Quote:
Originally Posted by Hornblower
Once Kepler nailed down the elliptical orbits and the equal-area rule, the position errors went away. That alone did not rule out a geocentric model. An exercise in vector algebra could have transformed the whole thing into one with a stationary Earth, the Sun orbiting it in a Kepler ellipse, and the other planets orbiting the Sun in Kepler ellipses. That would have been an adaptation of Tycho's model, and the resultant apparent motions of the planets would have been the same.
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This is true. But they would then have had to use elliptical orbits in this geocentric or hybrid universe, and that violates the original ancient Greek idea of "perfect" circular motion. Even Copernicus didn't dare to violate that principle.
The ancient Greeks did not merely think that earth was center of universe, but combined this with a bunch of philosophical nonsense also, such as the notion that all celestial motions were "perfect": perfect circles and made of "perfect" substances like a ghost. It would have been unthinkable to them to use ellipses for orbits , which is why Ptolomy tried to salvage geocentrism with "equants" "deferents" "epicycles" "eccentrics" and weird stuff like that with perfect circles, just to make the theory accord with measurement. But after Tycho/Kepler, perfect circles just couldn't do it any more. Of course, you are correct that these elliptical orbits were due to Newtonian gravitational thoery and that really was the clincher. But my point was that after Tycho/Kepler, this MAJOR paradigm shift from "perfect" circles to ellipses had to be made, and any honest thinker would say to himself" "how come the Greeks got all this "perfection" nonsense wrong , maybe the geocentric theory itself is nonsense also. So maybe I better rethink this whole thing from scratch and forget everything the Greeks taught"
The ancients were only able to hide their crude models under poor observations: they only got away with geocentrism with ad hoc inventions because of this lack of detail. After Tycho ramped up the accuracy I'll say by factor of 10, there was no hiding the details of the orbits any more. Ptolemy would never have been a good enough magician to hide the truth if Tycho's measurements were known in his day. If Tycho lived at same time in history as Ptolemy, the "Almagest" would have never been written, because Ptolemy wouldn't have had a clue how to handle Tycho's data. Even Kepler himself was reluctantly dragged into ellipses.
I really think after Kepler the ball game was over. And don't forget the harmonic 3rd law. How come this law works relative to sun and not relative to earth? Only possible answer: because the objects are orbiting sun.