Purpose: To present the evidence for and against the establishment of the
Copernican-Keplerian system as scientific fact as of 1633, the time of
Galileo's trial. To this end, it is necessary to clarify the meaning of
scientific fact. I will then turn to evidence in support of planetary
motion around the sun and finally to that in support of the Earth's motion
around the sun.
On Scientific Facts:
Science is known for producing many theories, but it is relatively rare that science offers scientific facts. Some theories are exceptionally good; those are such which are supported by reliable observational evidence and are highly successful at prediction. But theories are not set in stone; there is the expectation among scientists that theories are (and should be) revisable. Science involves making assumptions and accepting theories, even if those assumptions and theories are not (yet) demonstrable fact. In a study so prone to assumption revision, how can any certainty be established? At what point may a theory be accepted as a fact?
In the 1600's the Church found itself asking much the same questions. The Church was the authority of scientific facts and did not want to endorse any theories which might later be shown to be false. In Galileo's time as with today, the Church did not want unproven hypotheses to be taught as fact. The relevant question at Galileo's trial, then, was whether the evidence and support in favor of the Copernican-Keplerian system (herein referred to as the Copernican system) was strong enough for it to be established as a fact, in the way that the scientific community now accepts Darwin's theory of evolution as a scientific fact.
The reader is at his discretion to determine what is meant by ``enough'', although the following, which I take to be characteristics of scientific facts, may provide a helpful guide. A theory may be considered a scientific fact if it satisfies these criteria:
On Planetary Location:
With the above criteria for scientific facts in mind, I now turn to the consideration of planetary motion and the (alleged) falsification of the Ptolemaic theory that the sun, moon, and all the planets revolve around the Earth.
Before Galileo there was much suspicion about the veracity of the Ptolemaic system. Although it was able to predict, to some degree of accuracy, the apparent locations of the planets, the Ptolemaic system relied on an equant and non-uniform circular motion, leading to a complicated explanation of the appearance of retrograde loops in planetary position. It was against this background in 1543 that Copernicus posited an alternative theory. The actual path of the planets, he said, need not trace out loops; instead, these loops may be only apparent, the result of the combined motion of the planets and the Earth.
With the discovery of the telescope, Galileo was able to amass much evidence in favor of the motion of the planets in orbits around the sun. These discoveries included:
A further argument in favor of the Copernican theory with its nearly circular planetary orbits around the sun is that it had greater mechanical explanatory power than the Ptolemaic epicycles (with respect at least to planetary motion). The Copernican theory appears to be the more likely of the two theories to supply explanations for the motions of the planets.
I believe that at the time of Galileo's trial, most astronomers (and even many within the Church) had given up on the Ptolemaic theory (probably in part because of Galileo's writings). Many scientists believed that telescopic observations had falsified the Ptolemaic theory. The theory could likely be revised to explain the phases of Venus and elliptical planetary orbits (as determined by the 1631 transit of Mercury across the sun), but this would significantly complicate the theory. The Copernican theory appeared to most at the time to be the better theory. I point this out not to confuse the opinions of the community with evidence for the scientific factuality of the Copernican theory, but to convey the scientific context in 1633. I believe that after Galileo's observations, the Ptolemaic theory never enjoyed a strong scientific following. I conclude that, by 1633 the Copernican theory had demonstrated predictive superiority over the Ptolemaic and observation evidence had established as fact the falsity of the Ptolemaic theory.
Yet even if (as may be the case) the falsity of the Ptolemaic theory was a scientific fact, this is not to say there was proof of the Copernican theory. There were many scientists who, while denying the Ptolemaic system, did not accept the Copernican system. For many of them, the alternative Tychonic system, curiously ignored by Galileo, was appealing. The remainder of this brief will be a consideration of the distinctions between the Tychonic and Copernican systems.
On the Motion of the Earth:
Like the Copernican system, the Tychonic system places the planets in motion around the sun. The Copernican system, however, is the only one of the two to place the Earth in motion around the sun. Tycho Brahe, unconvinced of the Earth's motion, conceived of a system in which the sun was a satellite of the Earth. Relative to the positions of the sun, moon, Earth, and planets (though not with respect to the stars), the Copernican and Tychonic systems are observationally equivalent. These two systems are also mathematically equivalent; one can perform a geometric translation between them. It is clear, then, that appeals to evidence of planetary location (relative to the celestial bodies above mentioned) can not be sufficient alone to establish the Copernican theory as scientific fact.
These systems do differ, however, in the actual positions of the Earth and the sun, as relative to the fixed stars. Tycho devised an empirical test based on annual parallax of the stars to distinguish between the two systems, but as of 1633 there was no means to accurately determine stellar parallaxes, so the results of the test could be read as consistent with either system. Without some way of viewing a fixed point in the universe as a reference, there seems to be no way to way to distinguish between the two systems based on astronomical evidence.
Despite observational similarity in location, the Copernican and Tychonic systems differ in physical motion and so can be distinguished by appeal to mechanics. According to the Tychonic system, the Earth is fixed; according to the Copernican, the Earth is in motion. For evidence in favor of either system, then, one needs only to support or contradict the claim that the Earth is in motion.
Perhaps the most obvious objection to the Copernican theory is this: The Earth cannot be in motion because we don't observe this motion. To address this objection, Galileo significantly revised (Aristotelian) physics. Galileo explained that the Earth's change in location would not be observable relative to other objects on Earth, since there is no relative change in location. Galileo considered free fall motion and concluded that the assumption that the objects would not move along with a moving Earth is false. What Galileo did was to systematically establish, beyond reasonable doubt, the falsity of many of the assumptions underlying the claim that the Earth cannot be in motion.
Galileo offered two positive arguments in favor of the Earth's motion: sunspots and the existence of the tides. He believed that these arguments provided the strongest evidence in support of the Copernican theory, as they provided mechanical explanations for observed physical effects.
Galileo observed that sunspots undergo no detectable movement in a daily period; that is, the solar axis cannot sensibly change its tilt with respect to the Earth. For this to be the case under the Tychonic system, the sun's motion must be the combination of two rotations - one annual and parallel to the sun's axis and another daily and at an angle to the axis. However, under the Copernican system, this motion immediately follows from a mechanical explanation. One could argue that the Tychonic theory's explanation of the motion was needless complicated whereas it made physical sense according to the Copernican system, although perhaps this argument is not very strong.
Similarly, Galileo believed that the tides provided evidence for the Earth's motion. He asserted that the tides could not be explained physically without the motion of the Earth. He believed the rotation and revolution of the Earth provided a mechanical explanation of the tides. His theory of the tides is not without fault, though, for it implied one high tide (rather than the observed two) per day. Galileo's theory of tides was not accepted as a matter of fact by astronomers in 1633; in particular, some followers of Kepler attributed the cause of the tides to the moon. There does not appear to have been any evidence at the time to conclusively determine the superiority of Galileo's explanation of the tides.
It appears that, in contrast to the case for the motion of the planets around the sun, the evidence for the motion of the Earth is inconclusive. That is, many of the observations said to support the Copernican theory are also consistent with the Tychonic theory. Perhaps the strongest observational evidence offered by Galileo for the Copernican theory was his theory of tides, but that was not sufficiently supported. However, the case for the Copernican theory might be made not on the basis of observation, but on grounds of simplicity, as follows:
We have already demonstrated that the motion of the planets is not centered around the Earth, but around the sun. We then know that the sun is in some way privileged over the other celestial bodies. We observe that (at least) one of the Earth and sun must be in motion. Though it may be difficult to conceive (since we and our observations are on Earth), there is no scientific reason to consider that the Earth is in any way privileged. (The argument that the Earth was privileged by having a moon was defeated by the 1610 discovery of Jupiter's Galilean satellites.) It is conceptually simpler for the Earth to rotate around the sun than for the sun to rotate around the Earth. This supports the Copernican theory.
The observed motion of the planets is the same according to both theories, but the actual paths traced out by the planets is far simpler in the Copernican than in the Tychonic case. Observations show that either the Earth or the entire stellar sphere rotates daily. As it is much simpler for the Earth to move than all of the stars to do so, the Copernican theory is preferable to one in which the Earth is fixed (neither rotates on its axis nor revolves around the sun). The Tychonic theory appears needlessly complicated when compared with the mathematically equivalent, yet simpler, Copernican theory.
Furthermore, the Copernican theory can be seen to have greater explanatory power. According to the Tychonic theory, the planets orbit around the sun which is itself orbiting around the Earth. The gravitational (``magnetic'') forces at work must be able to explain how the planets are twice moved (once by the sun and once by the Earth). Under the Copernican theory, the planets are moved only once, and the source of this continuing motion can be attributed, as Kepler conjectured, to the sun. The motion of the Earth can be described in precisely the same way as the motion of the other planets. Whereas it is inconsistent with the Tychonic theory, it is consistent with the Copernican theory to identify the sun as the source of the motions of all of the planets, including the Earth. Accepting the premise that the center of motion is also the source of motion, Kepler argued in his Epitome that the Copernican theory is simpler than the Tychonic. As the sun is larger than the Earth, Kepler believed that it made more sense for the sun to be the source of the Earth's movement rather than vice versa. Additionally, Kepler's theory in which all of the planets, including the Earth, revolve around one body and share one source of motion is simpler than a theory in which there are several sources of motion.
The location of the Earth (with its period of revolution of 365 days) between Venus (225 days) and Mars (687 days) can be explained by the Copernican system. Kepler noted that the linear speeds of the planets farther from the sun are less than that of those closer. As a result of this observation, he suggested a specific inverse correlation between distance and speed, the occurrence of which could be explained by appeal to his belief that the sun was the cause of planetary motion. The fact that under the Copernican system the location of the Earth between Venus and Mars is a direct consequence of Kepler's 3/2 power rule, whereas the location of the Earth with respect to the other planets is only a coincidence under the Tychonic system can be seen as further support for the Copernican system. The Copernican theory, then, seems the more likely theory to yield simple answer to questions of planetary locations and how and why the planets move.
It is argued that the above reasoning, as well as the fact that the Copernican system offers a mechanical explanation for the tides, is sufficient to discredit the Tychonic system, leaving the Copernican system unchallenged. On the other hand, it is argued that establishing the simplicity (or superiority) of one system over another does not establish the one theory as a scientific fact. Instead, in this case it shows that the Copernican model is more elegant and more aesthetically pleasing. This is a philosophical rather than scientific argument. Appeal to Ockham's razor and explanatory power does make the Copernican theory the better theory and a more likely candidate for being established as scientific fact, but without bolstering this reasoning with observational evidence (such as that reviewed in this brief), the Copernican theory is not established as fact.
Conclusion:
It is my belief that the Copernican theory had demonstrated predictive superiority over the Ptolemaic theory and explanatory superiority over Tychonic. It remains to determine whether the Copernican theory, which had some very strong observational evidence as well as aesthetic appeal, should have been considered to be a scientific fact in 1633 or if it was just one of many theories being explored by scientists.