Editing Concentric spheres

{{Short description|Ancient Greek geocentric cosmological model}}
The [[cosmological model]] of '''concentric''' (or '''homocentric''') '''spheres''', developed by [[Eudoxus of Cnidus|Eudoxus]], [[Callippus]], and [[Aristotle]], employed [[celestial spheres]] all [[geocentric model|centered on the Earth]].<ref>{{cite book |last=Neugebauer |first=Otto |author-link=Otto Neugebauer |title=A History of Ancient Mathematical Astronomy |location=Berlin / Heidelberg / New York |publisher=[[Springer-Verlag]] |year=1975 |volume=2 |pages=677–85 |isbn=0-387-06995-X}}</ref><ref>{{cite book |last=Lloyd |first=G. E. R. |author-link=G. E. R. Lloyd |title=Aristotelian Explorations |location=Cambridge |publisher=[[Cambridge University Press]] |orig-year=1996 |year=1999 |chapter=Heavenly aberrations: Aristotle the amateur astronomer |pages=167–68 |isbn=0-521-55619-8}}</ref> In this respect, it differed from the [[epicycle|epicyclic]] and eccentric models with multiple centers, which were used by [[Ptolemy]] and other mathematical [[astronomer]]s until the time of [[Copernicus]].

==Origins of the concept of concentric spheres==
[[File:Animated Hippopede of Eudoxus.gif|thumb|Animation depicting Eudoxus' model of retrograde planetary motion. The two innermost homocentric spheres of his model are represented as rings here, each turning with the same period but in opposite directions, moving the planet along a figure-eight, or hippopede]]
[[Eudoxus of Cnidus]] was the first astronomer to develop the concept of concentric spheres. He was originally a student at Plato's academy and is believed to have been influenced by the cosmological speculations of [[Plato]] and [[Pythagoras]].<ref>{{cite journal|last1=Goldstein|first1=Bernard|title=A New View of Early Greek Astronomy|journal=Isis|date=September 3, 1983|volume=74|issue=3|pages=332–333|jstor=232593|doi=10.1086/353302 |s2cid=144808083}}</ref><ref name=Gale>"Eudoxus of Cnidus." Complete Dictionary of Scientific Biography. Vol. 4. Detroit: Charles Scribner's Sons, 2008. 465–467. Gale Virtual Reference Library. Web. 2 June 2014.</ref> He came up with the idea of homocentric spheres in order to explain the perceived inconsistent motions of the planets and to develop a uniform model for accurately calculating the movement of celestial objects.<ref name=Gale/> None of his books have survived to the modern day and everything we know about his cosmological theories comes from the works of [[Aristotle]] and [[Simplicius of Cilicia|Simplicius]]. According to these works, Eudoxus’ model had twenty-seven homocentric spheres with each sphere explaining a type of observable motion for each celestial object. Eudoxus assigns one sphere for the fixed stars which is supposed to explain their daily movement. He assigns three spheres to both the sun and the moon with the first sphere moving in the same manner as the sphere of the fixed stars. The second sphere explains the movement of the sun and the moon on the ecliptic plane. The third sphere was supposed to move on a “latitudinally inclined” circle and explain the latitudinal motion of the sun and the moon in the cosmos. Four spheres were assigned to [[Mercury (planet)|Mercury]], [[Venus (planet)|Venus]], [[Mars]], [[Jupiter (planet)|Jupiter]], and [[Saturn (planet)|Saturn]] which were the only known planets at that time. The first and second spheres of the planets moved exactly like the first two spheres of the sun and the moon. According to Simplicius, the third and fourth sphere of the planets were supposed to move in a way that created a curve known as a [[hippopede]]. The [[hippopede]] was a way to try and explain the [[Apparent retrograde motion|retrograde motions]] of planets.<ref>{{cite journal|last1=Yavetz|first1=Ido|title=On the Homocentric Spheres of Eudoxus|journal=Archive for History of Exact Sciences|date=February 1998|volume=52|issue=3|pages=222–225|jstor=41134047|bibcode = 1998AHES...52..222Y|doi=10.1007/s004070050017|s2cid=121186044}}</ref> Many historians of science, such as Michael J. Crowe, have argued that Eudoxus did not consider his system of concentric spheres to be a real representation of the universe but thought it was merely a mathematical model for calculating planetary motion.<ref>{{cite book|last1=Crowe|first1=Michael|title=Theories of the World from Antiquity to the Copernican Revolution|date=2001|publisher=Dover|location=Mineola, NY|isbn=0-486-41444-2|page=23}}</ref>

==Later additions to Eudoxus' model==
[[File:Eudoxus of Cnidus homocentric spheres model.png|thumb|Schematic model likely representing the first 4, out of a total of 27, spheres of Eudoxus' cosmic model following Giovanni Schiaparell. Each sphere has its own rotational axis that, together, generates a complex motion for the planet, in this illustration, the moon.]]
[[Callippus]], a contemporary of Eudoxus, attempted to improve his system by increasing the total number of homocentric spheres. He added two additional spheres for the sun and the moon as well as one additional sphere for Mars, Mercury, and Venus. These additional spheres were supposed to fix some of the calculation problems in Eudoxus’ original system. Callippus’ system was able to better predict the motions of certain celestial objects but his system still had many problems and was not able to account for many astronomical observations.<ref>{{cite book|last1=Dicks|first1=D.R.|title=Early Greek Astronomy to Aristotle|date=1985|publisher=[[Cornell University Press]]|location=Ithaca, NY|isbn=0801493102|pages=190–191}}</ref>

[[Aristotle]] developed his own system of concentric spheres in ''[[Metaphysics (Aristotle)|Metaphysics]]'' and [[On the Heavens|''De Caelo'' (On the Heavens)]]. He thought that both Eudoxus and Callippus had too few spheres within their models and added more spheres onto Callippus’ system. He added three spheres to Jupiter and Mars as well as four spheres to Venus, Mercury, the sun, and the moon for a total of fifty-five spheres. He later doubted the accuracy of his results and stated that he believed there were either forty seven or forty nine concentric spheres. Historians are unsure about how many spheres Aristotle thought there were in the cosmos with theories ranging from 43 to 55. Unlike Eudoxus, Aristotle believed that his system represented an actual model of the cosmos.<ref>{{cite journal|last1=Easterling|first1=H|title=Homocentric Spheres in De Caelo|journal=Phronesis|date=1961|volume=6|issue=2|pages=138–141|jstor=4181694|doi=10.1163/156852861x00161}}</ref>

==See also==

* [[Celestial spheres]]
* [[Geocentric model]]
* [[Historical models of the Solar System]]

==Notes==
{{reflist}}

==Further reading==
* {{cite book |last1=Lloyd |first1=G.E.R. |title=Early Greek Science: Thales to Aristotle |date=1974 |publisher=W. W. Norton and Company |location=London |isbn=0393005836 |url-access=registration |url=https://archive.org/details/earlygreekscienc00gerl }}
* {{cite book |last1=Neugebauer |first1=Otto |title=Astronomy and History Selected Essays |date=1983 |publisher=Springer |isbn=0387908447}}
* Kieffer, John S. "Callippus." ''Dictionary of Scientific Biography'' 3:21-22.

==External links==
* [https://www.youtube.com/watch?v=_SFzDYSqR_4 Working model and complete explanation of the Eudoxus's Spheres]
* [https://web.archive.org/web/20110516145329/http://www.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/Eudoxus/Astronomy/EudoxusHomocentricSpheres.htm Eudoxos of Knidos (Eudoxus of Cnidus): astronomy and homocentric spheres] Henry Mendell, Cal State U, LA
* [https://archive.today/20121212204138/http://faculty.fullerton.edu/cmcconnell/Planets.html%233 Models of Planetary Motion—Eudoxus], Craig McConnell, Ph.D., Cal State, Fullerton
* [http://classics.mit.edu/Aristotle/heavens.1.i.html Aristotle's ''On the Heavens'']
* [http://classics.mit.edu/Aristotle/metaphysics.html Aristotle's ''metaphysics'']

[[Category:Ancient Greek astronomy]]
[[Category:Early scientific cosmologies]]