The Copernican Revolution

by Thomas S. Kuhn

We all know the fairy tale of Nicolas Copernicus: he realized that the earth-centered model of the solar system was wrong, so he compiled lots of observations, did lots of calcuations, and proved that the sun-centered model was in fact the correct model. But because he feared the ire of the Catholic Church, he refused to publish his work until he was dying. After he published his book, everybody except the Church was convinced by his ironclad logic.

It didn’t happen that way. Not at all.

The standard system in use at the time was called the ‘geocentric’ (earth-centered) system, or the ‘Ptolemaic’ system, after Ptolemy, the Greek astronomer who perfected it in the second century of the current era. Here’s a simplified diagram of the Ptolemaic model:


Each planet (including the Sun and the Moon) orbits the earth in a perfect circle, but that circle is not quite centered on the earth; it is slightly displaced (the deferent). Moreover, the five “main” planets (Mercury, Venus, Mars, Jupiter, and Saturn) actually orbit around a point that itself orbits the earth. These little circles were called ‘epicycles’. These existed to account for the retrograde motion observed in planets:

Retrograde motion is actually due to the changing geometry as the earth overtakes and passes an outer planet, but in the Ptolemaic system, the earth was stationary, so Ptolemy hypothesized the planet itself goes in a little circle of its own.

I’m sure that you’ll be surprised by this: the real purpose of the Ptolemaic system was to calulate planetary positions for astrology. Right up into about 1700, astronomy and astrology were closely intertwined. The only reason anybody cared about the motions of the planets was so that they could prepare better horoscopes, and for that, they needed accurate tables from which they could precisely determine the positions of the planets at any time in the past or the near future.

The Catholic Church was interested for theological reasons: since the Bible in several places insinuates that the earth is stationary, and the Ptolemaic system confirmed this belief, the Church endorsed the Ptolemaic system.

The problem: bad results
The problem with all this was that the Ptolemaic system didn’t quite work; there were always minor errors in the tables derived from it. Astronomer-astrologers corrected the tables, but in the days before the printing press, it wasn’t easy to lay your hands on the latest, most accurate tables. So the astronomer-astrologers were always introducing additional minor kluges to patch up  the errors in the system. By the time Copernicus came along, the Ptolemaic system looked like Windows would look now if they had never started over with Windows 2, Windows 3, etc, and had simply kept issuing patches and extensions to Windows 1.0.

Copernicus knew about the sun-centered or heliocentric system; indeed, the idea was first floated by Aristarchus of Samos nearly 2,000 years earlier. Copernicus didn’t invent the heliocentric system; instead, he set out to show that it would produce better results than the Ptolemaic system. 

The heliocentric system had two fundamental advantages over the geocentric system. First, it produced a much more natural explanation for retrograde motion. Epicycles were unnecessary to the heliocentric system; retrograde motion came naturally from the simple geometry of the earth overtaking and passing an outer planet. This simplification was a big advantage for the heliocentric system.

The other intrinsic advantage was its simple explanation of why Mercury and Venus always stayed close to the Sun. Instead of artificially forcing them into lockstep with the Sun in their orbits around the earth (complete with little epicycles), the heliocentric system matched the observations with a simpler explanation.

Elliptical orbits
At this point, you’re probably thinking that Copernicus should have triumphed right then and there. But there was a nasty gotcha: the planets did not move in circles; they moved in elliptical orbits. Copernicus was still stuck in the belief that all orbits had to be perfect circles. When he used perfect circles to calculate the motions of the planets, he came up with results that were WORSE than the patched-up geocentric system produced. 

Not to worry: Copernicus could kluge with the best of them. He added deferents to his system, just like the Ptolemaic system had. The results still weren’t good enough. So then he added another kluge: equants — which I won’t explain here. Suffice it to say that they were another form of geometric kluge. 

After much futzing around with the data, Copernicus had a heliocentric model that produced tables of planetary positions that were just as good as those from the Ptolemaic system — but no better. And his deferents and equants were almost as klugey as those in the Ptolemaic system. 

This is why Copernicus held off publishing his results — they just weren’t good enough. He kept futzing over the model, adding kluges here and there, adjusting the numbers, in the vain hope that he could find a combination that produced better results. Remember, in those days, they didn’t have computers, so it was really hard to do the calculations. They didn’t even have slide rules or trigonometry; everything had to be done with laborious hand calculations. Copernicus was sure that he just needed to find the right combination of numbers to get his system working. So he put off publication.

The man who saved the day for Copernicus was Georg Rheticus, a German scholar who was an enthusiastic disciple of Copernicus. He had heard of Copernicus’ work and felt in his bones that Copernicus was right. He traveled to Poland to convince Copernicus to publish his work. After much wrangling, Copernicus yielded to Rheticus’ importunations and Rheticus took the manuscript back to Germany where it was published. He returned with the first printed copies as Copernicus lay on his deathbed. It was published under the title De Revolutionibus Orbium Celestium (On the Orbits of the Celestial Bodies).

Reception of De Revolutionibus
The book was little noticed at first. It was full of arcane mathematical calculations; see my review of another book on the subject for an example. The printer had inserted a preface that said, in effect, that Copernicus didn’t really mean to say that the earth orbited the sun; he was only offering an obscure mathematical technique that produced better results by calculating planetary positions as if the earth did indeed orbit the sun. This was a dirty trick, but it saved the Copernican system from immediate condemnation. 

It is possible that De Revolutionibus would have been forgotten, but another German by the name of Rheinhold took another step that guaranteed the prominence of the book. Three years after the publication of De Revolutionibus, Rheinhold issued a new set of tables of planetary positions based on the heliocentric model. Because he incorporated the latest observations into his tables, his results were easily the best available. Pretty soon everybody was using his tables — which naturally made Copernicus’ book look much better. 

For the next 67 years, not much happened. The Church burned Giordano Bruno for heresy, and one of the items on the list of charges was that Bruno had endorsed the heliocentric model. However, they would have burned him for other, more important heresies.

By the way, the Protestants were no better than the Catholics as regards religious intolerance of Copernicus’ heliocentric model. They condemned him just as vociferously. However, they were disunited and those who embraced Copernicanism could always find a safe place in Northern Europe. 

The the remainder of the 1500s, the astronomer-astrologers all embraced the Copernican model, not so much because its results were clearly superior to the Ptolemaic model; its popularity among the intelligentsia derived from its greater simplicity at first glance. It just seemed better — and they were sure that, if somebody could only find a better set of equants and deferents, it would produce better results than the Ptolemaic system. 

The Resolution
The matter wasn’t resolved for more than a century. It started with Tycho Brahe, a Danish noble who decided to settle things by coming up with the best possible data on planetary positions. He sweet-talked the Danish king into funding a huge white elephant of an observatory on an island, where Brahe carried out the most precise observations every obtained before the invention of the telescope. His results were truly impressive; it’s difficult to imagine how he was able to obtain such accurate results with the naked eye. Brahe was obsessed with accuracy.

But Brahe never did anything with his data. His assistant, Johannes Kepler, stole copies of the data and went to work with it. Kepler was, by modern standards, something of a kook. He took an almost mystical approach the mathematics of planetary motion, convinced that there were secret musical relationships in the heavens. He was frustrated that his frenetic calculations didn’t prove the “Music of the Spheres”, but he did stumble upon three mathematical relationships in planetary motions that revolutionized astronomy. 

A few years later Galileo built a telescope and showed beyond question that the Copernican model was in fact correct. When, fifty years later, Isaac Newton showed that Kepler’s laws were derived from more fundamental physical laws, the issue was finally decided. The Catholic Church caught up with scientific reality a few centuries later.