"enough evidence to promote his model"

I don't know what this is supposed to mean. For Galileo, his observations that Venus had phases, like the Moon, and that Jupiter had its own moons, and more, were enough to convince him that the Copernican theory was more likely to be correct than the geocentric model. We now know that he interpreted the evidence correctly.

The three links, especially the LW comment, go into details of what exactly this is supposed to mean.

TL;DR: The models that were popular in times of Galileo weren't stories told to poor villagers by the Evil Church; they were precise mathematical tools that could be used to predict in advance the positions of planets, eclipses, etc. They also had an elaborate explanations for what the parts of their models mean. And then comes Galileo with a theory that's inferior, built on arbitrary assumptions, doesn't agree with observation and fails to match the predictive capabilities of established models.

The strength of a model is its ability to predict the future, and therefore no sane, rational person could accept Galileo's model over the common ones based on the evidence they collected and analyzed so far. That's what I mean by "enough evidence to promote one model over another". It eventually took Newton, few decades later, to basically sort things out by providing a) an actual explanation for why stuff would orbit other stuff, and b) mathematical model that spat out better predictions than the previous models did while being also simpler. And only then scientific world moved to accept the new picture - when it became the one that matched available evidence the best (it still took a few hundred years to sort out the kinks though).

People in times of Galileo weren't stupid, the Church wasn't supressing astronomy, and Galileo himself got sacked for being an ass to authority.

Your version of the history and relationships among ideas at the time in physics and astronomy is hopelessly garbled. I respectfully suggest you read Kuhn's The Copernican Revolution. Your comments about people not being stupid, the Church's motivations, etc., if intended as a reply to me, are strawmen.

I'll add that to my ever-growing ToRead list. Since you seem to have read Kuhn, could you elaborate in which parts he disagrees with the sources referenced upthread?

> It eventually took Newton, few decades later, to basically sort things out by providing a) an actual explanation for why stuff would orbit other stuff

I'm not sure how you got here. By the standards you're applying to Galileo, Newton did nothing of the kind. The limit of Newton's explanation for why stuff orbits other stuff is "because it's stuff" (you might say "because the stuff has mass"... but all stuff has mass). That's not much of an explanation.

You can make a judgment call about the relative merits of "new theory, doesn't make numeric predictions well" and "very old theory, makes numeric predictions almost flawlessly, additionally predicts things that we know to be false".

"Because it's stuff" is considerably better than "because it's Quintessence", and "stuff is attracted to other stuff with a force F⃗ = GD̂m₁m₂/D², which accelerates it by a vector m/F⃗, whose integral is its velocity vector, whose integral ∫∫(GD̂(t)m₂/D²(t))dt² is its displacement, and the Sun has a whole hell of a lot of stuff in it, from which we can derive Kepler's Three Laws as follows…" is really a dramatically better explanation than "the natural motion of Quintessence is eternally circular".

But that was Newton, not Galileo. (And the notation of course is more or less modern, except to the extent I've screwed it up.)

The main problem with Copernicus's new theory in Galileo's time, as I understand it, was not that it didn't make numeric predictions well; the problem was that it predicted qualitative phenomena that were "known" to be false, like stellar parallax.

Not so, though. If you read the page about the Tychonic system, you saw that the objection to Copernicus was not "that theory requires stellar parallax, but there is no stellar parallax". It was "If that theory is true, then the fact that there is no stellar parallax implies that the stars are very far away". The Copernicans rightly responded "so what?" But the Tychonians trusted their guts, which told them that that was a priori impossible.

And everything you've said about Newton refers to answering the question of how much stuff is attracted to other stuff, not why it is. He was able to show that the natural motion of everything is circular (unless it's in perfect stasis), and to describe with great precision the form of the circles involved (and how they deform into ellipses), but there's no why anywhere. Newton can't justify the force of gravity varying with the square of distance except by observing that it happens to work in practice. He certainly can't explain why it's not zero -- it could have been zero. (Sure, it's very fair to say he told us why Kepler's laws obtained. But that wasn't the question, the question was "why is stuff attracted to other stuff?")

"...additionally predicts things that we know to be false."

What, specifically did the Tychonic system predict that was known to be false in the early 17th century? As far as I know, the interpretations of its model were kind of a mess, but the model itself was fine, up to the precision of then-known instruments.

Forgive me. "Overtly premised on things we know to be false." Though obviously any argument immediately predicts its own premises. ;)

From https://en.wikipedia.org/wiki/Tychonic_system :

> Tycho admired aspects of Copernicus's heliocentric model of the solar system, but felt that it had problems as concerned physics, astronomical observations of stars, and religion. Regarding the Copernican system Tycho wrote,

>> This innovation expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that.

> In regard to physics, Tycho held that the Earth was just too sluggish and heavy to be continuously in motion. According to the accepted Aristotelian physics of the time, the heavens (whose motions and cycles were continuous and unending) were made of "Aether" or "Quintessence"; this substance, not found on Earth, was light, strong, and unchanging, and its natural state was circular motion. By contrast, the Earth (where objects seem to have motion only when moved) and things on it were composed of substances that were heavy and whose natural state was rest

So, the Copernican system was acknowledged to be mathematically superior, and the Ptolemaic system was acknowledged to be a particularly obvious case of special pleading. The Earth was considered exceptional under the Tychonian system because it was too heavy to be constantly in motion -- as a large terrestrial object, its natural state was rest.

Interestingly enough, I remember learning about a Renaissance scientist who did several experiments to the effect that there is no such thing as a "natural state of rest" for terrestrial objects...

Furthermore, the idea that the Earth is exceptional is severely undermined by the moons of Jupiter. From them, you would see exactly what you see from Earth, and you could readily fit a Tychonian model with a sun going around Jupiter -- but why would you? (This is what I was referring to originally, but this particular argument is slightly weaker than I was thinking of.)

I'll also note that, as far as Wikipedia is concerned, the Tychonic system wasn't exactly well-established at the time:

> It was chiefly through the influence of the Jesuit scientists that the Roman Catholic Church adopted the Tychonic system, over a period of nine years (from 1611 to 1620), in a process directly prompted by the Galilean telescopic discoveries.

The model that most scientists at the time favored (including those in the Church) was the Tychonic system. In the Tychonic system the planets all revolved around the Sun, but the Sun then revolved around the stationary Earth. This had the advantage of correctly predicting things like the phases of Venus.

The reason that it was preferred over the Copernican system was that it additionally predicted that parallax of the stars should not be observed. At the time astronomers had looked for parallax as a way to test the Copernican system, and had not observed it. This was the strongest point in favor of the Tychonic system. As it happened, the stars were much further away than astronomers at the time realized, so the parallax was much smaller than they could have detected with the instruments of the time. (In fact, it took more than two centuries before parallax was detected.)

But the point is that I think that if any of us were alive at the time and took careful stock of all the evidence most of us would probably come to the same conclusion that most of the astronomers of time did. Namely that, while interesting, the Copernican system did not have as much evidence supporting it as the Tychonic system did. But if Galileo had built a Foucault pendulum instead, it would have been a very different story!