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3.1: Ptolemy and the Geocentric Model

Scientists of the 1500s and 1600s inherited a model of the universe whose basic features had been defined by Aristotle 2000 years earlier. The idea was simple. Earth was stationary at the center and the Sun, Moon, and other planets all moved around Earth. Each object was fixed to a spinning crystalline sphere. The stars were all fixed to an outermost sphere and were also carried around the Earth on circular orbits. Rest was the natural state for any object, so a mysterious power was required to keep the celestial bodies in motion. Medieval people pictured the whole universe as a set of concentric spherical shells centered on Earth. The "Terra immobilis" is in the center, surrounded by shells of water, air, and fire, with those surrounded in turn by shells that carried the Moon, Sun, planets, and finally the distant stars. This cozy arrangement fit with the powerful idea that humans were at the center of creation.

However, the Ptolemy's most successful realization of the Greek model was anything but simple. Motion seen from the center of a circular orbit is uniform. Yet it was known that the planets do not move among the stars at a constant rate. To account for this Ptolemy was forced to hypothesize that the center of the motion was displaced from the Earth, like the eccentric motion of a wheel when the hub is not at the center. Also, it was known that some planets can reverse their steady eastward motions among the stars — a phenomenon called retrograde motion. The Ptolemaic model therefore required the planets not only to move in circles around Earth, but also to move along smaller circles, called epicycles, around imaginary points along the main circular orbits. Mercury and Venus are never seen far from the Sun so they have a special status in Ptolemy's model. Their epicycle centers must lie on the line connecting the Earth and Sun. The Greeks had used geometry to estimate the distance to the stars as at least a million miles. Therefore the outermost crystalline sphere had to be whirring around at over a million mile per hour!

How good was the Ptolemaic model? Note that we do not call it a theory because it has no physical explanation for how and why the planets move the way they do. Ptolemy himself never claimed that it represented reality, only that it provided a convenient mathematical description to predict the planet positions. Initially the predictions were accurate to one or two arc minutes (this is about as good as the resolution of the human eye). But the eccentric motions adopted by Ptolemy were just approximations to the true motions of the planets and over the centuries the errors began to accumulate. A small error in a calendar will also accumulate into a serious problem over a span of centuries. By the 13th century, the predictions of the model could be off by as much a one or two degrees, several times the angular diameter of the Moon. Astronomers had to make increasingly complicated adjustments to the model in order to get correct answers. They even had to add tiny epicycles onto the larger epicycles. In 1252, Spain's King Alfonso X funded a special almanac of predicted planetary positions. Watching his astronomers laboriously calculate motions of epicycles upon epicycles, he commented that had he been present at the creation, he could have suggested a simpler arrangement.

This idea of looking for simpler arrangement has become a key element in the scientific method. As early as 1340, the English scholar William of Occam proposed the famous idea that among competing theories, the best theory is usually the simplest theory — that is, the one with the fewest assumptions or the fewest quantities that have to be combined to make a prediction. This principle is known as Occam's razor. Are the simplest and most elegant theories always correct? Or is the belief that the universe is simple merely a human conceit? You can judge for yourself as you study the subject of astronomy.