The Observational Equivalence of the Tychonic and Copernican Systems

by Frederick Gregory
Department of History
University of Florida

Suppose with respect to one's position on earth (E), the sun (S) and Mars (M)occupy the relative positions given in the figure at the left below. Suppose further that after the passage of a certain time the relative positions are as they appear in the figure at the right below.

The question is, what motions produced the change from the first to the second relative positions? Tycho says, "That's obvious. What has happened is that in the time it takes for the sun to travel 90 deg Westward around the earth, Mars moves 30 deg. Eastward around the sun." We can see what would happen in the diagrams below. Assume for the moment that the dotted lines ES and SM are rigidly attached to each other at S in the shape they have on the right side of the diagram below. Also, let the two motions Tycho referred to above (which actually occur simultaneously) take place one after the other; i.e., assume that as the rigid dotted arm ESM rotates 90 deg Westward it remains rigidly locked in position until it reaches the end of the rotation. Then unlock the line SM and let it complete its rotation Eastward 30 deg around the sun at S. I show this motion in the diagram at the right below by letting the dotted lines represent the initial position and the solid lines represent the final position. If the rotations happen as Tycho says, then the earth, the sun, and Mars end up in the relative positions depicted in the right-hand diagram above.
"No, no, no," says Copernicus. "That's not what happens. What occurs is that both the earth (E) and Mars (M) travels around the sun (S) as center and in the same Westward direction. In the time it takes E to move 90deg around the sun Mars (which travels slower than the earth)  goes through 60 deg. That's why they end up in the positions they do." To see this do as before; i.e., first let E move around S and then move M (Mars) 60 deg in the same direction.
The major point is that we cannot decide whether Tycho or Copernicus is right from any observation taken from earth. Each theoretical framework accounts for the relative positions of the bodies E, S, and M at every instant. The lines of sight as taken from the earth are the same in both systems. Even a telescope will not help here. If we are going to argues for or against one of these systems it will have to be on other than simple observational grounds.