To add to what others have already commented...
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. Rather, feasibility, simplicity, usefulness, and other such concerns will likely be factors in it.
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. They are very useful jargon.
Similarly, please never use 'begs the question' or any form of it when not referring to the logical fallacy.
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. An
[edit: sorry, the formatting of links and italics in this is all screwy. I've tried editing both the rich-text and the HTML and either way it looks ok while i'm editing it but the formatted terms either come out with no surrounding spaces or two surrounding spaces]
In the latest Rationality Quotes thread, CronoDAS quoted Paul Graham: