wheeler]], pp. 755–756.</ref> Newton demonstrated that the same [[Newton's laws of motion|laws of motion]] and gravity apply to earthly and to celestial matter, making Aristotle's division between the two obsolete. [[Edmund Halley]] (1720)<ref name=m756>[[#Misner|Misner, Thorne and Wheeler]], p. 756.</ref> and [[Jean-Philippe de Chéseaux]] (1744)<ref>{{cite book |author=de Cheseaux JPL |title=Traité de la Comète |date=1744 |publisher=Lausanne |pages=223ff |author-link=Jean-Philippe de Cheseaux}}. Reprinted as Appendix II in {{cite book |author=Dickson |first=F. P. |title=The Bowl of Night: The Physical Universe and Scientific Thought |date=1969 |publisher=M.I.T. Press |isbn=978-0-262-54003-2 |location=Cambridge, Massachusetts |language=en-us}}</ref> noted independently that the assumption of an infinite space filled uniformly with stars would lead to the prediction that the nighttime sky would be as bright as the Sun itself; this became known as [[Olbers' paradox]] in the 19th century.<ref>{{cite journal |author=Olbers HWM |author-link=Heinrich Wilhelm Matthäus Olbers |date=1826 |title=Unknown title |journal=Bode's Jahrbuch |volume=111}}. Reprinted as Appendix I in {{cite book |author=Dickson |first=F. P. |title=The Bowl of Night: The Physical Universe and Scientific Thought |date=1969 |publisher=M.I.T. Press |isbn=978-0-262-54003-2 |location=Cambridge, Massachusetts |language=en-us}}</ref> Newton believed that an infinite space uniformly filled with matter would cause infinite forces and instabilities causing the matter to be crushed inwards under its own gravity.<ref name="Misner-p755" /> This instability was clarified in 1902 by the [[Jeans instability]] criterion.<ref>{{cite journal|last1=Jeans |first1=J. H. |date=1902 |title=The Stability of a Spherical Nebula |journal=[[Philosophical Transactions of the Royal Society A]] |volume=199 |pages=1–53 |issue=312–320 |doi=10.1098/rsta.1902.0012 |bibcode=1902RSPTA.199....1J |jstor=90845 |doi-access= }}</ref> One solution to these paradoxes is the [[Carl Charlier|Charlier]] universe, in which the matter is arranged hierarchically (systems of orbiting bodies that are themselves orbiting in a larger system, ''ad infinitum'') in a [[fractal]] way such that the universe has a negligibly small overall density; such a cosmological model had also been proposed earlier in 1761 by [[Johann Heinrich Lambert]].<ref name=r196 /><ref>[[#Misner|Misner, Thorne and Wheeler]], p. 757.</ref>
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