This is a linkpost for https://www.cricetuscricetus.co.uk/post/copernicus-galileo-kepler-they-all-lacked-proof

Neither Copernicus, Galileo, nor Kepler had proof

22nd Nov 2023

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How do you get a geocentric model with ellipses? Venus clearly does not go in an ellipse around the Earth. Did Riccioli just add a bunch of epicycles to the ellipses?

Googling... oh, it was a Tychonic model, where Venus orbits the sun in an ellipse (in agreement with Kepler), but the sun orbits the Earth.

Kepler's ellipses wiped out the fully geocentric models where all the planets orbit around the Earth, because modeling their orbits around the Earth still required a bunch of epicycles and such, while modeling their orbits around the sun now involved a simple ellipse rather than just slightly fewer epicycles. But it didn't straightforwardly, on its own wipe out the geoheliocentric/Tychonic models where most planets orbit the sun but the sun orbits the Earth.

The Ptoloemaic system can be made as accurate as the Copernican system , so long as you keep adding epicycles. One of the things that tells us is that is that there is more to truth than observational accuracy. They other is that simplicity is important, and probably important for determining which observationally accurate theory is the truest.

The Copernican system actually had more epicycles than the Ptolemaic one.

But yes, you could keep adding epicycles to the Ptolemaic system and change parameters to match the accuracy even of today's planetary movements.

But epicycles couldn't explain hyperbolic movements of objects that only fly into the solar system once.

I'm sure they could if you're willing to sum up an infinity of them. Epicycles are fundamentally equivalent to a Fourier series/transform. The only reason to drop them is that obviously they're a very high complexity rule that can be much more efficiently compressed if you only look at the phenomenon in a different reference frame.

I think those are good lessons to learn from the episode, but it should be pointed out that Copernicus' model *also* required epicycles in order to achieve approximately the same predictive accuracy as the most widely used Ptolemaic systems. Sometimes later, Kepler-inspired corrected versions of Copernicus' model, are projected back into the past making the history both less accurate and interesting, but more able fit a simplistic morality tale.

This article shatters a number of myths about the development of Astronomy. It was pretty much unknown to me until recently that Kepler's ellipses also fitted a Geocentric model made by Riccioli, for example.