8.1 Ptolemaic system  (Page 2/2)

Now, ingenious as this cosmology was, it turned out to be unsatisfactory for astronomy. Heavenly bodies did, in fact, notmove with perfect circular motions: they speeded up, slowed down, and in the cases of the planets even stopped and reversedtheir motions. Although Aristotle and his contemporaries tried to account for these variations by splitting individualplanetary spheres into component spheres, each with a component of the composite motion, these constructions were very complexand ultimately doomed to failure. Furthermore, no matter how complex a system of spheres for an individual planet became,these spheres were still centered on the Earth. The distance of a planet from the Earth could therefore not be varied in thissystem, but planets vary in brightness, a variation especially noticeable for Venus, Mars, and Jupiter. Since in anunchangeable heaven variations in intrinsic brightness were ruled out, and since spheres did not allow for a variation inplanetary distances from the Earth, variations in brightness could not be accounted for in this system.

Thus, although Aristotle's spherical cosmology had a very long life, mathematicians who wished to make geometrical models toaccount for the actual motions of heavenly bodies began using different constructions within a century of Aristotle'sdeath. These constructions violated Aristotle's physical and cosmological principles somewhat, but they were ultimatelysuccessful in accounting for the motions of heavenly bodies. It is in the work of Claudius Ptolemy, who lived in the secondcentury CE, that we see the culmination of these efforts. In his great astronomical work, Almagest ,

Ptolemy used three basic constructions, the eccentric, the epicycle, and the equant. An eccentric construction is one inwhich the Earth is placed outside the center of the geometrical construction. Here, the Earth, E, is displaced slightly from thecenter, C, of the path of the planet. Although this construction violated the rule that the Earth was the center of the cosmos and all planetary motions, the displacement was minimal and wasconsidered a slight bending of the rule rather than a violation. The eccentric in the figure below is fixed; it couldalso be made movable. In this case the center of the large circle was a point that rotated around the Earth in a smallcircle centered on the Earth. In some constructions this little circle was not centered in the Earth.

The second construction, the epicycle, is geometrically equivalent to the simple movable eccentric. In this case, theplanet moved on a little circle the center of which rotated on the circumference of the large circle centered on the ontheEarth. When the directions and speeds of rotation of the epicycle and large circle were chosen appropriately, the planet,as seen from the Earth, would stop, reverse its course, and then move forward again. Thus the annual retrograde motion of theplanets (caused, in heliocentric terms by the addition of the Earth's annual motion to the motion of the planet) could roughlybe accounted for.

Ptolemy combined all three constructions in the models of the planets, Sun, and Moon. A typical construction might thus be asin the picture below, where E is the Earth, C the geometric center of the eccentric circle, Q the equant point, F the centerof the epicycle, and P the planet. As mentioned before, the eccentric was often not fixed but moved in a circle about theEarth or another point between the Earth and the equant point.

Aristotelian cosmology and Ptolemaic astronomy entered the West, in the twelfth and thirteenth centuries, as distinct textualtraditions. The former in Aristotle's Physics and On the Heavens and the many commentaries on these works; the latter in the Almagest and the technical astronomical literature that had grown around it, especially thework of Islamic astronomers working in the Ptolemaic paradigm. In the world of learning in the Christian West(settled in the universities founded around 1200 CE), Aristotle's cosmology figured in all questions concerned withthe nature of the universe and impinged on many philosophical and theological questions. Ptolemy's astronomy was taught aspart of the undergraduate mathematical curriculum only and impinged only on technical questions of calendrics, positionalpredictions, and astrology.

Copernicus's innovations was therefore not only putting the Sun in the center of the universe and working out a completeastronomical system on this basis of this premise, but also trying to erase the disciplinary boundary between the textualtraditions of physical cosmology and technical astronomy.