What is a fair, balanced assessment of Aristarchus's contribution of heliocentrism?

Hi
After reading numerous articles online on Aristarchus’s contribution to heliocentrism, I’m inclined to think of his conclusions more as guesswork/belief rather than scientific. After all he could not prove any of his theories, and I am still not sure whether he was a Pythagorean mystic (as some claim) or not. Is there any evidence that he was?
I look forward to your feedback.

Pretty much everyone upto and including Copernicus and Galileo was “guesswork/belief” as opposed to proof, the later famously proffered evidence that clearly did not prove his claims; one of the many reasons he got into deep doo doo with the Church.

Some Greek, Indian, Arab (but notably not Chinese) astronomers also occasionally claimed a Heliocentric model, but always a minority. Al-Biruni discusses it in some detail IIRC and so did Selecus.

If I’m remembering my Dead Greek Guys correctly, Aristarchus was able to make sufficient measurements to correctly prove (even within his considerable margin of error) that the Sun was larger than the Earth. That’s not proof for heliocentrism, but it’s certainly significant evidence.

And Copernicus and Galileo did considerably better than guesswork. Galileo was rather a dick about it, but it was academically-sound dickery.

Galileo’s two main discoveries were i) Jupiter’s moons, proving that something’s did not orbit the Earth and ii) The phases of Venus, which suggested that planet orbited the sun.

Neither were (or are) bang on evidence for a heliocentric model. Galileo’s “proof” that the earth orbited the Sun were

  1. The Planet’s all orbited circular; which his own telescopes showed was not the case and

  2. The tides.
    Both were obviously wrong.

The planets’ orbits aren’t circular, but they’re still pretty close to circles. A circles-only heliocentric model qualitatively matches observations in every particular, differing only in fine details, while a circles-only geocentric model doesn’t work at all, and even with the elaborations to make things work, still leaves several points unexplained. For instance,while Ptolemy’s model could produce retrograde motion (via epicycles), and explained why the planets were brightest during retrograde, had no explanation at all for why retrograde motion occurs when the planet is in opposition to the Sun. He also had no explanation for why two of the planets never showed retrograde motion, nor for why those two always stayed relatively close to the Sun in the sky. All of these points are easily explained in a heliocentric model, even one using only uniform circular motion.

The Ptolemaic model, with its complex system of epicycles and equants, ***simulates the planetary motions ***(as viewed from Earth) quite accurately — so accurately that modern planetariums use Ptolemy’s system! (Circular motion is much easier to reproduce than elliptical motion, though the Antithykera machine had a special mechanism to make the lunar orbit elliptical!)

The Ptolemaic model had one specific flaw — the planetary “phases” it predicted (angles wrt sun and earth) were very different than Copernicus’ predictions. It was observations of Venus’ phases that put the final nail into Ptolemy’s coffin.

Thank you all. What I’m still wondering is why the Ptolemaic system works from our perspective on earth but not from space.

Motions along two of the three dimensions are almost correct. The 3rd dimension (distance from Earth) is wrong so Ptolemy gives bad estimates not only for planets’ phases but for their apparent brightnesses.

From a “neutral” standpoint, i.e. that of the super-massive Sun, orbits are almost exactly simple ellipses, but in a geocentric model, the orbits appear very complex. Copernicus of course never caught on that the orbits were elliptical; like Ptolemy he used a complicated system of epicycles. I think Copernicus is overrated, and Kepler underrated. Note that the great astronomer who followed Copernicus, Tycho Brahe, reverted to the mixed geo/helio-centric model of Heraclides — though I see now Wikipedia doubts this attribution:

Returning to Aristarchus, it is interesting that his heliocentrism is especially famous because Archimedes mentioned him and adopted his hypothesis in his Sand Reckoner. I’ll guess that that smartest-mathematician-ever was a heliocentrist but avoided aggravation by mentioning it only briefly!

Make that “One of the three dimensions.” I think Ptolemy ignored declinations of the planets(?).

I had read somewhere that the ptolemaic system somehow forces the circular orbits to behave like ellipses. I didn’t understand how that could be possible. Kepler was the better scientist I think but a poor communicator/writer. Galileo was a better PR man. Did Kepler’s name come up in Galileo’s trial?