Hypothesis: Copernicus


Nicolaus Copernicus is credited with setting the earth in motion, which he did, and with putting the sun at the center of the planetary system, which he came close to doing. He wrote of the sun: “In the center of all rests the sun. For who would place this lamp of a very beautiful temple in another or better place than this, from which it can illuminate everything at the same time?... And so the sun, as if resting on a kingly throne, governs the family of stars which wheel around.” Since his system is pretty familiar, I don’t think there’s much to say about it, except to point out how it accounts for the observed loopings of the planets.

A Mars year is longer than an earth year, which means that earth passes Mars at regular intervals. Every time this happens, let’s see what the apparent, perceived motion of Mars is, for us on earth who are watching it.

As you can see, Mars appears to move backwards. So much for the looping. On the other irregularity of motion, the fact that Mars itself seems to speed up and slow down, independent of the moving earth watching it, Copernicus, rejecting the uneven motion created by Ptolemy’s equant, instead used two epicycles per planet, but the effect is observationally identical to Ptolemy’s equant model. Here is a Ptolemaic representation of Mars, with the epicycle removed, to compare with the Copernican, with two epicycles. As I fade back and forth, the position of Mars does change a bit, but the direction does not. The difference is less than a minute, and therefore observationally indistinguishable. In fact, Copernicans would regularly use the equant instead of the double epicycle when doing their calculations, because the math is easier.

Copernicus used these double epicycles, because he insisted that only regular, uniform circular motion could be found in the heavens, but the equant made unequal motion for the planet.

“We must however confess that these movements are circular or are composed of many circular movements, in that they maintain these irregularities in accordance with a constant law and with fixed periodic returns: and that could not take place, if they were not circular. For it is only the circle which can bring back what is past and over with... Many movements are recognized in that movement, since it is impossible that a simple heavenly body should be moved irregularly by a single sphere. For that would have to take place either on account of the inconstancy of the motor virtue -- whether by reason of an extrinsic cause or its intrinsic nature -- or on account of the inequality between it and the moved body. But since the mind shudders at either of these suppositions, and since it is quite unfitting to suppose that such a state of affairs exists among things which are established in the best system, it is agreed that their regular movements appear to us as irregular, whether on account of their circles having different poles or even because the earth is not at the center of the circles in which they revolve.”

So, you see that Copernicus is still a mathematician, not a physicist, and is trapped at looking at everything from a geometrical viewpoint. He allows the earth to have motion, but “shudders” at anything non-geometric (for example, physical) actually moving it.

Ironically, Copernicus’s circle-based motion actually causes the planet to move in an oval! Ptolemy had a circular path for the deferent, with uneven motion, and Copernicus has a collection of even circular motions that make a non-circular path! Does this suggest anything to you?

Now, I said that Copernicus “came close” to putting the sun at the center. While the paths of the planets do encompass the sun, their motions have nothing whatsoever to do with that big ball of fire. Instead, Copernicus used the center of the earth’s orbit to base his orbits on. That is, the entire Copernican system is based on the orbit of the earth, not on the sun. While Ptolemy had the earth at the center, Copernicus has the earth’s center at the center, which is not the same location as the sun. Once Copernicus had determined the center of the earth’s orbit, the actual sun played absolutely no role whatsoever in his system. Why didn’t Copernicus use the sun? Well, because he followed Ptolemy. More on that later.

The tables of predicted observations of the planets made using the Copernican system were much more accurate than those based on Ptolemy. Does this prove that the earth goes around the sun? How much of this improvement was based on his better data? We’ll come back to this after we acquaint ourselves with the third planetary model of Kepler’s era.

Next: Hypothesis: Tycho Brahe