Equivalence of Hypotheses


Now that we’ve covered the three different, contending models of Kepler’s day, let’s see how he approached the problem. Kepler was a convinced Copernican, who dealt humorously with the literalism of those who used the Bible to argue against the motion of the Earth. For example, take the first two verses of Psalm 24:

The earth is the LORD's, and the fulness thereof; the world, and they that dwell therein.
For he hath founded it upon the seas, and established it upon the floods.

Kepler writes in the Introduction to his New Astronomy:

“Suppose someone were to assert from Psalm 24, that the earth is founded upon rivers, in order to support the novel and absurd philosophical conclusion that the earth floats upon rivers. Would it not be correct to say to him that he should regard the Holy Spirit as a divine messenger, and refrain from wantonly dragging him into physics class?”

But, how could Kepler prove the Copernican outlook to be right? In what testable way does the Copernican system differ from that of Ptolemy? Pondering the matter, Kepler came to a shocking conclusion: it doesn’t. Yes, that’s right, there’s actually no observable difference between the systems of Ptolemy, Copernicus, and Brahe, so long as their parameters are all adjusted to take into account the same observations. That is, even though Brahe’s better observations allowed him to make better predictions of planetary observations, those observations could have been used to make the Ptolemaic system equally accurate.

Let’s compare the three systems. Leaving aside the rotation of the earth for Copernicus (or the rotation of the entire universe for Ptolemy and Tycho Brahe), you can see where the sun and Mars will appear to be. Notice that shifting between the different systems makes no difference in the apparent positions. We can even create new systems where a point between the earth and the sun is the center!

Let’s perform the transformation between the three systems, using all of the planets together. First, we’ll take the Ptolemaic system, eliminate the solid orbs, and adjust the orbit sizes as before. Now, let’s pause the motion to concentrate. I can transform this Ptolemaic system into that of Brahe, simply by moving the orbits to the sun. Now, I will go back and forth while the planets are moving.

Now, we have to introduce the double-epicycle. Here it is, fading in.

Now, as we watch the motion of the Tychonic system, I’m going to draw a circle around the mean sun. Sure looks like the earth fits right in, doesn’t it? Now, I’ll erase the orbit of the sun around the earth. What does this look like now? It’s just the Copernican system with the camera focused on the earth. If I center the sun instead of the earth, we have the Copernican hypothesis!

Just for fun, here’s another model, which would have been invented by Ptolemy if he lived on the moon. Such a dweller on the lunar surface could create this lunatic model, in which the moon is the center of the universe. And who’s to say this model is wrong? It creates identical results to the other models we’ve discussed.

So, if there is no difference between these models, if all motion is relative, measured with respect to an arbitrary idea of stillness, how can we come to firm truth in astronomy?

Next: Kepler's Apparent Sun