From Richard Panek, The 4% Universe: Dark Matter, Dark Energy, and the Race to Discover the Rest of Reality (Boston and New York: Mariner Books Houghton Mifflin Harcourt, 2011):
When Plato challenged his students, in the fourth century B.C., to describe the motions of the celestial bodies through geometry, he didn’t expect the answers on paper to represent what was actually happening in the heavens. That knowledge was unknowable because it was unattainable; you couldn’t go into the sky and examine it for yourself. What Plato wanted instead was an approximation of the knowledge. He wanted his students to try to find the math to match not the facts but the appearances.
One student, Eudoxus, arrived at an answer that, in one form or another, would survive for two thousand years. For mathematical purposes he imagined the heavens as a series of nesting, concentric, transparent spheres. Some of these spheres carried the heavenly bodies. Others interacted with those spheres to retard or accelerate their motions, in order to account for the appearance that the heavenly bodies all slow down or speed up through their orbits. Eudoxus assigned the Sun and the Moon three spheres each. To each of the five planets (Mercury, Venus, Mars, Saturn, Jupiter) he assigned an extra sphere to accomodate the appearance that they sometimes briefly reverse their motions against the backdrop of stars, moving east to west from night to night rather than west to east. And then he added a sphere for the realm of the stars. In the end his system consisted of twenty-seven spheres.
Another student of Plato’s, Aristotle, amended this system. He assumed the spheres were not just mathematical constructs but physical realities; to accomodate the mechanics of an interlocking system, he added counterturning spheres. His total: fifty-six. Around A.D. 150, Ptolemy of Alexandria assumed the task of compiling the existing astronomical wisdom and simplifying it, and he succeeded: His night sky was overrun with only forty spheres. The math still didn’t match the appearances exactly, but close enough was good enough — as good as it was ever going to get. (7-8)
Three news items from more modern astronomy: