Celestial spheres

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 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. 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. Others disagreed about the relative place of the spheres of Mercury and Venus: Ptolemy placed both of them beneath the Sun and with Venus beneath 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.

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. When scholars applied Ptolemy's epicycles, they presumed that each planetary sphere was exactly thick enough to accommodate them. 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.

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. 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. 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, both Xenophanes and Parmenides held that the universe was spherical. 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. 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 geoconcentric 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 ' 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. 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, recent studies have proposed that it was also intended to be physically real or have withheld judgment, noting the limited evidence to resolve the question.

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, 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.

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. 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. In the Ptolemaic model, each planet is contained in two or more spheres, 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. 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.

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. 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.

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. An outer sphere, inhabited by angels, appeared in some accounts.

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. In chapters 15-16 of his Book of Optics, Ibn al-Haytham also discovered that the celestial spheres do not consist of solid matter.

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.

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.

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. By the end of the Middle Ages, the common opinion was that celestial bodies were moved by external intelligences, identified with the angels of revelation.

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.

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, 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 three 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.".

But this is only an impossibility for a spherist cosmology in which different planetary spheres cannot intersect, 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).

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. 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, 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.

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.

In Johannes Kepler's 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. In Kepler's celestial mechanics the cause of planetary motion became the rotating sun, itself rotated by its own motive soul. However, an immobile stellar sphere was a lasting remnant of physical celestial spheres in Kepler's cosmology.

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.

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

See also

• Firmament
• Musica universalis
• Primum Mobile

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External links

• Dennis Duke, Animated Ptolemaic model of the nested spheres