As astronomical observations became more comprehensive, and as sea-faring became more widespread, the need for better star-charts in order to have more accurate time-keeping and navigation became imperative. In order to meet this demand for increased accuracy, the method of epicycles outlined by Ptolemy became more and more complicated, and was extended in different ways by different mathematical astronomers until it became hard to say what the Ptolemaic system was. Instead there were a whole set of different calculations all based on the Ptolemaic system, all getting increasingly complicated. And none of them quite agreed with the full range of good naked-eye observations. (p. 139. Most of the material in this post is from Thomas Kuhn’s book The Copernican Revolution and page numbers are from that book.)

Part of the problem was that some of the earlier observations were simply erroneous, a problem that plagued Ptolemaic and Copernican astronomy alike, and these went away later as better observations came along (p. 139). But other problems were more substantive.

This state of affairs was unsatisfactory to say the least. But while many astronomers felt that the Ptolemaic system, although complicated, could ultimately be made to work with further tinkering, Copernicus felt that this was a sign that the two-sphere model itself was at fault and needed to be replaced, and thus proposed his new model.

But because his system, like that of Ptolemy, used circles for the orbits, it also needed epicycles to give more detailed predictions. And as the observational data got better, it too started getting very complicated.

As Kuhn says:

His full system was little if any less cumbersome than Ptolemy’s had been. Both employed over thirty circles; there was little to choose between them in economy. Nor could the two systems be distinguished by their accuracy. When Copernicus had finished adding circles, his cumbersome sun-centered system gave results as accurate as Ptolemy’s, but did not give more accurate results. Copernicus had failed to solve the problem of the planets. (p. 169)

The Copernican model had some aesthetic and qualitative advantages over the Ptolemaic system. It provided a more natural qualitative explanation for the retrograde (zig-zag) motion of planets like Mars as observed from the Earth and answered some important questions concerning the ordering of the planets. Kuhn continues:

Judged on purely practical grounds, Copernicus’s new planetary system was a failure; it was neither more accurate nor significantly simpler than its Ptolemaic predecessors. But historically the new system was a great success; the De Revolutionibus did convince a few of Copernicus’ successors that sun-centered astronomy held the key to the problem of the planets, and these men finally provided the simple and accurate solution that Copernicus had sought. (p. 171)

This is an important point to appreciate about scientific revolutions. They very rarely give demonstrably better results than their predecessors right at the start. What usually happens is that they have an appeal (often aesthetic) that attracts others to work within the new model and solve the puzzles and problems generated by it. And if the new model proves fruitful over time in solving more puzzles, then it gains adherents.

It is important to understand that Copernicus’ work initially was restricted to the community of astronomers. Copernicus was widely respected as one of Europe’s leading astronomers and reports about his work, including his heliocentric hypothesis had been circulating since 1515, so when his De Revolutionibus was published in 1543, it was hardly a surprise to other astronomers. But even those who were skeptical of the idea of a moving Earth accepted that it was the most comprehensive account of celestial motions since Ptolemy.

But while astronomers hailed his work and used his tables and methods, most were skeptical of the central idea of a moving Earth. They dismissed it as some kind of artificial trick that turned out to be useful in providing calculations for the motion of planets (similar to the way that Planck’s quantum hypothesis was initially conceived). This idea that the motion described by a model was a convenient fiction was not unprecedented. Ptolemy himself had said that not all of his own epicycles had to be considered physically real. Some were to be thought of as mathematical fictions that gave numerically sound results (p. 186).

But the very fact that the Copernican model was useful attracted new people to study it and thus its ideas spread within the astronomical community, and its central thesis did gain a few converts, although they were a small minority. One of the key converts was Johannes Kepler, who (as we shall see later) was to play a key role in removing the epicycles from Copernicus’ model and sealing its superiority.