Greek
Spheres and Circles
The Greeks used a geometrical rather than a numerical approach to understand the same celestial
motions. Influenced by Plato's metaphysical concept of the perfection of circular
motion, the Greeks sought to represent the motion of the divine celestial bodies by using
spheres and circles. This explanatory method was not upset until Kepler replaced the circle with the ellipse in 1609.
Plato's student Eudoxus of Cnidus, c.408-c.355 ©, was the first to offer a solution along these lines. He assumed that each planet is attached to one of a group of connected concentric spheres centered on the Earth, and that each planet rotates on differently oriented axes to produce the observed motion. With this scheme of crystalline spheres he failed to account for the variation in brightness of the planets; the scheme was incorporated, however, into Aristotle's cosmology during the 4th century ©. Thus the Hellenic civilization that culminated with Aristotle attempted to describe a physical cosmology. In contrast, the Hellenistic civilization that followed the conquests of Alexander the Great developed over the next four centuries soon predominant mathematical mechanisms to explain celestial phenomena. The basis for this approach was a variety of circles known as eccentrics, deferents, and epicycles. The Hellenistic mathematician Apollonius of Perga, c.262-c.190 ©, noted that the annual motion of the Sun can be approximated by a circle with the Earth slightly off-center, or eccentric, thus accounting for the observed variation in speed over a year. Similarly, the Moon traces an eccentric circle in a period of 27 1/3 days. The periodic reverse, or retrograde, motion of the planets across the sky required a new theoretical device. Each planet was assumed to move with uniform velocity around a small circle (the epicycle) that moved around a larger circle (the deferent), with a uniform velocity appropriate for each particular planet. Hipparchus, c.190-120 ©, the most outstanding astronomer of ancient times, made refinements to the theory of the Sun and Moon based on observations from Nicaea and the island of Rhodes, and he gave solar theory essentially its final form. It was left for Ptolemy, c.100-c.165, to compile all the knowledge of Greek astronomy in the Almagest and to develop the final lunar and planetary theories.
With Ptolemy the immense power and versatility of these combinations of circles as explanatory mechanisms reached new heights. In the case of the Moon, Ptolemy not only accounted for the chief irregularity, called the equation of the center, which allowed for the prediction of eclipses. He also discovered and corrected another irregularity, evection, at other points of the Moon's orbit by using an epicycle on a movable eccentric deferent, whose center revolved around the Earth. When Ptolemy made a further refinement known as prosneusis, he was able to predict the place of the Moon within 10 min, or 1/6¡, of arc in the sky; these predictions were in good agreement with the accuracy of observations made with the instruments used at that time. Similarly, Ptolemy described the motion of each planet in the Almagest, which passed, with a few notable elaborations, through Islamic civilization and on to the Renaissance European civilization that nurtured Nicolaus Copernicus.
The revolution associated with the name of Copernicus was not a revolution in the technical astronomy of explaining motions, but rather belongs to the realm of cosmology. Prodded especially by an intense dislike of one of Ptolemy's explanatory devices, known as the equant, which compromised the principle of uniform circular motions, Copernicus placed not the Earth but the Sun at the center of the universe; this view was put forth in his De revolutionibus orbium caelestium (On the Revolutions of the Heavenly Spheres, 1543). In that work, however, he merely adapted the Greek system of epicycles and eccentrics to the new aement. The result was an initial simplification and harmony as the diurnal and annual motions of the Earth assumed their true meaning, but no overall simplification in the numbers of epicycles needed to achieve the same accuracy of prediction as had Ptolemy. It was therefore not at all clear that this new cosmological system held the key to the true mathematical system that could accurately explain planetary motions.