Celestial spheres

Not to be confused with celestial sphere. For other uses, see Celestial (disambiguation).

Geocentric celestial spheres; Peter Apian's Cosmographia (Antwerp, 1539)

Thomas Digges' 1576 Copernican heliocentric model of the celestial orbs

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others. In these celestial models the stars and planets are carried around by being embedded in rotating spheres made of an aetherial transparent fifth element (quintessence), like jewels set in orbs.

In the geocentric model adopted in the Middle Ages, the planetary spheres (i.e. those that contained planets) were arranged outwards from the spherical, stationary Earth at the centre of the universe in this order: the spheres of the Moon, 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 precession of the equinoxes, a tenth to account for the supposed trepidation of the equinoxes, and even an eleventh to account for the changing obliquity of the ecliptic.^[1] 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.^[2][3] 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, such as al-Bitruji, placed the sphere of Venus above the Sun and that of Mercury below it.^[4]

In modern science, the orbits of the planets are simply the paths of those planets through mostly empty space. For medieval scholars, on the other hand, celestial spheres were actually thick spheres of rarefied matter nested one within the other, each one in complete contact with the sphere above it and the sphere below.^[5] When scholars applied Ptolemy's epicycles, they presumed that each planetary sphere was exactly thick enough to accommodate them.^[5] Combining this information with astronomical observations allowed scholars to calculate that the distance to the far edge of Saturn (or to the inside of the stellar sphere) was 73,387,747 miles.^[6]

In the heliocentric celestial orbs model introduced by Copernicus, the ascending order of the planets and their spheres going outwards from the Sun at the centre was Mercury, Venus, Earth-Moon, Mars, Jupiter and Saturn.

History

Antiquity

In Greek antiquity the ideas of celestial spheres and rings first appeared in the cosmology of Anaximander in the early 6th century BC.^[7] In his cosmology both the Sun and Moon are circular open vents in tubular rings of fire enclosed in tubes of condensed air that constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre, shaped rather like the space station in the film 2001. The fixed stars are also open vents in such wheel rims, but there are so many such wheels for the stars that their contiguous rims altogether form a continuous spherical shell encompassing the Earth. But according to Anaximander's cosmogony, all these wheel rims had originally been formed out of an original sphere of fire wholly encompassing the Earth that had disintegrated into many individual rings.^[8] Hence in Anaximanders's cosmogony, in the beginning was the sphere, out of which celestial rings were formed, and from which the stellar sphere was then composed from some of those rings. The order of the distances of the wheel rims of the Sun, Moon and stars was: Sun highest, Moon next and then the sphere of the stars the lowest.

Following Anaximander, his pupil Anaximenes (c. 585–528/4) held that the stars, sun, moon and the planets are all made of fire. But whilst the stars are fastened on a revolving crystal sphere like nails or studs, the sun, moon and planets, and also the Earth, all just ride on air like leaves because of their breadth.^[9] And whilst the fixed stars are carried around in a complete circle by the stellar sphere, the sun, moon and planets do not revolve under the Earth between setting and rising again like the stars do, but rather on setting they go laterally around the Earth like a cap turning halfway around the head until they rise again. Anaximenes may have been the first to distinguish the planets from the fixed stars in respect of their irregular movements. And unlike Anaximander, he relegated the fixed stars to the region most distant from the Earth. The most enduring feature of Anaximenes' cosmos was its conception of the stars being fixed on a crystal sphere as in a rigid frame, which became a fundamental principle of cosmology down to Copernicus and Kepler.

After Anaximenes, Pythagoras, Xenophanes and Parmenides all held that the universe was spherical.^[10] And much later in the fourth century BC Plato's Timaeus proposed that the body of the cosmos was made in the most perfect and uniform shape, that of a sphere containing the fixed stars.^[11] But it posited that the planets were spherical bodies set in rotating bands or rings rather than wheel rims as in Anaximander's cosmology. However instead of bands Plato's student Eudoxus then developed a 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 27 spheres in all ' ^[12][13]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.^[13][14] Each planet is attached to the innermost of its own particular set of spheres. Although historians of Greek science have traditionally considered Eudoxus's model to be purely mathematical,^[15][16] recent studies have proposed that it was also intended to be physically real^[17] or have withheld judgment, noting the limited evidence to resolve the question.^[18]

In his 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 which form a unified planetary system,^[19] 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 of the number of movers, is to be determined by astronomical investigation, but he added additional spheres to those proposed 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. Each of these concentric spheres is moved by its own god — an unchanging divine unmoved mover, and who moves its sphere simply by virtue of being loved by it.^[20]

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.

The astronomer Ptolemy (fl. ca. 150 AD) defined geometrical predictive models of the motions of the stars and planets in his Almagest and extended them to a unified physical model of the cosmos in his Planetary hypotheses.^{[21][22][23][24]} By using 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.^[25] In the Ptolemaic model, each planet is contained in two or more spheres,^{[citation needed]} 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.^[26] Through the use of the epicycle, eccentric, and equant, this model of compound circular motions could account for all the irregularities of a planet's apparent movements in the sky.^[27]

Middle Ages

Christian and Muslim philosophers modified Ptolemy's system to include an unmoved outermost region, the empyrean heaven, which came to be identified as the dwelling place of God and all the elect.^[28] The outermost moving sphere, which moved with the daily motion affecting all subordinate spheres, was moved by an unmoved mover, the Prime Mover, who was identified with God. Each of the lower spheres was moved by a subordinate spiritual mover (a replacement for Aristotle's multiple divine movers), called an intelligence.^[29]

Medieval Christians identified the sphere of stars with the Biblical firmament and sometimes posited an invisible layer of water above the firmament, to accord with Genesis.^[30] An outer sphere, inhabited by angels, appeared in some accounts.^[31]

Around the turn of the millennium, the Arabic astronomer and polymath Ibn al-Haytham (Alhacen) presented a development of Ptolemy's geocentric epicyclic models in terms of nested spheres. Despite the similarity of this concept to that of Ptolemy's Planetary Hypotheses, al-Haytham's presentation differs in sufficient detail that it has been argued that it reflects an independent development of the concept.^[32] In chapters 15–16 of his Book of Optics, Ibn al-Haytham also said that the celestial spheres do not consist of solid matter.^[33]

Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi in regard to whether the celestial spheres are real, concrete physical bodies or "merely the abstract circles in the heavens traced out… by the various stars and planets." Setia points out that most of the learned, and the astronomers, said they were solid spheres "on which the stars turn… and this view is closer to the apparent sense of the Qur'anic verses regarding the celestial orbits." However, al-Razi mentions that some, such as the Islamic scholar Dahhak, considered them to be abstract. Al-Razi himself, was undecided, he said: "In truth, there is no way to ascertain the characteristics of the heavens except by authority [of divine revelation or prophetic traditions]." Setia concludes: "Thus it seems that for al-Razi (and for others before and after him), astronomical models, whatever their utility or lack thereof for ordering the heavens, are not founded on sound rational proofs, and so no intellectual commitment can be made to them insofar as description and explanation of celestial realities are concerned."^[34]

Near the end of the twelfth century, the Spanish-Arabian Muslim astronomer al-Bitrūjī (Alpetragius) sought to explain the complex motions of the planets using purely concentric spheres, which moved with differing speeds from east to west. This model was an attempt to restore the concentric spheres of Aristotle without Ptolemy's epicycles and eccentrics, but it was much less accurate as a predictive astronomical model.^[35][36]

In the thirteenth century, scholars in European universities dealt with the implications of the rediscovered philosophy of Aristotle and astronomy of Ptolemy. One issue that arose concerned the nature of the celestial spheres. Through an extensive examination of a wide range of scholastic texts, Edward Grant has demonstrated that scholastic philosophers generally considered the celestial spheres to be solid in the sense of three-dimensional or continuous, but most did not consider them solid in the sense of hard. The consensus was that the celestial spheres were made of some kind of continuous fluid.^[37]

Later in the century, the Islamic theologian Adud al-Din al-Iji (1281–1355), under the influence of the Ash'ari doctrine of occasionalism, which maintained that all physical effects were caused directly by God's will rather than by natural causes, rejected philosophy and astronomy,^[38] and maintained that the celestial spheres were "imaginary things" and "more tenuous than a spider's web".^[39] Al-Iji's rejection of astronomy was, in turn, challenged by al-Sharif al-Jurjani (1339–1413), who maintained that "even if they do not have an external reality, yet they are things that are correctly imagined and correspond to what [exists] in actuality".^[39]

Dynamics

Main article: Dynamics of the celestial spheres

Ancient, medieval and Renaissance astronomers and philosophers developed diverse theories about the dynamics of the celestial spheres. They attempted to explain the spheres' motions in terms of the materials of which they were thought to be made, external movers such as celestial intelligences, and internal movers such as motive souls or impressed forces. Most of these models were qualitative, although a few incorporated quantitative analyses that related speed, motive force and resistance.^[40] By the end of the Middle Ages, the common opinion in Europe was that celestial bodies were moved by external intelligences, identified with the angels of revelation.^[41]

Renaissance

Kepler's diagram of the celestial spheres, and of the spaces between them, following the opinion of Copernicus (Mysterium Cosmographicum, 2nd ed., 1621)

Early in the sixteenth century Nicolaus Copernicus drastically reformed the model of astronomy by displacing the Earth from its central place in favour of the sun, yet he called his great work De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres). Although Copernicus does not treat the physical nature of the spheres in detail, his few allusions make it clear that, like many of his predecessors, he accepted non-solid celestial spheres.^[42] Copernicus rejected the ninth and tenth spheres, placed the orb of the Moon around the Earth and moved the Sun from its orb to the center of the world. The planetary orbs circled the center of the world in the order Mercury, Venus, the great orb containing the Earth and the orb of the Moon, then the orbs of Mars, Jupiter, and Saturn. Finally he retained the eighth starry sphere, which he held to be unmoving.^[43]

In the course of the sixteenth century, a number of philosophers, theologians, and astronomers, among them Francesco Patrizi, Andrea Cisalpino, Peter Ramus, Robert Bellarmine, Giordano Bruno, Jerónimo Muñoz, Michael Neander, Jean Pena, and Christoph Rothmann, abandoned the concept of celestial spheres.^[44] Rothmann argued from the observations of the comet of 1585 that the lack of observed parallax indicated that the Comet was beyond Saturn, while the absence of observed refraction indicated the celestial region was of the same material as air, hence there were no planetary spheres.^[45]

Tycho Brahe's investigations of a series of comets from 1577 to 1585, aided by Rothmann's discussion of the comet of 1585 and Michael Maestlin's tabulated distances of the comet of 1577, which passed through the planetary orbs, led Tycho to conclude^[46] that "the structure of the heavens was very fluid and simple." Tycho opposed his view to that of "very many modern philosophers" who divided the heavens into "various orbs made of hard and impervious matter." Since Grant has been unable to identify such a large number of believers in hard celestial spheres before Copernicus, he concludes that the idea first became dominant sometime after the publication of Copernicus's De revolutionibus in 1542 and either before, or possibly somewhat after, Tycho Brahe's publication of his cometary observations in 1588.^[47][48]

In Johannes Kepler's mature celestial physics, the spheres were regarded as the purely geometrical spatial regions containing each planetary orbit rather than as the rotating physical orbs of the earlier Aristotelian celestial physics. The eccentricity of each planet's orbit thereby defined the lengths of the radii of the inner and outer limits of its celestial sphere and thus its thickness. The role of these geometrical spherical shells in Kepler's Platonist geometrical cosmology is to determine the sizes and orderings of the five Platonic polyhedra within which the spheres were supposedly spatially embedded.^[49] In Kepler's celestial mechanics the cause of planetary motion became the rotating sun, itself rotated by its own motive soul.^[50] However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler's cosmology.

Literary and symbolic expressions

"Because the medieval universe is finite, it has a shape, the perfect spherical shape, containing within itself an ordered variety....
"The spheres ... present us with an object in which the mind can rest, overwhelming in its greatness but satisfying in its harmony."

C. S. Lewis, The Discarded Image, p. 99

Dante and Beatrice gaze upon the highest Heaven; from Gustave Doré's illustrations to the Divine Comedy, Paradiso Canto 28, lines 16–39

In Cicero's Dream of Scipio, the elder Scipio Africanus describes an ascent through the celestial spheres, compared to which the Earth and the Roman Empire dwindle into insignificance. A commentary on the Dream of Scipio by the late Roman writer Macrobius, which included a discussion of the various schools of thought on the order of the spheres, did much to spread the idea of the celestial spheres through the Early Middle Ages.^[51]

Nicole Oresme, Le livre du Ciel et du Monde, Paris, BnF, Manuscrits, Fr. 565, f. 69, (1377)

Some late medieval figures inverted the model of the celestial spheres to place God at the center and the Earth at the periphery. Near the beginning of the fourteenth century Dante, in the Paradiso of his Divine Comedy, described God as a light at the center of the cosmos.^[52] Here the poet ascends beyond physical existence to the Empyrean Heaven, where he comes face to face with God himself and is granted understanding of both divine and human nature.

Later in the century, the illuminator of Nicole Oresme's Le livre du Ciel et du Monde, a translation of and commentary on Aristotle's De caelo produced for Oresme's patron, King Charles V, employed the same motif. He drew the spheres in the conventional order, with the Moon closest to the Earth and the stars highest, but the spheres were concave upwards, centered on God, rather than concave downwards, centered on the Earth.^[53] Below this figure Oresme quotes the Psalms that "The heavens declare the Glory of God and the firmament showeth his handiwork."^[54]

See also

• Firmament
• Geocentric model
• Musica universalis
• Primum Mobile

Notes

1. ^ Francis R. Johnson, "Marlowe's "Imperiall Heaven," ELH, 12 (1945): 35–44, p. 39
2. ^ Bruce S. Eastwood, Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, (Leiden: Brill) 2007, pp. 36–45
3. ^ 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)
4. ^ 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
5. ^ ^{a b} Lindberg, Beginnings of Western Science, p. 251.
6. ^ Lindberg, Beginnings of Western Science, p. 252.
7. ^ See chapter 4 of Heath's Aristarchus of Samos 1913/97 Oxford University Press/Sandpiper Books Ltd; see p.11 of Popper's The World of Parmenides Routledge 1998
8. ^ Heath ibid pp26–8
9. ^ See chapter 5 of Heath’s 1913 Aristarchus of Samos
10. ^ For Xenophanes' and Parmenides' spherist cosmologies see Heath ibid chapter 7 and chapter 9 respectively, and Popper ibid Essays 2 & 3.
11. ^ F. M. Cornford, Plato's Cosmology: The Timaeus of Plato, pp. 54–7
12. ^ Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.
13. ^ ^{a b} Lloyd, "Heavenly aberrations," p. 173.
14. ^ Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.
15. ^ Dreyer, History of the Planetary Systems, pp. 90–1, 121–2
16. ^ Lloyd, Aristotle, p. 150.
17. ^ Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics," Studies in History and Philosophy of Science, 4 (1973): 165–72.
18. ^ G. E. R. Lloyd, "Saving the Phenomena," Classical Quarterly, 28 (1978): 202–222, at p. 219.
19. ^ Aristotle, Metaphysics 1073b1–1074a13, pp. 882–883 in The Basic Works of Aristotle Richard McKeon, ed., The Modern Library 2001
20. ^ "The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle Metaphysics 1072b4.
21. ^ Neugebauer, History of Ancient Mathematical Astronomy, pp. 111–12, 148
22. ^ Pedersen, Early Physics and Astronomy p. 87
23. ^ Crowe, Theories of the World, pp.45, 49–50, 72,
24. ^ Linton, From Eudoxus to Einstein, pp.63–64, 81.
25. ^ Taliaferro, Translator's Introduction to the Almagest, p,1; Dreyer, History of the Planetary Systems, pp.160, 167.
26. ^ Andrea Murschel, "The Structure and Function of Ptolemy's Physical Hypotheses of Planetary Motion," Journal for the History of Astronomy, 26(1995): 33–61.
27. ^ Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 917–926.
28. ^ Grant, Planets, Stars, and Orbs, pp. 382–3.
29. ^ Grant, Planets, Stars, and Orbs, pp. 526–45.
30. ^ Lindberg, Beginnings of Western Science, pp. 249–50.
31. ^ Lindberg, Beginnings of Western Science, p. 250.
32. ^ Y. Tzvi Langermann (1990), Ibn al Haytham's On the Configuration of the World, p. 11–25, New York: Garland Publishing.
33. ^ Edward Rosen (1985), "The Dissolution of the Solid Celestial Spheres", Journal of the History of Ideas 46 (1), p. 13–31 [19–20, 21].
34. ^ Adi Setia (2004), "Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey", Islam & Science 2, http://findarticles.com/p/articles/mi_m0QYQ/is_2_2/ai_n9532826/, retrieved 2010-03-02 
35. ^ Bernard R. Goldstein, Al-Bitrūjī: On the Principles of Astronomy, New Haven: Yale Univ. Pr., 1971, vol. 1, pp. 6, 44–5
36. ^ Grant, Planets, Stars, and Orbs, pp. 563–4.
37. ^ Grant, Planets, Stars, and Orbs, pp. 328–30.
38. ^ Huff, Toby (2003), The Rise of Early Modern Science: Islam, China, and the West, Cambridge University Press, p. 175, ISBN 0521529948 
39. ^ ^{a b} pp. 55–57 of Ragep, F. Jamil (2001). "Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science". Osiris. 2nd Series 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–71. Bibcode 2001Osir...16...49R. doi:10.1086/649338. ISSN 0369-7827. JSTOR 301979. 
40. ^ Grant, Planets, Stars, and Orbs, p. 541.
41. ^ Grant, Planets, Stars, and Orbs, p. 527.
42. ^ Nicholas Jardine, "The Significance of the Copernican Orbs," Journal for the History of Astronomy, 13(1982): 168–194, esp. pp. 177–8.
43. ^ Hilderich von Varel (Edo Hildericus), Propositiones Cosmographicae de Globi Terreni Dimensione, (Frankfurt a. d. Oder, 1576), quoted in Peter Barker and Bernard R. Goldstein, "Realism and Instrumentalism in Sixteenth Century Astronomy: A Reappraisal, Perspectives on Science 6.3 (1998): 232–258, pp. 242–3.
44. ^ Michael A. Granada, "Did Tycho Eliminate the Celestial Spheres before 1586?" Journal for the History of Astronomy, 37 (2006): 126–145, pp. 127–9.
45. ^ Bernard R. Goldstein and Peter Barker, "The Role of Rothmann in the Dissolution of the Celestial Spheres," The British Journal for the History of Science, 28 (1995): 385–403, pp. 390–1.
46. ^ Michael A. Granada, "Did Tycho Eliminate the Celestial Spheres before 1586?" Journal for the History of Astronomy, 37 (2006): 126–145, pp. 132–8.
47. ^ Grant, "Celestial Orbs," 2000, pp. 185–6.
48. ^ Grant, Planets, Stars, and Orbs, pp. 345–8.
49. ^ See Judith Field's Kepler's geometric cosmology for details of Kepler's cosmology
50. ^ See p514–5 of Kepler's 1630 Epitome of Copernican Astronomy Vol.1 Bk4.2.3 for his arguments that the Sun has a driving soul on p896 of the Encyclopedia Britannica edition
51. ^ Macrobius, Commentary on the Dream of Scipio, transl. by William Harris Stahl, New York: Columbia Univ. Pr., 1952; on the order of the spheres see pp. 162–5.
52. ^ C. S. Lewis, The Discarded Image: An Introduction to Medieval and Renaissance Literature, Cambridge: Cambridge Univ. Pr., 1964, p. 116. ISBN 0-521-09450-X
53. ^ Nicole Oreseme, "Le livre du Ciel et du Monde", 1377, retrieved 2 June 2007.[1]
54. ^ Ps. 18: 2; quoted in Nicole Oresme, Le livre du ciel et du monde, edited and translated by A, D. Menut and A. J. Denomy, Madison: Univ. of Wisconsin Pr., 1968, pp. 282–3.

Bibliography

• Aristotle Metaphysics, in 'The Basic Works of Aristotle' Richard McKeon (Ed) The Modern Library, 2001
• Clagett, Marshall Science of Mechanics in the Middle Ages University of Wisconsin Press 1959
• Cohen, I.B. & Whitman, A. Principia University of California Press 1999
• Cohen & Smith (eds) The Cambridge Companion to Newton CUP 2002
• Copernicus, Nicolaus On the Revolutions of the Heavenly Spheres, in Great Books of the Western World : 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952
• Crowe, Michael J. (1990). Theories of the World from Antiquity to the Copernican Revolution. Mineola, NY: Dover Publications, Inc. ISBN 0-486-26173-5. http://books.google.com.au/books?id=IGlhN0MI87oC&printsec=frontcover#v=onepage&q=&f=false. 
• Duhem, Pierre. "History of Physics." The Catholic Encyclopedia. Vol. 12. New York: Robert Appleton Company, 1911. 18 Jun. 2008 <http://www.newadvent.org/cathen/12047a.htm>.
• Duhem, Pierre. Le Système du Monde: Histoire des doctrines cosmologiques de Platon à Copernic, 10 vols., Paris: Hermann, 1959.
• Duhem, Pierre. Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds, excerpts from Le Système du Monde, translated and edited by Roger Ariew, Chicago: University of Chicago Press, 1987 ISBN 0-226-16923-5
• Dreyer, John Louis Emil (2007) [1905]. History of the Planetary Systems from Thales to Kepler. New York, NY: Cosimo. ISBN 1602064415. http://www.archive.org/details/historyofplaneta00dreyuoft. 
• Eastwood, Bruce, "Astronomy in Christian Latin Europe c. 500 – c. 1150," Journal for the History of Astronomy, 28(1997): 235–258.
• Eastwood, Bruce, Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, Leiden: Brill, 2007. ISBN 978-90-04-16186-3.
• Eastwood, Bruce and Gerd Graßhoff, Planetary Diagrams for Roman Astronomy in Medieval Eyrope, ca. 800-1500, Transactions of the American Philosophical Society, vol. 94, pt. 3, Philadelphia, 2004. ISBN 0-87169-943-5
• Field, J. V., Kepler's geometrical cosmology. Chicago: Chicago University Press, 1988 ISBN 0-226-24823-2
• Golino, Carlo (ed.)Galileo Reappraised University of California Press 1966
• Grant, Edward, "Celestial Orbs in the Latin Middle Ages," Isis, 78(1987): 153–73; reprinted in Michael H. Shank, ed., The Scientific Enterprise in Antiquity and the Middle Ages, Chicago: Univ. of Chicago Pr., 2000. ISBN 0-226-74951-7
• Grant, Edward, Planets, Stars, and Orbs: The Medieval Cosmos, 1200–1687, Cambridge: Cambridge Univ. Pr., 1994. ISBN 0-521-56509-X
• Grant, Edward The Foundations of Modern Science in the Middle Ages, Cambridge: Cambridge Univ. Pr., 1996. ISBN 0-521-56762-9
• Gingerich, Owen The Eye of Heaven, American Institute of Physics 1993
• Hutchins, Robert Maynard; Adler, Mortimer J., eds (1952). Ptolemy, Copernicus, Kepler. Great Books of the Western World. 16. Chicago, Ill: William Benton. 
• Heath, Thomas Aristarchus of Samos Oxford University Press/Sandpiper Books Ltd. 1913/97
• Jarrell, R.A. The contemporaries of Tycho Brahe in Taton & Wilson (eds)1989
• Koyré, Alexandre: Galileo Studies (translator Mepham) Harvester Press 1977 ISBN 0-85527-354-2
• Kepler Epitome of Copernican Astronomy (Bks 4 & 5) published in Great Books of the Western World : 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952
• Lewis, C. S., The Discarded Image: An Introduction to Medieval and Renaissance Literature, Cambridge: Cambridge University Press 1964 ISBN 0-521-09450-X
• Lindberg, David C. (1992). The Beginnings of Western Science. Chicago: University of Chicago Press. ISBN 0-226-48231-6. 
• Lindberg, David C. (ed) Science in the Middle Ages Chicago: Univ. of Chicago Pr., 1978. ISBN 0-226-48233-2
• Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 978-0-521-82750-8. http://books.google.com.au/books?id=B4br4XJFj0MC&printsec=frontcover#v=onepage&q=&f=false. 
• Lloyd, G. E. R., Aristotle: The Growth and Structure of his Thought, pp. 133–153, Cambridge: Cambridge Univ. Pr., 1968. ISBN 0-521-09456-9.
• Lloyd, G. E. R., "Heavenly aberrations: Aristotle the amateur astronomer," pp. 160–183 in his Aristotelian Explorations, Cambridge: Cambridge Univ. Pr., 1996. ISBN 0-521-55619-8.
• Mach, Ernst The Science of Mechanics Open Court 1960.
• McCluskey, Stephen C., Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge Univ. Pr., 1998. ISBN 0-521-77852-2
• Neugebauer, Otto, A History of Ancient Mathematical Astronomy, 3 vols., New York: Springer, 1975. ISBN 0-387-06995-X
• Pederson, Olaf (1993) [1974]. Early Physics and Astronomy: A Historical Introduction. Cambridge: Cambridge University Press. ISBN 0-521-40340-5. http://books.google.com.au/books?id=z7M8AAAAIAAJ&printsec=frontcover#v=onepage&q=&f=false. 
• Popper, Karl The World of Parmenides Routledge 1996
• Rosen, Edward Three Copernican Treatises Dover 1939/59.
• Sambursky, S. The Physical World of Late Antiquity Routledge & Kegan Paul, 1962
• Schofield, C. The Tychonic and Semi-Tychonic World Systems in Taton & Wilson (eds) 1989
• Sargent, Steven (ed) On the threshold of exact science: Selected writings of Annaliese Maier on Late Medieval Natural Philosophy University of Pennsylvania Press 1982
• Sorabji, Richard Matter, Space and Motion London: Duckworth, 1988 ISBN 0-7165-2205-6
• Sorabji, Richard (ed) Philoponus and the Rejection of Aristotelian Science London & Ithaca NY 1987
• Sorabji, Richard The Philosophy of the Commentators, 200–600 AD: Volume 2 Physics Duckworth 2004
• Taliaferro, R. Catesby (1946). Translator's Introduction to the Almagest. In Hutchins (1952, pp.1–4). 
• R. Taton & C. Wilson (eds.)The General History of Astronomy: Volume 2 Planetary astronomy from the Renaissance to the rise of astrophysics Part A Tycho Brahe to Newton Cambridge: Cambridge Univ. Pr., 1989
• Thoren, Victor E., "The Comet of 1577 and Tycho Brahe's System of the World," Archives Internationales d'Histoire des Sciences, 29 (1979): 53–67.
• Thoren, Victor E., Tycho Brahe in Taton & Wilson 1989

External links

• Dennis Duke, Animated Ptolemaic model of the nested spheres
• Henry Mendell, Vignettes of Ancient Mathematics: Eudoxus of Cnidus Ptolemy, Almagest