<P> 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 . </P> <P> 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 . </P> <P> In his Almagest, the astronomer Ptolemy (fl . ca . 150 AD) 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 . </P> <P> 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 . </P>

The celestial sphere model of the heavens could not explain which of the following facts