Celestial spheres
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 apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element, like gems set in orbs. Since it was believed that the fixed stars were unchanging in their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.
Context
In modern thought, the orbits of the planets are viewed as the paths of those planets through mostly empty space. Ancient and medieval thinkers, however, considered the celestial orbs to be 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. By combining this nested sphere model with astronomical observations, scholars calculated what became generally accepted values at the time for the distances to the Sun: about, to the other planets, and to the edge of the universe: about. The nested sphere model's distances to the Sun and planets differ significantly from modern measurements of the distances, and the size of the universe is now known to be inconceivably large and continuously expanding.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". Even following the adoption of Copernicus's heliocentric model of the universe, new versions of the celestial sphere model were introduced, with the planetary spheres following this sequence from the Sun at the centre: Mercury, Venus, Earth-Moon, Mars, Jupiter and Saturn.
Mainstream belief in the theory of celestial spheres did not survive the Scientific Revolution. In the early 1600s, Kepler continued to discuss celestial spheres, although he did not consider that the planets were carried by the spheres but held that they moved in elliptical paths described by Kepler's laws of planetary motion. In the late 1600s, Greek and medieval theories concerning the motion of terrestrial and celestial objects were replaced by Newton's law of universal gravitation and Newtonian mechanics, which explain how Kepler's laws arise from the gravitational attraction between bodies.
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. 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. Hence, in Anaximander'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 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. 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. 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.
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. 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 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. Although historians of Greek science have traditionally considered these models to be merely geometrical representations, recent studies have proposed that they were 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 that 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 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.
Image:PeuerbachSuperioribus2.png|thumb|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.
In his Almagest, the astronomer Ptolemy developed geometrical predictive models of the motions of the stars and planets 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 Ptolemy's physical 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. Ptolemy's model of nesting spheres provided the general dimensions of the cosmos, the greatest distance of Saturn being 19,865 times the radius of the Earth and the distance of the fixed stars being at least 20,000 Earth radii.
The planetary spheres 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 with Venus above Mercury, but noted others placed them both above the Sun; some medieval thinkers, such as al-Bitruji, placed the sphere of Venus above the Sun and that of Mercury below it.
Middle Ages
Astronomical discussions
A series of astronomers, beginning with the Muslim astronomer al-Farghānī, used the Ptolemaic model of nesting spheres to compute distances to the stars and planetary spheres. Al-Farghānī's distance to the stars was 20,110 Earth radii which, on the assumption that the radius of the Earth was, came to. An introduction to Ptolemy's Almagest, the Tashil al-Majisti, believed to be written by Thābit ibn Qurra, presented minor variations of Ptolemy's distances to the celestial spheres. In his Zij, Al-Battānī presented independent calculations of the distances to the planets on the model of nesting spheres, which he thought was due to scholars writing after Ptolemy. His calculations yielded a distance of 19,000 Earth radii to the stars.Around the turn of the millennium, the Arabic astronomer and polymath Ibn al-Haytham presented a development of Ptolemy's geocentric 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 said that the celestial spheres do not consist of solid matter.
Near the end of the twelfth century, the Spanish Muslim astronomer al-Bitrūjī sought to explain the complex motions of the planets without Ptolemy's epicycles and eccentrics, using an Aristotelian framework of purely concentric spheres that moved with differing speeds from east to west. This model was much less accurate as a predictive astronomical model, but it was discussed by later European astronomers and philosophers.
In the thirteenth century the astronomer al-'Urḍi proposed a radical change to Ptolemy's system of nesting spheres. In his Kitāb al-Hayáh, he recalculated the distance of the planets using parameters which he redetermined. Taking the distance of the Sun as 1,266 Earth radii, he was forced to place the sphere of Venus above the sphere of the Sun; as a further refinement, he added the planet's diameters to the thickness of their spheres. As a consequence, his version of the nesting spheres model had the sphere of the stars at a distance of 140,177 Earth radii.
About the same time, scholars in European universities began to address the implications of the rediscovered philosophy of Aristotle and astronomy of Ptolemy. Both astronomical scholars and popular writers considered the implications of the nested sphere model for the dimensions of the universe. Campanus of Novara's introductory astronomical text, the Theorica planetarum, used the model of nesting spheres to compute the distances of the various planets from the Earth, which he gave as 22,612 Earth radii or. In his Opus Majus, Roger Bacon cited Al-Farghānī's distance to the stars of 20,110 Earth radii, or, from which he computed the circumference of the universe to be. Clear evidence that this model was thought to represent physical reality is the accounts found in Bacon's Opus Majus of the time needed to walk to the Moon and in the popular Middle English South English Legendary, that it would take 8,000 years to reach the highest starry heaven. General understanding of the dimensions of the universe derived from the nested sphere model reached wider audiences through the presentations in Hebrew by Moses Maimonides, in French by Gossuin of Metz, and in Italian by Dante Alighieri.