In order to understand the investigation process and Galilei's trail we recommend to look at - Lexicon Galileo's trial.
In 1615, the Special Theological Advisory Committee determined that the Copernican theory according to which the earth revolves around the sun, was "philosophically foolish," i.e., physically foolish (See the ban on the Heliocentric theory). How did the Church scholars arrive at a conclusion that is so extreme and strange from our point of view, given that we know that the sun does indeed revolve around the earth. In order to understand the prohibition of the Copernican theory, we must become acquainted with the physical and astronomical claims for and against it. It seems that Galileo and the rest of those supporting the Copernican theory did not have convincing arguments in favor of the earth's movement. In his Dialogue Concerning the Two Chief World Systems Galileo managed to show that the movement of the earth is possible, but he did not succeed in showing that it was necessary.
What were the main claims of the astronomers and natural philosophers (physicists) who supported the geocentric theory? These people worked within the framework of Aristotelian physics and they were the ones behind the Theological Advisory Committee's decision. True to his method, Aristotle showed that the earth is at the center of the world and does not revolve around the sun or any other star. Aristotle's proof was based on the well known fact that all heavy objects fall to the ground. The ground prevents these objects from moving toward the center of the earth. All heavy bodies, claimed Aristotle, strive to reach the center of the world. But the center of the world is already occupied by another heavy body, i.e., the earth. Because the earth is made of heavy material, the center of the earth unites with the center of the world. In other words, all objects fall to the center of the world and are stopped by the earth. There is no reason to justify the movement of the earth, which is a heavy body, around a distant center, when the earth is already located in the natural place of heavy objects, i.e., at the center of the world. The planets, however, are made from ethereal matter, lighter than any substance known on earth, and this is the reason why they are in the sky, and capable of rotating around the earth.
The Copernicans contended that the planets are heavy, and that not all heavy bodies strive to reach the center of the world. Contrary to the Aristotelians, they could not explain how the planets revolve around the sun. At most, Galileo only succeeded in showing that the Aristotelian explanation is unacceptable. Galileo concentrated on refuting the Aristotelian theory, mainly by discussing the similarities between the stars and the earth, and presenting changes in the heavens, contrary to the Aristotelian claim that the celestial ether never changes. His telescopic observations of the moon were central to his explanation that the planets are made from matter similar to that of the earth, and that the same physical laws prevail in both heaven and earth. If the planets too are made of heavy material, this refutes the Aristotelian claim that all heavy bodies strive to reach the center of the universe, for here we have various heavy bodies which do not move toward the center of the earth.
The supporters of the geocentric theory had an explanation for the movement of the stars. The fact that they were made of ether explained their circular motion. The supporters of the Copernican theory had to explain why the stars moved, but until the time of Newton's explanation, they did not have a convincing claim. Galileo, however showed that periodic movement was a natural property of bodies which will continue their motion. The law of inertia showed that bodies will continue their uniform movement, and the pendulum served as an example of a heavy body constantly moving at a changing velocity. Galileo's new mechanics served as the basis for refuting the Aristotelian claims regarding the movement of the earth. With regard to the question of the supporters of the geocentric theory then, why, if the earth moves, do we not feel that motion? They claimed that the fact that we do not feel the motion indicates that the earth does not move. Galileo responded to this central claim in the Dialogue by means of the ship example and the law of inertia. He showed that we do not feel periodic motion. Galileo ignored the fact that the earth's motion is not uniform. Newton showed how the motion of the earth may be felt, although its effect is small. It should be remembered that in 1616, when the Copernican theory was rejected, Galileo has still not published his claims that the motion cannot be felt, which contradict Aristotelian physics.
Those who objected to the Copernican theory also raised an observational, astronomical claim against this theory. As the earth revolves around the sun, the distance from the sun of various places in the world changes from winter to summer, so that the difference from winter to summer is equal to the diameter of the earth's orbit around the sun. Thus, if we look from the earth to a star (whose place in the heavens is fixed) we should see it at a somewhat different angle in summer and in winter, in the same way that we see a distant building from different angles when we stand in two different places.
The change in the star's angle of sight is called parallax. According to the Copernican theory a parallax should have been observed, but it was not observed. Copernicus and his followers explained that it was not observed because the stars are very distant, so that the distance traveled by the earth from summer to winter, is negligible when compared to its enormous distance from the stars. Those who subscribed to the Copernican theory claimed that this was the reason why astronomers had not observed this phenomenon. A parallax was first observed in 1838, almost 300 years after the publication of Copernicus' De Revolutionibus Orbitum. The angle of change is so small that it does not exceed the second of an arc, i.e., less than one millionth of an arc. It's no wonder that they failed to notice such a small change in the seventeenth century.
The supporters of the moving earth theory managed to show that the movement of the earth was possible, but not that the earth actually moves. In his Dialogue, Galileo attempted to explain the ebb and flow of the tide as a by-product of the earth's movement, thus proving this movement according to its cause. However, Galileo's explanation was problematic, and few were convinced. Galileo's followers ultimately rejected this explanation which does not conform with Newton's physics. Newton was the man who supplied crucial proof in favor of the heliocentric theory.
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