# Would Copernicus have been more convincing if he’d been more accurate?

As a follow-up to yesterday’s post, I was wondering if Copernicus would have been more convincing if he’d used ellipses in his model instead of circles. By using circles Copernicus had to use epicycles like Ptolemy, though not so many. Still, it gave the impression that epicycles were necessary. If that’s the case then why not have a stationary Earth as well? The discovery that planetary motion would be better described by ellipses didn’t come about till Kepler’s work almost a century later. As far as the post title goes, I think Dr* T’s Theory #1 applies here: Any tabloid heading that starts ‘Is this.…’, ‘Could this be…’ etc. can be safely answered ‘No’

So my post title is a bit of a cliché, but the reason I’ve used it is that if the answer is no, then something strange is happening. More accurate is less convincing?

The reason I think that is that Copernicus’ model wasn’t isolated from the rest of thought for that period. It used and built on a number of assumptions of the time. One of those ideas was the creation of the universe by a perfect being. Another was the idea that a circle was a perfect shape, derived from classical geometry. By telling people the Sun was at the centre of the universe and not the Earth, Copernicus was asking people to make a big shift in their thinking. A lot of people thought it nonsense. If he’d made the orbits elliptical as well then many people who would have been willing to listen to Copernicus’ ideas would have balked at that, reducing his potential audience further. In terms of numbers, the population of mathematically minded people who could examine his work was small enough already.

If he’d reduced the number of initial readers further, would his ideas have spread enough for others to pick them 50 years later? It’s impossible to say, but if Copernicus hadn’t given Kepler the idea of a putting the Sun at the centre of universe, could Kepler have discovered it independently? It’s hard to say but, given how Kepler struggled with letting go of circles and using ellipses, I think it’s unlikely.

This is why I’m wary of histories of science that are purely about who got it right and who got it wrong. Copernicus’ use of circles isn’t ‘right’, but it was necessary at the time.

I’ve «cough» borrowed the portrait of Copernicus from Prof Reike’s page on Copernicus. It’s well worth visiting if you want to find out more about the astronomer.

You can read more about Kepler’s discovery of the elliptical path of planets at:

Boccaletti 2001. From the epicycles of the Greeks to Keplerʼs ellipse — The breakdown of the circle paradigm

Thanks for these last couple of posts. I wanted to add though that, rather than, as you seem to suggest, Copernicus keeping circles to make his heliocentric ideas more palatable to his audience, it was his desire to bolster the classical ideal of uniform circular motion that led him to heliocentrism. His use of circles was not just “necessary at the time” but a fundamental driver to the development of his theory — as, in fact, was his reverence for Ptolemy, on whose

Almagest Copernicus modelled the structure ofDe Revolutionibus.Thanks for adding that. I think that shows even more that setting up Ptolemy and Copernicus in opposition to each other doesn’t work historically. I know that’s well-known to Renaissance historians, but it’s surprising how much of the popular belief about this period is wrong. It reminds me I really need to get a copy of Gingerich’s “The Book Nobody Read”.

Just another point to make here. We know that ellipses are correct, because Kepler eventually convinced everyone about it. But Kepler had available a much larger, and much more accurate set of data on planetary motions, compiled by Tycho. It was only when circular orbits no longer matched the data, that Kepler abandoned circles. Copernicus had only the data currently available at the time (and he made almost no observations himself). He simply reworked the cosmological system to heliocentrism with the same data. The result was predictive models just as accurate as geocentrism–very important to make heliocentrism even plausible from the standpoint of technical astronomy.

But the major objections to heliocentrism since antiquity always had come from physics–how can we justify a moving earth, when it so visibly appears stationary to us? Accuracy or inaccuracy of the mathematical system played little role.

The main motive for Kepler’s discoveries was to adjust the recorded observations to take account of Copernicus’s discovery that the Earth as the observation point was not stationary but orbited round the Sun.

Further to my comment of 5 April 2011, how does Galileo fit into this? Galileo and Kepler were contemporories and were both in agreement with Copernicus, but Galileo did not agree with Kepler’s elliptical orbits. However Galileo did discover the law of falling bodies v^2=d which can be incorporated into Kepler’s system. The works of both Galileo and Kepler suffered from religious prohibition, which explains even to-day why these works are not as well known as they should be.

Further to my comment of 15 April 2011, the connection between Galileo’s v^2=d at the empty focus end of the elliptical orbit and Kepler’s v^2=(1/r) at the Sun focus end is mathematically incredibly interesting and not at all straight forward. Kepler’s version can be adapted for further research purposes by including a constant V being the maximum velocity, then the variable velocities can be expressed as V/#r where # is my notation for square root. In this way the same velocity arises on both the accelerating side as well as the decelerating side, but in opposite directions. As one of the properties of all perfect ellipses d is the distance from the curve to the empty focus, and r is the distance from the curve to the Sun focus, d+r equals the major axis of the elliptical orbit.

Further to my previous comments, in about 1600 to 1603, Kepler wrote a paper which does not seem to be mentioned among his listed works. This paper contains the title Conic Section and is written in both Latin and German. What this paper contains is mention of pins and thread. This would indicate that Kepler knew about the way a perfect ellipse should be drawn, even though the paper’s description is not complete. Kepler does mention elsewhere that one of his biggest problems was trying to reconcile Apollonius’s conic section with the perfect ellipse which is a cylindric section containing foci.