Celestial spheres
The celestial spheres, or celestial orbs, were the fundamental entities of the
In modern thought, the
Albert Van Helden has suggested that from about 1250 until the 17th century, virtually all educated Europeans were familiar with the Ptolemaic model of "nesting spheres and the cosmic dimensions derived from it".
Mainstream belief in the theory of celestial spheres did not survive the
History
Early ideas of spheres and circles
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; these rings constitute the rims of rotating chariot-like wheels pivoting on the Earth at their centre. 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 all together form a continuous spherical shell encompassing the Earth. All these wheel rims had originally been formed out of an original sphere of fire wholly encompassing the Earth, which 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, from some of which the stellar sphere was in turn composed. As viewed from the Earth, the ring of the Sun was highest, that of the Moon was lower, and the sphere of the stars was lowest.
Following Anaximander, his pupil Anaximenes (c. 585 – c. 528/4) held that the stars, Sun, Moon, and 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. 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.
Emergence of the planetary spheres
Instead of bands, Plato's student Eudoxus 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 26 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] 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.[14] Although historians of Greek science have traditionally considered these models to be merely geometrical representations,[15][16] recent studies have proposed that they were 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 that 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 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. 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]
In his
The planetary spheres were arranged outwards from the spherical, stationary Earth at the centre of the universe in this order: the spheres of the
Middle Ages
Astronomical discussions
A series of astronomers, beginning with the Muslim astronomer
Around the turn of the millennium, the
Near the end of the twelfth century, the
In the thirteenth century the astronomer
About the same time, scholars in European
Philosophical and theological discussions
Philosophers were less concerned with such mathematical calculations than with the nature of the celestial spheres, their relation to revealed accounts of created nature, and the causes of their motion.
Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi about 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."[48]
Christian and Muslim philosophers modified Ptolemy's system to include an unmoved outermost region, the
Edward Grant, a historian of science, has provided evidence that medieval 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.[52]
Later in the century, the
Medieval astronomers and philosophers developed diverse theories about the causes of the celestial spheres' motions. 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.[55] 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.[56] 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.[57]
Renaissance
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.[58] 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 universe. The planetary orbs circled the center of the universe in the following 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 sphere of the stars, which he held to be stationary.[59]
The English almanac maker, Thomas Digges, delineated the spheres of the new cosmological system in his Perfit Description of the Caelestiall Orbes … (1576). Here he arranged the "orbes" in the new Copernican order, expanding one sphere to carry "the globe of mortalitye", the Earth, the four classical elements, and the Moon, and expanding the sphere of stars infinitely to encompass all the stars and also to serve as "the court of the Great God, the habitacle of the elect, and of the coelestiall angelles."[60]
In 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.[61] Rothmann argued from 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.[62]
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[63] 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." Edward Grant found relatively few believers in hard celestial spheres before Copernicus and concluded that the idea first became common sometime between the publication of Copernicus's De revolutionibus in 1542 and Tycho Brahe's publication of his cometary research in 1588.[64][65]
In his early Mysterium Cosmographicum, Johannes Kepler considered the distances of the planets and the consequent gaps required between the planetary spheres implied by the Copernican system, which had been noted by his former teacher, Michael Maestlin.[66] Kepler's Platonic cosmology filled the large gaps with the five Platonic polyhedra, which accounted for the spheres' measured astronomical distance.[67][page needed] In Kepler's mature celestial physics, the spheres were regarded as the purely geometric 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 radii of the inner and outer limits of its celestial sphere and thus its thickness. In Kepler's celestial mechanics, the cause of planetary motion became the rotating Sun, itself rotated by its own motive soul.[68] However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler's cosmology.
Literary and visual 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.
In
Some late medieval figures noted that the celestial spheres' physical order was inverse to their order on the spiritual plane, where God was at the center and the Earth at the periphery. Near the beginning of the fourteenth century
The late-16th-century Portuguese epic
See also
Notes
This article has an unclear citation style. (May 2023) |
- ^ Grant, Planets, Stars, and Orbs, p. 440.
- ^ a b Lindberg, Beginnings of Western Science, p. 251.
- ^ Van Helden, Measuring the Universe, pp. 28–40.
- ^ Grant, Planets, Stars, and Orbs, pp. 437–8.
- ^ Van Helden, Measuring the Universe, p. 3.
- ^ Van Helden, Measuring the Universe, pp. 37, 40.
- ^ 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
- ^ Heath ibid pp26–8
- ^ See chapter 5 of Heath’s 1913 Aristarchus of Samos
- ^ For Xenophanes' and Parmenides' spherist cosmologies see Heath ibid chapter 7 and chapter 9 respectively, and Popper ibid Essays 2 & 3.
- ^ F. M. Cornford, Plato's Cosmology: The Timaeus of Plato, pp. 54–7
- ^ Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.
- ^ a b Lloyd, "Heavenly aberrations," p. 173.
- ^ Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 677–85.
- ^ Dreyer, History of the Planetary Systems, pp. 90–1, 121–2
- ^ Lloyd, Aristotle, p. 150.
- ^ Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics," Studies in History and Philosophy of Science, 4 (1973): 165–72.
- ^ G. E. R. Lloyd, "Saving the Phenomena," Classical Quarterly, 28 (1978): 202–222, at p. 219.
- ^ Aristotle, Metaphysics 1073b1–1074a13, pp. 882–883 in The Basic Works of Aristotle Richard McKeon, ed., The Modern Library 2001
- ^ "The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle Metaphysics 1072b4.
- ^ Neugebauer, History of Ancient Mathematical Astronomy, pp. 111–12, 148
- ^ Pedersen, Early Physics and Astronomy p. 87
- ^ Crowe, Theories of the World, pp.45, 49–50, 72,
- ^ Linton, From Eudoxus to Einstein, pp.63–64, 81.
- ^ Taliaferro, Translator's Introduction to the Almagest, p,1; Dreyer, History of the Planetary Systems, pp.160, 167.
- ^ a b Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, pp. 917–926.
- ^ Andrea Murschel, "The Structure and Function of Ptolemy's Physical Hypotheses of Planetary Motion," Journal for the History of Astronomy, 26(1995): 33–61.
- ^ Francis R. Johnson, "Marlowe's "Imperiall Heaven," ELH, 12 (1945): 35–44, p. 39
- ^ Bruce S. Eastwood, Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, (Leiden: Brill) 2007, pp. 36–45
- ^ 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)
- ISBN 0-300-01387-6
- ^ Van Helden, Measuring the Universe, pp. 29–31.
- ^ Van Helden, Measuring the Universe, p. 31.
- ^ a b Van Helden, Measuring the Universe, pp. 31–2.
- ^ Langermann, Y. Tzvi (1990). Ibn al Haytham's on the Configuration of the World. New York: Garland Publishing. pp. 11–25.
- JSTOR 2709773..
- ^ Goldstein, Bernard R. (1971). Al-Bitrūjī: On the Principles of Astronomy. Vol. 1. New Haven: Yale University Press. pp. 40–5.
- ^ Goldstein, Al-Bitrūjī, p. 6.
- ^ Grant, Planets, Stars, and Orbs, pp. 563–6.
- ^ Grant, Planets, Stars, and Orbs, pp. 433–43.
- ^ Grant, Planets, Stars, and Orbs, pp. 434–8.
- ^ Van Helden, Measuring the Universe, pp. 33–4.
- ^ Van Helden, Measuring the Universe, p. 36.
- ^ Van Helden, Measuring the Universe, p. 35.
- ^ Lewis, The Discarded Image, pp. 97–8.
- ^ Van Helden, Measuring the Universe, p. 38.
- ^ Van Helden, Measuring the Universe, pp. 37–9.
- ^ Adi Setia (2004), "Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey", Islam & Science, 2, retrieved 2 March 2010
- ^ Grant, Planets, Stars, and Orbs, pp. 382–3.
- ^ Lindberg, Beginnings of Western Science, pp. 249–50.
- ^ Lindberg, Beginnings of Western Science, p. 250.
- ^ Grant, Planets, Stars, and Orbs, pp. 328–30.
- ISBN 978-0-521-52994-5.
- ^ S2CID 142586786.
- ^ Grant, Planets, Stars, and Orbs, p. 541.
- ^ Grant, Planets, Stars, and Orbs, p. 527.
- ^ Grant, Planets, Stars, and Orbs, pp. 526–45.
- ^ Nicholas Jardine, "The Significance of the Copernican Orbs", Journal for the History of Astronomy, 13 (1982): 168–94, pp. 177–78.
- ^ 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): 232–58, pp. 242–23.
- ^ Koyre, From the Closed World, pp. 28–30.
- ^ Michael A. Granada, "Did Tycho Eliminate the Celestial Spheres before 1586?", Journal for the History of Astronomy, 37 (2006): 126–45, pp. 127–29.
- ^ 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. 390–91.
- ^ Michael A. Granada, "Did Tycho Eliminate the Celestial Spheres before 1586?", Journal for the History of Astronomy, 37 (2006): 126–45, pp. 132–38.
- ^ Grant, "Celestial Orbs," pp. 185–86.
- ^ Grant, Planets, Stars, and Orbs, pp. 345–48.
- ^ Grasshoff, "Michael Maestlin's Mystery".
- ^ Field, Kepler's geometric cosmology.
- ^ Johannes Kepler, Epitome of Copernican Astronomy, vol. 1, book 4.2.3, pp. 514–15 (1630).
- ^ 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. 162–165.
- ISBN 0-521-09450-X.
- ^ Nicole Oreseme, "Le livre du Ciel et du Monde", 1377, retrieved 2 June 2007.[1]
- ^ 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. 282–283.
- ^ Luiz Vaz de Camões, The Lusiads, translated by Landeg White. Oxford University Press, 2010.
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External links
- Working model and complete explanation of the Eudoxus's Spheres
- Dennis Duke, Animated Ptolemaic model of the nested spheres Archived 8 September 2006 at the Wayback Machine
- Henry Mendell, Vignettes of Ancient Mathematics: Eudoxus of Cnidus Ptolemy, Almagest
- M. Blundevile his exercises, p 282 – Depiction of celestial spheres in a 1613 book