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Epictetus comments on The Galileo affair: who was on the side of rationality? - Less Wrong
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Astronomy and epistemology aren't quite the same. Predicting where Saturn would be on a given date requires accurate observation, and nobody objected to Coperniucus as a calculational tool. For example, the Jesuits are teaching Copernicus in China in Chinese about 2 years after he publishes, which implies they translated and shipped it with some alacrity.
The heavens were classically held to be made of different stuff; quintessense (later called aether) was not like regular matter -- this is obvious from the inside, because it maintains perpetual motion where normal matter does not. A lot of optical phenomena (eg. twinkling stars, the surface of the moon) were not seen as properties of the objects in question but properties of regular 4-elements matter between us and them.
By a modern standard, the physics is weird and disjointed... but that is historically how it was seen.
It's worth noting that Copernicus' use of circular orbits required the use of epicycles to make the theory fit the observations.
Epicycles are sort of like Fourier analysis. Just like you can break down a non-sine function into sine waves, you can break down a non-circular orbit into a combination of circles.
But if you're going to use epicycles anyway, why prefer Copernicus to Ptolemy?
Fewer epicycles means easier calculations. Still, it isn't clear why you should prefer the Copernican system to the Tychonic (the other major contender in Galileo's time) when evaluating based on some mix of accuracy and ease of calculation (if your goal is to know "where Saturn would be on a given date").
Going by wiki, Copernicus' system had more epicycles.
Whoops, you're right. It seems as though Copernicus dropped an equant at the cost of adding even more epicycles. Hardly an unambiguously preferable trade-off.
According to Koestler (The Sleepwalkers) Copernicus just hated Ptolemy's "eccentrics" because a good Platonist God does not do ugly assymetrical work like that. http://en.wikipedia.org/wiki/Deferent_and_epicycle