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.[3][4] 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.[4] 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. 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, Venus, Mars, Jupiter, and 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 retrograde motions of planets.[5] 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.[6]
Later additions to Eudoxus' modeledit
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.[7]
Aristotle developed his own system of concentric spheres in Metaphysics and 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.[8]
^Goldstein, Bernard (September 3, 1983). "A New View of Early Greek Astronomy". Isis. 74 (3): 332–333. doi:10.1086/353302. JSTOR 232593. S2CID 144808083.
^ ab"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.
^Yavetz, Ido (February 1998). "On the Homocentric Spheres of Eudoxus". Archive for History of Exact Sciences. 52 (3): 222–225. Bibcode:1998AHES...52..222Y. doi:10.1007/s004070050017. JSTOR 41134047. S2CID 121186044.
^Crowe, Michael (2001). Theories of the World from Antiquity to the Copernican Revolution. Mineola, NY: Dover. p. 23. ISBN0-486-41444-2.
^Easterling, H (1961). "Homocentric Spheres in De Caelo". Phronesis. 6 (2): 138–141. doi:10.1163/156852861x00161. JSTOR 4181694.
Further readingedit
Lloyd, G.E.R. (1974). Early Greek Science: Thales to Aristotle. London: W. W. Norton and Company. ISBN0393005836.
Neugebauer, Otto (1983). Astronomy and History Selected Essays. Springer. ISBN0387908447.
Kieffer, John S. "Callippus." Dictionary of Scientific Biography 3:21-22.
External linksedit
Working model and complete explanation of the Eudoxus's Spheres
Henry Mendell, Cal State U, LA
Models of Planetary Motion—Eudoxus, Craig McConnell, Ph.D., Cal State, Fullerton
Aristotle's On the Heavens
Aristotle's metaphysics
April 10, 2024
concentric, spheres, cosmological, model, concentric, homocentric, spheres, developed, eudoxus, callippus, aristotle, employed, celestial, spheres, centered, earth, this, respect, differed, from, epicyclic, eccentric, models, with, multiple, centers, which, we. The cosmological model of concentric or homocentric spheres developed by Eudoxus Callippus and Aristotle employed celestial spheres all centered on the Earth 1 2 In this respect it differed from the epicyclic and eccentric models with multiple centers which were used by Ptolemy and other mathematical astronomers until the time of Copernicus Contents 1 Origins of the concept of concentric spheres 2 Later additions to Eudoxus model 3 See also 4 Notes 5 Further reading 6 External linksOrigins of the concept of concentric spheres edit nbsp 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 hippopedeEudoxus 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 3 4 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 4 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 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 Venus Mars Jupiter and 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 retrograde motions of planets 5 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 6 Later additions to Eudoxus model editCallippus 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 7 Aristotle developed his own system of concentric spheres in Metaphysics and 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 8 See also editCelestial spheres Geocentric model Historical models of the Solar SystemNotes edit Neugebauer Otto 1975 A History of Ancient Mathematical Astronomy Vol 2 Berlin Heidelberg New York Springer Verlag pp 677 85 ISBN 0 387 06995 X Lloyd G E R 1999 1996 Heavenly aberrations Aristotle the amateur astronomer Aristotelian Explorations Cambridge Cambridge University Press pp 167 68 ISBN 0 521 55619 8 Goldstein Bernard September 3 1983 A New View of Early Greek Astronomy Isis 74 3 332 333 doi 10 1086 353302 JSTOR 232593 S2CID 144808083 a b 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 Yavetz Ido February 1998 On the Homocentric Spheres of Eudoxus Archive for History of Exact Sciences 52 3 222 225 Bibcode 1998AHES 52 222Y doi 10 1007 s004070050017 JSTOR 41134047 S2CID 121186044 Crowe Michael 2001 Theories of the World from Antiquity to the Copernican Revolution Mineola NY Dover p 23 ISBN 0 486 41444 2 Dicks D R 1985 Early Greek Astronomy to Aristotle Ithaca NY Cornell University Press pp 190 191 ISBN 0801493102 Easterling H 1961 Homocentric Spheres in De Caelo Phronesis 6 2 138 141 doi 10 1163 156852861x00161 JSTOR 4181694 Further reading editLloyd G E R 1974 Early Greek Science Thales to Aristotle London W W Norton and Company ISBN 0393005836 Neugebauer Otto 1983 Astronomy and History Selected Essays Springer ISBN 0387908447 Kieffer John S Callippus Dictionary of Scientific Biography 3 21 22 External links editWorking model and complete explanation of the Eudoxus s Spheres Eudoxos of Knidos Eudoxus of Cnidus astronomy and homocentric spheres Henry Mendell Cal State U LA Models of Planetary Motion Eudoxus Craig McConnell Ph D Cal State Fullerton Aristotle s On the Heavens Aristotle s metaphysics Retrieved from https en wikipedia org w index php title Concentric spheres amp oldid 1127081189, wikipedia, wiki, book, books, library,
