Proven in what sense? In the past one hundred years, it has been shown that the laws of general relativity hold–so that any frame of reference is valid. If you could show that there was a preferred reference frame, it would invalidate GR.
Ah, great debates.
rocks
Stellar parallaxes invalidating Brahe? Simple. You basically have two possibilities: 1) everything revolves around the Earth, or 2) not (yes, I know about the argument from GR; it’s wrong, as I shall shortly indicate). Now, perform a Gedankenexperiment; you sail some thousands of klicks above the North Pole, and fix on some star; let us say, Sirius. If Sirius revolves around the Earth, then, over the course of a year, we will see it describing a circle in the sky normal to the axis of revolution (but not necessarily a great circle (diameter) if it’s embedded in a crystal sphere, or some such). If, OTOH, Sirius and Sol are (more or less) fixed with relation to each, and the Earth is revolving around the Sun, then the line-of-sight to Sirius must change in six months, and Sirius’ location will show parallax. If you can demonstrate stellar parallax, then you can kill most geocentric systems (the one in which the Sun and the Moon revolve around the Earth, and everything else revolves around the Sun, takes a little more work).
As for GR, the notion that there are no privileged frames of reference in it is, mildly put, a misunderstanding. There are no privileged inertial (i.e., unaccelerated) frames in GR. An orbit, however, is an accelerated frame, and it can be shown that the laws of physics must be interpreted differently in accelerated and inertial frames. Thus, GR does not allow us to assume that the Earth is standing still, and everything revolves around it.
“I don’t just want you to feel envy. I want you to suffer, I want you to bleed, I want you to die a little bit each day. And I want you to thank me for it.” – What “Let’s just be friends” really means
That’s SR (special relativity). Accelerated frames are allowed in GR.
Yes, they’re allowed for, but the laws of physics are different in accelerated frames. It’s possible to differentiate between an inertial FOR and an accelerated FOR.
All inertial frames are equivalent, and that’s where the laws of physics are determined (to take two examples: Coriolis effect is an actual force in an angularly accelerated FOR, and objects can move at FTL speeds in such a frame. But we don’t derive physical laws from such a frame).
“I don’t just want you to feel envy. I want you to suffer, I want you to bleed, I want you to die a little bit each day. And I want you to thank me for it.” – What “Let’s just be friends” really means
The second sentence is true, but the first sentence is false. The laws of physics are the same in all frames of reference. In fact, that was one of the three main principles that Einstein used to guide his development of GR.
rocks
And let’s not forget that, in GR, the Earth isn’t accelerating, other than its rotation about its axis. Gravity is a fictitious force in GR, and the Earth moves along a geodesic in space-time.
“There are only two things that are infinite: The Universe, and human stupidity-- and I’m not sure about the Universe”
–A. Einstein
RM Mentock writes:
“I don’t just want you to feel envy. I want you to suffer, I want you to bleed, I want you to die a little bit each day. And I want you to thank me for it.” – What “Let’s just be friends” really means
The Sun does not revolve around the Earth. the Earth does not revolve around the Sun.
Everything revolves around The Straight Dope! ALL PRAISE MIGHTY CECIL!!!
The rest of you are heretics. Die, he suggested. 
You should tell the truth, expose the lies and live in the moment."-Bill Hicks
“You should tell the lies, live the truth and expose yourself.” - Bill Clinton
I’m not sure what you mean by this. It is fairly easy to tell if your reference frame is “accelerated,” but that’s a local measurement. I just noticed in another post that you said “GR does not allow us to assume that the Earth is standing still, and everything revolves around it.” But it does.
Here is a quote from Einstein: “The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS [coordinate system] could be used with equal justification. The two sentences, ‘the sun is at rest and the earth moves,’ or ‘the sun moves and the earth is at rest,’ would simply mean two different conventions concerning two different CS.” (The Evolution of Physics, by Albert Einstein and Leopold Infeld)
ObGalileo: Boris B’s (posted 04-14-2000 05:50 PM) second link says that Galileo was “excommunicated … when he totally refused to recant his heliocentric view.” Of course, he did recant, didn’t he? And his famous eppur si muove may be a legend. The other two links appear to be both from Florence–perhaps it’s just a local legend for the tourist trade?
rocks
Oh? And how then is the Coriolis effect explained in the geocentric model?
“I don’t just want you to feel envy. I want you to suffer, I want you to bleed, I want you to die a little bit each day. And I want you to thank me for it.” – What “Let’s just be friends” really means
Well… Galileo was working with a heliocentric system that did have some flaws.
The geocentric model, from the Catholic perspective, had the benefits of being endorsed by Ptolemy and Aristotle. The view was simply that the stars are embedded in a crystal shell surrounding the Earth. Inside that crystal shell are a series of crystal spheres inside which are embedded the sun, the moon, and the focus of the planets’ epicycles. Ptolemy explained the retrograde motion of the planets with epicycles: the planets theoretically revolved on circles with a fixed point on the crystal shell at the center. It wasn’t perfect, but neither were the instruments of astronomical measurement at the time.
Anyway, the heliocentric Copernican system predicted the motions just as well as the Ptolemaic system, but not necessarily better. In order to make the predicted motions of the planets match the observed motions, it was necessary to add epicycles just like Ptolemy’s system. (Mathematicians didn’t stop with just one epicycle, either. Sometimes they added “epicycles on epicycles,” sometimes to the fifth or sixth degree.)
It wasn’t until Johannes Kepler finally concluded that planets don’t move in circles, but in ellipses with the sun at one focus that the geocentric view finally became obsolete. It could no longer predict the motions of the planets better than its competing system.
Kepler had access to Tycho Brahe’s highly accurate observations of the positions of the planets. Tycho’s observatory, Uranienborg, was a product of Renaissance ingenuity and was more accurate than anything Ptolemy or Aristotle had access to. Kepler had to develop mathematics that explained the observed motions, and the Copernican system (the one that Galileo was arguing disproved the Catholic dogma) was simply not up to the task.
The question of stellar parallax has been answered sufficiently.
The point is that Galileo was not operating on the certainty provided by Kepler. If the church challenged him to predict the motions of the planets within 2 minutes of arc, he would have given inaccurate predictions. (Mind you, so would anyone in the church. But still, what would that prove?)
It’s sort of like nowadays listening to Michio Kaku talk about how everyone should accept the superstring theory because it’s such an “elegant and beautiful” theory. Yes, but you can’t prove it, and you can’t use it to make predictions that differ from the Einsteinian physics we already have. For all we know, in fifty years, people will be wondering why no one would listen to Kaku because everything he said has turned out to be correct. And who knows, maybe in a hundred years people will be writing scathing e-books about critics of superstring theory and about the repressive political and religious environment in 2000.
I think it’s been pretty much established that Galileo wasn’t the abused genius that a lot of sources make him out to be, but religious groups did try to suppress scientific information as a means of eliminating evidence that God may not exist. Galileo, as it happened, has become a pretty good martyr for the anti-Catholic and anti-Christian and anti-religion movements, since he’s practically a household name (I don’t know why he’s managed to rise above other noted individuals like Copernicus and Brahe… serendipity, I say, serendipity!). So the church has a mostly-undeserved mark of nastiness that it doesn’t entirely deserve, and Galileo has gotten a lot of free press. Oh well, that’s the kind of thing that makes the world go 'round, ain’t it?
-SPOOFE
The advantage of the Copernican system over the Ptolomaic system is not that Copernicus predicted the motions exactly, while Ptolomy did not. The advantage is, that if you take either system to a first approximation (i.e., no epicycles, equants, or other nonsense, just circular motion), then the Copernicus is MUCH closer than Ptolomy to observation. The simplest form of the Copernican system already predicts retrograde motion, variations of angular size/brightness, and why Mercury and Venus never stray far from the Sun in the sky. The simplest form of the Ptolomaic system just can’t do this.
“There are only two things that are infinite: The Universe, and human stupidity-- and I’m not sure about the Universe”
–A. Einstein
The sphere of air revolves around the Earth just like the sun and planets do.
Peace.
Chronos
I won’t dwell on this one, but “the simplest form” of the Ptolemaic system still includes epicycles. The epicycle is the basis for Ptolemy’s explanation of planetary motion. It’s the only way he could reconcile a geocentric universe with the observed motions of the planets. Ancient astronomers may have made some false assumptions, but they weren’t idiots. They could plot the paths of the planets across the sky over the course of several nights and observe the occasional retrograde motion. If Ptolemy hadn’t been able to predict these motions within an acceptable margin of error (for the time), then no one would have seriously considered his system. They probably would have reluctantly accepted the sun-centered cosmology proposed by Aristarchus of Samos, or less likely, formed a doctrine that the planets were physical manifestations of the gods.
Granted, the Copernican system did not rely so heavily upon the epicycle. But in the early Renaissance, no one was proceeding on the assumption that epicycles were wrong, which is why few were eager to discard the Ptolemaic system.
I guess Galileo did have one other argument against the geocentric model of the Catholic church, and that was his discovery of the four large (Galilean) moons of Jupiter, which proved the existence of heavenly bodies revolving around something other than the Earth. Still, this is indirect proof by any standard. The conflict between Galileo and Catholicism was not entirely free of politics on either side.
Grant no more. According to Koestler’s The Sleepwalkers, Copernicus used more epicycles than Ptolemy.
rocks
The Sleepwalkers! I read that book for my overview of astronomy class… but then I sold it back… 
Anyway, Copernicus did use more epicycles than Ptolemy. But Copernicus was living in a different time. Astronomers of Copernicus’ time were adding extra epicycles to Ptolemy’s system as well, trying to get the predicted motions right. It was something of a fad, I suppose.
Ptolemy was probably satisfied with simply explaining away retrograde motion, even if the calculations were a bit off.
Probably? What is that?
The old astronomer/astrologers were using Ptolemy to predict eclipses. They thought it was hot shit (another term for occam’s razor) that you could explain the motions of the sun, the moon, and all the planets with only 40 epicycles.
rocks