Editing Celestial spheres (section)

===Emergence of the planetary spheres===

Instead of bands, Plato's student Eudoxus developed a [[Eudoxus of Cnidus#Eudoxan planetary models|planetary model]] using [[concentric spheres]] for all the planets, with three spheres each for his models of the Moon and the Sun and four each for the models of the other five planets, thus making 26 spheres in all.<ref>Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.</ref><ref name="Lloyd p. 173">Lloyd, "Heavenly aberrations," p. 173.</ref> [[Callippus]] modified this system, using five spheres for his models of the Sun, Moon, Mercury, Venus, and Mars and retaining four spheres for the models of Jupiter and Saturn, thus making 33 spheres in all.<ref name="Lloyd p. 173"/> Each planet is attached to the innermost of its own particular set of spheres. Although the models of Eudoxus and Callippus qualitatively describe the major features of the motion of the planets, they fail to account exactly for these motions and therefore cannot provide quantitative predictions.<ref>Neugebauer, ''History of Ancient Mathematical Astronomy,'' vol. 2, pp. 677–85.</ref> Although historians of Greek science have traditionally considered these models to be merely geometrical representations,<ref>Dreyer, ''History of the Planetary Systems'', pp. 90–1, 121–2</ref><ref>Lloyd, ''Aristotle'', p. 150.</ref> recent studies have proposed that they were also intended to be physically real<ref>Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics," ''Studies in History and Philosophy of Science'', 4 (1973): 165–72.</ref> or have withheld judgment, noting the limited evidence to resolve the question.<ref>G. E. R. Lloyd, "Saving the Phenomena," ''Classical Quarterly,'' 28 (1978): 202–222, at p. 219.</ref>

In his ''[[Metaphysics (Aristotle)|Metaphysics]]'', [[Aristotle]] developed a physical cosmology of spheres, based on the mathematical models of Eudoxus. In Aristotle's fully developed celestial model, the spherical Earth is at the centre of the universe and the planets are moved by either 47 or 55 interconnected spheres that form a unified planetary system,<ref>Aristotle, ''Metaphysics'' 1073b1–1074a13, pp. 882–883 in ''The Basic Works of Aristotle'' Richard McKeon, ed., The Modern Library 2001</ref> whereas in the models of Eudoxus and Callippus each planet's individual set of spheres were not connected to those of the next planet. Aristotle says the exact number of spheres, and hence the number of movers, is to be determined by astronomical investigation, but he added additional spheres to those proposed by Eudoxus and Callippus, to counteract the motion of the outer spheres. Aristotle considers that these spheres are made of an unchanging fifth element, the [[Aether (classical element)|aether]]. Each of these concentric spheres is moved by its own god—an unchanging [[Unmoved mover|divine unmoved mover]], and who moves its sphere simply by virtue of being loved by it.<ref>"The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle ''Metaphysics'' 1072b4.</ref>

[[Image:PeuerbachSuperioribus2.png|thumb|Ptolemaic model of the spheres for Venus, Mars, Jupiter, and Saturn with [[epicycle]], eccentric [[deferent]] and [[equant]] point. [[Georg von Peuerbach]], ''Theoricae novae planetarum'', 1474.]]

In his ''[[Almagest]]'', the astronomer [[Ptolemy]] (fl. c. 150 AD) developed geometrical predictive models of the motions of the stars and planets and extended them to a unified physical model of the [[cosmos]] in his ''Planetary hypotheses''.<ref>Neugebauer, ''History of Ancient Mathematical Astronomy,''  pp. 111–12, 148</ref><ref>Pedersen, ''[[#Pederson-1993|Early Physics and Astronomy]]'' [https://books.google.com/books?id=z7M8AAAAIAAJ&pg=PA87 p. 87]</ref><ref>Crowe, ''[[#Reference-Crowe-1990|Theories of the World]]'', pp.45, 49–50, 72,</ref><ref>Linton, ''[[#Reference-Linton-2004|From Eudoxus to Einstein]]'', pp.63–64, 81.</ref> By using [[Eccentric (mechanism)|eccentrics]] and [[epicycles]], his geometrical model achieved greater mathematical detail and predictive accuracy than had been exhibited by earlier concentric spherical models of the cosmos.<ref>[[R. Catesby Taliaferro|Taliaferro]], ''[[#taliaferro-1946|Translator's Introduction to the Almagest]]'', p,1; Dreyer, ''[[#dreyer-2007|History of the Planetary Systems]]'', [https://archive.org/stream/historyofplaneta00dreyuoft#page/160/mode/1up/ pp.160], [https://archive.org/stream/historyofplaneta00dreyuoft#page/167/mode/1up/ 167].</ref> In Ptolemy's physical model, each planet is contained in two or more spheres,<ref name="Neugebauer, pp. 917">Neugebauer, ''History of Ancient Mathematical Astronomy'', vol. 2, pp. 917–926.</ref> but in Book 2 of his ''Planetary Hypotheses'' Ptolemy depicted thick circular slices rather than spheres as in its Book 1. One sphere/slice is the [[deferent]], with a centre offset somewhat from the Earth; the other sphere/slice is an [[epicycle]] embedded in the deferent, with the planet embedded in the epicyclical sphere/slice.<ref>Andrea Murschel, [http://adsabs.harvard.edu/abs/1995JHA....26...33M "The Structure and Function of Ptolemy's Physical Hypotheses of Planetary Motion,"] ''Journal for the History of Astronomy,'' 26(1995): 33–61.</ref> Ptolemy's model of nesting spheres provided the general dimensions of the cosmos, the greatest distance of Saturn being 19,865 times the radius of the Earth and the distance of the fixed stars being at least 20,000 Earth radii.<ref name="Neugebauer, pp. 917"/>

The planetary spheres were arranged outwards from the spherical, stationary Earth at the centre of the universe in this order: the spheres of the [[Moon]], [[Mercury (planet)|Mercury]], [[Venus]], [[Sun]], [[Mars]], [[Jupiter]], and [[Saturn]]. In more detailed models the seven planetary spheres contained other secondary spheres within them. The planetary spheres were followed by the stellar sphere containing the fixed stars; other scholars added a ninth sphere to account for the [[Axial precession (astronomy)|precession of the equinoxes]], a tenth to account for the supposed [[Trepidation (astronomy)|trepidation of the equinoxes]], and even an eleventh to account for the changing [[obliquity of the ecliptic]].<ref>Francis R. Johnson, "Marlowe's "Imperiall Heaven," ''ELH'', 12 (1945): 35–44, p. 39</ref> In antiquity the order of the lower planets was not universally agreed. Plato and his followers ordered them Moon, Sun, Mercury, Venus, and then followed the standard model for the upper spheres.<ref>Bruce S. Eastwood, ''Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance,'' (Leiden: Brill) 2007, pp. 36–45</ref><ref>In his ''De Revolutionibus'' Bk1.10 Copernicus claimed the empirical reason why Plato's followers put the orbits of Mercury and Venus above the Sun's was that if they were sub-solar, then by the Sun's reflected light they would only ever appear as hemispheres at most and would also sometimes eclipse the Sun, but they do neither. (See p521 ''Great Books of the Western World 16 Ptolemy–Copernicus–Kepler'')</ref> Others disagreed about the relative place of the spheres of Mercury and Venus: Ptolemy placed both of them beneath the Sun with Venus above Mercury, but noted others placed them both above the Sun; some medieval thinkers, such as [[al-Bitruji]], placed the sphere of Venus above the Sun and that of Mercury below it.<ref>al-Biţrūjī. (1971) ''On the Principles of Astronomy'', 7.159–65, trans. Bernard R. Goldstein, vol. 1, pp. 123–5.  New Haven: Yale Univ. Pr.  {{ISBN|0-300-01387-6}}</ref>