Ptolemy & Homer

Some people think Copernicus's model of planetary orbits was able to "save the appearances" of elliptical orbits where the older theory of Ptolemy's epicycles was not and this was why the Copernican model gained scientific consensus. This is not true, especially since there were at least five competing theories at the time. In fact Kepler's 3 Laws were originally mathematical approximations of Ptolemy's epicycles. Epicycles can reproduce any orbit, even this complex one, which required 1,000 epicycles:

What the ancients called epicycles we would today call a complex Fourier series. For the mathematical formalism, see Hanson's Isis article; cf. also Christián Carman's “Deferentes, epiciclos y adaptaciones.”

We can understand why

Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle [...]. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astronomy the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them. [...]

—Summa Theologica, I, q. 32, a. 1 ad 2