Caption: An animation of uniform circular motion.

Uniform Circular Motion in Ancient Greek Astronomy:

1. The ancient Greek astronomers (hereafter the ancients) starting with Aristotle (384--322 BCE) if NOT earlier, believed that the natural motion of the Heavens was uniform circular motion. By "natural" we mean the most elementary physical motion.

2. This theory was reasonable. To 1st order, it does seem as if the Heavenly bodies (AKA astronomical objects) move around the Earth in uniform circular motion, or, in the case of the fixed stars, around the celestial axis that passes through the Earth which the ancients knew was much smaller than the Heavens.

3. But more detailed observation shows irregularities in the motions of the planets (here including the Sun and the Moon), most obviously the apparent retrograde motions of the planets which do NOT however occur for the Sun and the Moon.

4. To deal with the irregularities, the ancients theorized that all motions in the Heavens were either (1) the result of compounded uniform circular motions or (2) could be decomposed in terms of uniform circular motions. The first concept is a physical theory and the second descriptive theory. In fact, the ancients and their successors up to circa 1600 probably did NOT clearly differentiate the two concepts.

5. As a physical theory, compounded uniform circular motions is incomplete since you CANNOT calculate what compounded uniform circular motions are necessary for matching the actual Heavens, but only fit compounded uniform circular motions to the Heavens. Effectively, this made the first concept virtually the same as the second.

6. In fact, the fit of compounded uniform circular motions to the Heavens using epicycle models is vastly non-unique as proven by 13 centuries of fitting efforts from Ptolemy (c.100--c.170 CE) to Nicolaus Copernicus (1473--1543).

7. Modern scientists would have abandoned compounded uniform circular motions and tried for a better physical theory. Why didn't the ancients and their successors up to circa 1600 do that?

   Three factors can be suggested all of which probably contributed:

   1. The observations were NOT of sufficient quality and quantity to force abandonment.
   2. The lack of sufficient mathematical tools and, in particular, calculus which is needed for a general treatment of non-uniform motions.
   3. Just the accidental lack of someone with a brilliant new idea. Historically, that person did eventually arrive: Johannes Kepler (1571--1630) with elliptical orbits.

8. Note that Kepler had the best observations ever available to him, but they did NOT overwhelmingly force him to elliptical orbits. It was the combination of observations and brilliant theorizing. And Kepler did NOT have calculus to help him though he did have better mathematical tools than anyone before.

   One can see that the first two factors against going beyond compounded uniform circular motions can be overcome by someone with a brilliant new idea (i.e., Kepler).