A paper I wrote for PHI 251 (Philosophy and Classical Physics) at Uniky. It is an analysis and comparison, based on mid-sixteenth-century knowledge, of the theories of Copernicus and Ptolemy. Note that 1550 predates Galileo and Kepler; hence their observations are irrelevant within the scope of this paper.

On the Rotations of the Spheres

The year is 1550. Two opposing models of heavenly motion are contending for the minds of astronomers and philosophers. They are both based on circular motions of the planets, and each seems to provide a close mathematical approximation to the observed motions of the heavens. There the similarity ends. One model, put forth by Ptolemy fourteen centuries ago, places the Earth at the centre of the universe, and explains the motions of the planets in terms of many superimposed circular rotations and revolutions. The other, by a recently deceased Polish philosopher named Kopernik (Latinised as Copernicus), turns established scientific and religious thought on its head by placing the Sun, not the Earth, at the centre of the universe, and claiming that the Earth is in constant motion about the Sun.

The Ptolemaic system is based on millennia of astronomy, theology, and physics. It has as a direct ancestor the Aristotelian conception of the universe, as developed by Aristotle, Eudoxus, and others. Aristotle and his followers believed that the motions of the heavens about the Earth could be expressed in terms of the natural motion of the heavens---that being a perfect circle. However, this view did not completely correspond to reality. In particular, it did not explain irregularities---such as retrograde motion, where the planets for the period of a few nights reverse their normal course; and changes in apparent speed---observed in the motions of the planets. Ptolemy adapted Aristotle's system to explain the actual apparent motions of the planets. He introduced a complicated system of epicycles, eccentrics, deferents, and circles-within-circles which gave predictions closely adhering to the observed data.

The Copernican system, however, eliminates much of Aristotle's system and Ptolemy's machinery. Some things remain: the planets and stars move in circular orbits around a common point. However, Copernicus places this point not at the centre of the Earth, but rather just outside the sun (the point is not placed precisely at the centre of the sun in order to account for the apparent speeding-up and slowing-down of planetary motions). In addition, the firmament, rather than rotating once a day, remains fixed. In this model, only gravity and the orbit of the moon are governed by the Earth. The Earth itself, like the planets, orbits the sun---in this case, once a year, accounting for the progression of the seasons and of the fixed stars. In addition, the Earth rotates on its own axis once a day, accounting for the daily transition from darkness to light.

Despite their many differences, the Ptolemaic and Copernican systems do share one thing in common: they are often considered as models only. That is, many scholars have viewed the two systems from an instrumentalist standpoint: the `correctness' should be determined by the accuracy of the model's predictions, rather than their correspondence to reality. This is in opposition to the Aristotelian tradition, which is realist---it purports to explain the actual operation of the universe as it is. In Ptolemy's case, the instrumentalist view is most likely taken because the model is so complicated. The system of inscribed circles is so terribly complicated that one has no real reason, theological or otherwise, for believing that it corresponds to the actuality of things.

In Copernicus's case, there are likely other reasons for taking an instrumentalist stance. Copernicus himself almost certainly believed that his model painted a true picture of the heavens. However, religious and scholarly expediency demand that scholars treat his theory as merely a mathematical model---a claim that the Earth is not at the centre of the Universe would go against years of scientific and theological thought. In an effort to save Copernicus's theory from the wrath of the Church, Andreas Osiander, a Protestant scholar, inserted an anonymous introduction into Copernicus's Revolutions. This introduction argues for an instrumentalist view of astronomy---that this new theory, as well as the old ones, were simply means for calculating mathematically the motion of the spheres.

From an instrumentalist perspective, Copernicus's model is probably a much better one. It is based on a few basic axioms, outlined in his Commentariolus. It requires only three simple circular motions: the motion of the planets and the Earth about the sun, the rotation of the Earth, and the motion of the moon about the Earth. Ptolemy's system, in contrast, requires each planet to have a number of circular motions which, taken together, explain the planet's motion. Because of its conceptual simplicity, the Copernican model lends itself better to mathematical calculation and prediction---to instrumentalists, the only thing that truly matters.

One ought, however, to consider the models as actual, realist, descriptions of the workings of the Universe. The only real problem with the Ptolemaic system here is that it involves so many circles. Thousands of years of experience has not given us any measurements terribly at odds with Ptolemy's predictions. Beyond the complexity of the spheres, this theory is in accord with all common sense and recorded experience. In addition, most importantly, it is in accords with the Bible and the mind of the Church and Pope.

The Copernican system, on the other hand, holds up less well. While it simplifies celestial mechanics, it does not consider the terrestrial at all. In particular, it does not explain the fact that we do not feel the Earth's motion. Under this model, we ought to feel a constant easterly wind as the earth rotates on its axis. For that matter, the Earth must, given its size, spin very quickly in order to account for the perceived daily motion of the firmament. Such a rapid circular motion ought, by all rights, throw us (and perhaps, given the speed of the rotation, its own matter) into space like clay off a pottery wheel. Finally, this model seriously complicates our theories of gravity---why should objects fall to the centre of the Earth when that centre is itself moving? Natural motion cannot be so arbitrary. Copernicus does not even attempt to answer these objections. Others have offered explanations, but none is very satisfactory.

We must, in light of these facts, say that the Ptolemaic system is almost certainly closer to the truth than that of the esteemed Polish gentleman. We should not, however, claim that the Ptolemaic system is perfect. Certainly we have not made precise enough measurements to establish the absolute truth of any theory. In all reality, the heavens move in ways our philosophies have not yet divined. That is for future astronomers to determine. However, we may be certain that, when the truth is finally discovered (if, indeed, it shall be revealed to mortals), it will resemble Ptolemy's and Aristotle's systems rather than Copernicus's.

-- Neil Moore

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