It is theoretically possible to accurately describe the motions of celestial bodies using epicycles, though one might need infinite epicycles, and epicycles would themselves need to be on epicycles. If you think there's something wrong with the math, it won't be in its inability to describe the motion of celestial bodies.

But I don't think there's anything "wrong with the math" - I even said precisely that:

A believer in epicycles would likely have thought that it must have been correct because it gave mathematically correct answers. And it actually did . Epicycles actually did precisely calculate the positions of the stars and planets (not absolutely perfectly, but in principle the theory could have been adjusted to give perfectly precise results). If the mathematics was right, how could it be wrong?

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While 'accurate' and 'precise' are used as synonyms in ordinary language, please never use them that way when talking technically about the meanings of words.

I was trying to talk about how people actually use them, and one of the things I was suggesting is that people do actually tend to treat them as synonymous.

Similarly, please never use 'begs the question' or any form of it when not referring to the logical fallacy.

Isn't this a little picky? The way I used 'begs the question', in the sense of 'raises the question', is fairly common usage. Language is constantly evolving and if you wanted to claim that people only should use terms and phrases in line with their original meanings you'd have throw away most language.