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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.<ref>Grant, ''Planets, Stars, and Orbs,'' pp. 328-30.</ref>
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.<ref>Grant, ''Planets, Stars, and Orbs,'' pp. 328-30.</ref>

'''Parisian impetus dynamics and the spheres'''

In the 14th century the logician and natural philosopher Jean Buridan, Rector of Paris University, subscribed to the Avicennan variant of Aristotelian impetus dynamics according to which impetus is conserved forever in the absence of any resistance to motion, rather than being evanescent and self-decaying as in the Hipparchan variant. In order to dispense with the need for positing continually moving intelligences or souls in the celestial spheres, which he pointed out are not posited by the Bible, Buridan applied the Avicennan self-conserving impetus theory to their endless rotation by extension of a terrestrial example of its application to rotary motion in the form of a rotating millwheel that continues rotating for a long time after the originally propelling hand is withdrawn, driven by the impetus impressed within it.<ref>See p112 of Edward Grant's 1996 The Foundations of Modern Science in the Middle Ages for his account of Buridan's application of impetus dynamics to celestial motion.</ref><ref>According to Buridan's theory impetus acts in the same direction or manner in which it was created, and thus a circularly or rotationally created impetus acts circularly thereafter.</ref> Earlier [[Franciscus de Marchia]] had given a partial impetus dynamics account of celestial motion in the form of the sphere’s angel continually impressing impetus in its sphere whereby it was moved directly by impetus and only indirectly by its moving angel.<ref>See p112 ''The Foundations of Modern Science in the Middle Ages'' Edward Grant 1996</ref>This hybrid mechanico-animistic explanation was necessitated by the fact that de Marchia only subscribed to the Hipparchan-Philoponan impetus theory in which impetus is self-dissipating rather than self-conserving, and thus would not last forever but need constant renewal even in the absence of any resistance to motion.

Buridan wrote on the impetus of the celestial spheres as follows:

:"God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more...And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus."<ref>''Questions on the Eight Books of the Physics of Aristotle'': Book VIII Question 12 English translation in Clagett's 1959 ''Science of Mechanics in the Middle Ages'' p536</ref> - -

However, having discounted the possibility of any resistance due to a contrary inclination to move in any opposite direction and due to any external resistance, Buridan obviously also discounted any inherent resistance to motion in the form of an inclination to rest within the spheres themselves, such as the inertia posited by Averroes and Aquinas. And in fact contrary to that inertial variant of Aristotelian dynamics, according to Buridan "prime matter does not resist motion". But this then raises the question within Aristotelian dynamics of why the motive force of impetus does not therefore move them with infinite speed. The impetus dynamics answer seemed to be that it was a secondary kind of motive force that produced uniform motion rather than infinite speed, just as it seemed Aristotle had supposed the planets' moving souls do, or rather than uniformly accelerated motion like the primary force of gravity did by producing increasing amounts of impetus.


===Renaissance===
===Renaissance===

Revision as of 17:56, 28 June 2008

This article is about material celestial spheres from Antiquity to the Renaissance. For modern uses of the celestial sphere in astronomy and navigation, see Celestial sphere.
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 celestial entities of the cosmological celestial mechanics first invented by Eudoxus, and developed by Aristotle, Ptolemy, Copernicus and others.[1] In this celestial model 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 geocentric models the spheres were most commonly arranged outwards from the centre in this order: the sphere of the Moon, the sphere of Mercury, the sphere of Venus, the sphere of the Sun, the sphere of Mars, the sphere of Jupiter, the sphere of Saturn, the starry firmament, and sometimes one or two additional spheres.[citation needed] 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] there were other disagreements about the relative place of the spheres of Mercury and Venus. 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, Saturn.

History

Antiquity

In his Metaphysics, Aristotle adopted and developed a celestial physics of uniformly rotating geo-concentric nested spheres first devised and developed by the astronomers Eudoxus and Callippus.[3] In Aristotle's fully developed celestial mechanics, the spherical Earth is at the centre of the universe and the planets and stars are moved by either 48 or 56 completely interconnected spheres altogether, whereas in the models of Eudoxus and Callippus each planet's individual set of spheres were not connected to those of the next planet.[4] Each planet is attached to the innermost of its own particular set of 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.[5]Aristotle says the exact number of spheres is to be determined by astronomical investigation, but he disagreed with the numbers imputed by the contemporary astronomers Eudoxus and Callippus, adding many more. The exact number of divine unmoved movers is to be determined by metaphysics, and Aristotle assigned one unmoved mover per sphere.[6]

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 a geometrical model of the universe in his Almagest[citation needed] and extended it to a physical model of the cosmos in his Planetary hypotheses. In doing so, he achieved greater mathematical detail and predictive accuracy that had been lacking in earlier spherical models of the cosmos. In the Ptolemaic model, each planet is moved by two or more spheres, but in Book 2 of his Planetary Hypotheses Ptolemy depicted circular bands as in Plato’s Timaeus model rather than spheres as in its Book 1.[citation needed] One sphere/band is the deferent, with a centre offset somewhat from the Earth; the other sphere/band is an epicycle embedded in the deferent, with the planet embedded in the epicyclical sphere/band.

Middle Ages

Christian and Muslim philosophers modified Ptolemy's system to include an unmoved outermost region, which was the dwelling place of God and all the elect. The outermost moving sphere, which moved with the daily motion affecting all subordinate spheres, was moved by a fixed 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.[citation needed]

Around the turn of the millennium, the Arabian 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.[7] In chapters 15-16 of his Book of Optics, Ibn al-Haytham also discovered that the celestial spheres do not consist of solid matter.[8]

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.[9][10]

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.[11]

Parisian impetus dynamics and the spheres

In the 14th century the logician and natural philosopher Jean Buridan, Rector of Paris University, subscribed to the Avicennan variant of Aristotelian impetus dynamics according to which impetus is conserved forever in the absence of any resistance to motion, rather than being evanescent and self-decaying as in the Hipparchan variant. In order to dispense with the need for positing continually moving intelligences or souls in the celestial spheres, which he pointed out are not posited by the Bible, Buridan applied the Avicennan self-conserving impetus theory to their endless rotation by extension of a terrestrial example of its application to rotary motion in the form of a rotating millwheel that continues rotating for a long time after the originally propelling hand is withdrawn, driven by the impetus impressed within it.[12][13] Earlier Franciscus de Marchia had given a partial impetus dynamics account of celestial motion in the form of the sphere’s angel continually impressing impetus in its sphere whereby it was moved directly by impetus and only indirectly by its moving angel.[14]This hybrid mechanico-animistic explanation was necessitated by the fact that de Marchia only subscribed to the Hipparchan-Philoponan impetus theory in which impetus is self-dissipating rather than self-conserving, and thus would not last forever but need constant renewal even in the absence of any resistance to motion.

Buridan wrote on the impetus of the celestial spheres as follows:

"God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more...And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus."[15] - -

However, having discounted the possibility of any resistance due to a contrary inclination to move in any opposite direction and due to any external resistance, Buridan obviously also discounted any inherent resistance to motion in the form of an inclination to rest within the spheres themselves, such as the inertia posited by Averroes and Aquinas. And in fact contrary to that inertial variant of Aristotelian dynamics, according to Buridan "prime matter does not resist motion". But this then raises the question within Aristotelian dynamics of why the motive force of impetus does not therefore move them with infinite speed. The impetus dynamics answer seemed to be that it was a secondary kind of motive force that produced uniform motion rather than infinite speed, just as it seemed Aristotle had supposed the planets' moving souls do, or rather than uniformly accelerated motion like the primary force of gravity did by producing increasing amounts of impetus.

Renaissance

Paul Wittich's 1578 Capellan geoheliocentric planetary model in which the Martian and Solar orbits do not intersect

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.[16]

However, it seems a crucial physical reason for his heliocentrism in order to save the celestial spheres may have been that he rejected the possibility of interpenetrating spheres, but for some reason thought Martian parallax at opposition is greater than solar parallax,[17] whereby Mars must then be nearer the Earth than the sun is, but also whereby the Martian and solar spheres must intersect on all geocentric and geoheliocentric planetary models. They can only be non-intersecting with Mars less than 1 AU away at opposition in the pure heliocentric model.

As Copernicus's pupil and herald Rheticus expressed this in his 1540 Copernican Narratio Prima published 3 years before Copernicus's De Revolutionibus, "Mars unquestionably shows a parallax sometimes greater than the sun's, and therefore it seems impossible that the earth should occupy the centre of the universe.".[18] But this is only an impossibility for a spherist cosmology in which different planetary spheres cannot intersect,[19]but not for non-spherist astronomy, as illustrated by the non-spherist Tychonic geocentric model, for example, in which the Martian and solar orbits intersect (as also do the orbits of Mercury and Venus with those of Mars and of Jupiter as drawn). [20]

Tycho Brahe's 1587 geoheliocentric planetary model in which the Martian and Solar orbits intersect

But although Martian parallax at its maximum of some 23 arcseconds is indeed greater than the sun's at some 9 arcseconds, such differences are thought to have been instrumentally observationally indiscernible at that time before telescopes and micrometers, when the maximum discernible resolution by human naked eye observation is reckoned to be no more than some 30 arcseconds. Moreover at the time the traditionally accepted value for solar parallax, even by Tycho Brahe, was some 3 arcminutes.

This all raises the question of the basis on which astronomers compared Martian and solar parallax and what the consensus in the 16th century was, if any, on which is greater. The (geoheliocentric) planetary models of such as Paul Wittich and Nicolaus Reimers(aka Ursus) supposed that of Mars was never greater, whereas those of Copernicus and Tycho supposed it was greater at opposition.[21] This all seems to imply disagreement in the 16th century about the observational facts of Martian parallax, but about which crucial issue the history of science literature is silent.

Yet it seems it was a firm belief in the greater oppositional parallax of Mars within geocentrism that undermined belief in the solid celestial spheres as physically possible because of the intersecting spheres problem,[22] to which the only pro-spherist solution was pure heliocentrism. But heliocentrism was observationally 'refuted' by the apparent lack of any annual stellar parallax. Thus Tycho's view that heliocentrism was observationally refuted by the fact of no discernible stellar parallax enforced his rejection of solid spheres to sustain his observationally unjustified belief that Mars was less than 1 AU from the Earth at opposition. But his rejection of the spheres was at least observationally buttressed by his observations of the 1577 comet.

Ursus's 1588 geoheliocentric planetary model in which the Martian and Solar orbits do not intersect

Tycho Brahe's observations that the comet of 1577 displayed less daily parallax than the Moon implied it was superlunary and so, impossibly, must pass through some planetary orbs in its transit. This led him to conclude 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.[23][24]

In Johannes Kepler's celestial physics the spheres were regarded as the purely geometrical spatial regions containing each planetary orbit rather than physical bodies as rotating orbs as in preceding Aristotelian celestial physics. The eccentricity of each planet's elliptical orbit and its major and minor axes thereby defined the lengths of the radii of the inner and outer limits of its celestial sphere and thus its thickness. The intermediate causal 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.[25]

Thus in Kepler's celestial mechanics the previous ultimate causal role of the spheres became a non-ultimate intermediate role as the ultimate causal focus shifted on the one hand to the Platonic regular polyhedra within which Kepler held they were embedded and which thus ultimately defined the dimensions and eccentricities of planetary orbits, and on the other hand to the rotating sun as the central inner driver of planetary motion, itself rotated by its own motor soul.[26]However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler's cosmology.

But solid physical spheres still featured in both Galileo's and Newton's early celestial mechanics. Galileo initially considered the planets to be rolling around the upper surfaces of fixed perfectly smooth spheres driven by their own impetus and gravity. And Newton calculated the centrifugal pressure that would be exerted by the Moon on the lower concave surface of the lunar orb in his 1660s analysis of lunar gravity. Thus for a long time Galileo fiercely resisted the Tychonic theory that comets are superlunary because it destroyed his initial spherist celestial mechanics by knocking away the counter-gravitational supporting surfaces of the rolling planets. For he was unable to explain circular orbits as closed curve projectiles driven by a centrifugal impetus and centripetal gravity.

Literary and symbolic expressions

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.[27]

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.[28] 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.[29] Below this figure Oresme quotes the Psalms that "The heavens declare the Glory of God and the firmament showeth his handiwork."[30]

See also

Notes

  1. ^ Before Aristotle, in his Timaeus Plato had previously proposed the planets were transported on rotating bands.
  2. ^ 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)
  3. ^ See e.g. The Homocentric Spheres of Eudoxus, Ch 4 of Dreyer's History of Astronomy
  4. ^ See Aristotle's Metaphysics12.8
  5. ^ "The final cause, then, produces motion by being loved, but all other things move by being moved" Aristotle Metaphysics 1072b4.
  6. ^ See Metaphysics 12.8, p881-884 in The Basic Works of Aristotle Richard McKeon (Ed) The Modern Library 2001
  7. ^ Y. Tzvi Langerman (1990), Ibn al Haytham's On the Configuration of the World, p. 11-25, New York: Garland Publishing.
  8. ^ Edward Rosen (1985), "The Dissolution of the Solid Celestial Spheres", Journal of the History of Ideas 46 (1), p. 13-31 [19-20, 21].
  9. ^ Bernard R. Goldstein, Al-Bitrūjī: On the Principles of Astronomy, New Haven: Yale Univ. Pr., 1971, vol. 1, pp. 6, 44-5
  10. ^ Grant, Planets, Stars, and Orbs, pp. 563-4
  11. ^ Grant, Planets, Stars, and Orbs, pp. 328-30.
  12. ^ See p112 of Edward Grant's 1996 The Foundations of Modern Science in the Middle Ages for his account of Buridan's application of impetus dynamics to celestial motion.
  13. ^ According to Buridan's theory impetus acts in the same direction or manner in which it was created, and thus a circularly or rotationally created impetus acts circularly thereafter.
  14. ^ See p112 The Foundations of Modern Science in the Middle Ages Edward Grant 1996
  15. ^ Questions on the Eight Books of the Physics of Aristotle: Book VIII Question 12 English translation in Clagett's 1959 Science of Mechanics in the Middle Ages p536
  16. ^ Nicholas Jardine, "The Significance of the Copernican Orbs," Journal for the History of Astronomy, 13(1982): 168-194, esp. pp. 177-8.
  17. ^ At least according to his pupil Rheticus
  18. ^ See p136 of Edward Rosen's 1939/59 Three Copernican Treatises.
  19. ^ This crucially important point that the rationale of Rheticus's point is the presumption of the impossibility of intersecting spheres, and thus of a physically realist spherist cosmology, has been made by American historian of astronomy Owen Gingerich as follows "Rheticus's statement is a stark non-sequitur unless seen in the context of the intersecting spheres." in his chapter 'The Search for a Plenum Universe' on p145 of The Eye of Heaven American Institute of Physics 1993. But Gingerich never explains why and indeed whether it was unquestionable that Mars came closer, citing no observational basis for this belief.
  20. ^ See the diagram of Tycho's geoheliocentric model shown here. This was also true of the Tychonicist Gassendi's 1647 drawing of the model, but in which it seems the orbit of Venus also even intersects that of Saturn. (See Jarrell's article The contemporaries of Tycho Brahe in Part 2A of the 1989 Taton & Wilson General History of Astronomy). This means e.g. Mercury and Venus at opposition must have less parallax than Mars and Jupiter at opposition.
  21. ^ Albeit Tycho's observations failed to demonstrate any Martian parallax whatever at opposition. But Copernicus and Tycho both put the distance to Mars at opposition at approximately half an AU.
  22. ^ But it must be noted that even in Ursus's model although the Martian and Solar orbits do not intersect, as drawn both those of Mercury and Venus intersect that of Mars, and Venus's orbit also intersects Jupiter's. In fact Wittich's geoheliocentric model was the only one without any intersecting orbits whatever, and thus compatible with solid celestial orbs, which seems to have been its guiding purpose. See the diagrams of Ursus's and Wittich's models shown here to confirm these points
  23. ^ Grant, "Celestial Orbs," 2000, pp. 185-6.
  24. ^ Grant, Planets, Stars, and Orbs, pp. 345-8.
  25. ^ See Judith Field's Kepler's geometric cosmology for details of Kepler's cosmology
  26. ^ 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
  27. ^ 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.
  28. ^ 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
  29. ^ Nicole Oreseme, "Le livre du Ciel et du Monde", 1377, retrieved 2 June 2007.[1]
  30. ^ 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.

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  • Aristotle Metaphysics, in 'The Basic Works of Aristotle' Richard McKeon (Ed) The Modern Library, 2001
  • 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 Encyclopedia Britannica Inc 1952
  • 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.
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  • Field, J. V., Kepler's geometrical cosmology. Chicago: Chicago University Press, 1988 ISBN 0-226-24823-2
  • 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
  • Gingerich, Owen The Eye of Heaven, American Institute of Physics 1993
  • Jarrell, R.A. The contemporaries of Tycho Brahe in Taton & Wilson (eds)1989
  • Koyré, Alexandre: Galileo Studies (translator Mepham) Harvester Press 1977 ISBN-10: 0855273542
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  • McCluskey, Stephen C., Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge Univ. Pr., 1998. ISBN 0-521-77852-2
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  • Schofield, C. The Tychonic and Semi-Tychonic World Systems in Taton & Wilson (eds) 1989
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  • Thoren, V.E. Tycho Brahe in Taton & Wilson 1989
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