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”).
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.
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