Few days ago, we were having lunch at the Climate Studies Division. It’s an ordinary lunch, with each of us bringing our own food we bought from the cafeteria or cooked at home. Then the issue of the sun being the center of the universe came up.
I think it is difficult to prove the Copernican assertion that the sun is the center of the universe. Even for the case of the sun and the planets, it is not obvious to me that the planets, including the earth, revolve around the sun. It is true that that the orbits are simpler if we make this assumption, but does it correspond to reality? This is the essence of the third point of St. Bellarmine in his letter to Foscarini. It is possible that the Sun revolves around the earth and the other planets revolve around the sun as in Tycho Brahe’s model. But how do we differentiate between these two?
Let us assume that the Newtonian physics is valid, i.e. the laws of motion and gravitation. Of all planetary orbits, the precession of Mercury’s perihelion cannot be accounted by Newtonian physics in the heliocentric model. The usual answer provided is Einstein’s General Theory of Gravitation. But let us stick to Newtonian physics. Let us propose the following thesis statement: “The anomalous precession of Mercury’s perihelion of 0.43 arc second per year, which is computed using General Relativity, can also be computed using Newtonian physics in the Tychonian model.” The motion of the sun around the earth would generate non-inertial forces on Mercury making it precess.
This thesis statement can be easily proved or disproved using a computer simulation. I cannot still find a theoretical analysis for this. I am tried attacking this problem years ago using epicycles in geometric algebra, by approximating an elliptical orbit as a sum of an eccentric, deferent, and epicycle, as done by Copernicus. This is only as far as I have done. I still have to make the sun rotate around the earth and construct the differential equation for Mercury’s corrected orbit. The solution may require expansion using several epicyclical Fourier harmonics. I’ll go back to this problem again when I have time.
