Accuracy and Technique in the Copernican Model
Despite the promise of a new, clean, simple system of pure circles, Copernicus ultimately presented just as complicated a geometry as Ptolemy. He complained, in the Preface to De revolutionibus orbium caelestium [On the Revolutions of the Heavenly Spheres], about the complex and inconsistent mathematics of the Ptolemaic astronomers:
" . . . I was impelled to consider a different system of deducing the motions of the universe's spheres for no other reason than the realization that mathematicians do not agree among themselves in their investigations of this subject.... in determining the motions not only of [the sun and moon] but also of the other five planets, they do not use the same principles, assumptions, and explanations of the apparent revolutions and motions. For while some employ only homocentrics, others utilize eccentrics and epicycles, and yet they do not quite reach their goal."
The result was that mathematicians all disagreed among themselves, still could not match model to phenomenon, still could not calculate correctly, and continued to "contradict the first principles of uniform motion." Their lack of symmetry left astronomers with a mathematical monstrosity, rather than a clear deduction of the structure of the universe.
And yet Copernicus also left readers with complicated mathematics and the old tricks. These geometrical figures are from his text -- employing eccentrics and epicycles. Readers quickly discovered that the calculations were no simpler.
One still had to work through complicated constructions, and try different techniques for each of the planets. A coherent system, with everything in one diagram, as promised in the opening illustration, still could not be attained. -- and worse, the claim for a superior accuracy evaporated upon examination.
If Ptolemy gave results as accurate for calculation of planetary position, why bother to change to the Copernican model?