In 1543, the Polish astronomer Nicholas Copernicus published his book On the Revolutions of the Heavenly Spheres, describing the heliocentric model of the solar system. The book was printed in Nuremburg, where Andreas Osiander, a Lutheran theologian, knowing that the book was likely to meet with opposition from Luther and Melancthon, added a preface to the book stating that the system it described was not to be taken as physically true but only as a mathematical convenience for carrying out astronomical calculations. Many people assumed that this preface had been written by Copernicus himself, but Galileo clearly perceived that it was in complete contradiction to the tenor of the entire book and had to have been written by someone else.
Copernicus assumed that the motions of the planets around the sun were circular. This meant that his theory required epicycles in order to make accurate predictions, just as Ptolemy's model did. The chief virtue of the Copernican model was not mathematical but conceptual simplicity. For instance, it explained the retrograde motion of the planets (when they appear to move opposite to the usual direction relative to the stars) in a natural way, and it made more physical sense considering the sun's much larger size than earth's.
Galileo, in his early years as a professor of mathematics at the Universities of Pisa and Padua, knew about the Copernican theory, but he continued to teach the accepted Ptolemaic system and to use it for astronomical calculations. During this time he was mostly occupied with studies of mechanics. It seems that Galileo came to believe in the physical reality of the Copernican system on the basis of his theory of tides. This theory, now discarded, explained the tides as a kind of sloshing of the seas set up by the earth's changing motions about the sun. (The general idea behind the theory can be conveyed by imagining a tub of water carried in a whirligig ride at an amusement park.)
In the summer of 1609, while in Venice to visit some friends, Galileo heard about the invention in Holland of a ``spyglass'' that could make distant objects appear near. The military applications of such a device are obvious, and Galileo, probably motivated mainly by the financial prospects, set about to re-invent it independently. Having constructed a telescope of about twenty power, he turned it on the sky and rapidly made several key discoveries:
1. The four major moons of Jupiter.
2. The phases of Venus.
3. The changes in apparent sizes of Venus and Mars.
4. The mountains of the moon.
5. Sunspots.
6. The small apparent sizes of the stars.
The first three of these discoveries were striking confirmations of the correctness of the heliocentric theory. The moons of Jupiter constitute a solar system in miniature and prove that at least some celestial objects revolve around a body other than the earth. The phases of Venus and changes in apparent size of the planets had been predicted by Copernicus, and the failure to see these effects had been considered up to then as evidence against the heliocentric theory. Galileo showed that the failure to detect these effects previously was simply due to the inadequacy of the unaided human visual system.
The next pair of discoveries, of mountains on the moon and sunspots, do not seem, to us, to be relevant to the debate between the geocentric and heliocentric theories. However, the Ptolemaic system was closely intertwined with Aristotelian philosophy and even with Christian theology. It was believed that whereas all things on earth are subject to change, growth, decay, and death, things above the orbit of the moon are changeless, perfect, and eternal. The very elements of which celestial bodies are made were considered to be completely different from the terrestrial ones. But Galileo's telescope showed that there were mountains on the moon, making it look as if that body must be very similar to earth. Likewise, the solar spots appeared, moved about, and disappeared, acting much like earthly storm clouds. The spots also demonstrated the sun's rotation on its axis, and Galileo argued that their apparent paths across the face of the sun indicated a moving point of view.
Finally, Galileo noticed that the fixed stars appear no larger through a telescope than they do with the unaided eye. This observation removed another difficulty with the heliocentric theory. Decades earlier, Tycho Brahe, the foremost astronomer of the sixteenth century, had pointed out that if the earth moves around the sun, then the stars should show an annual parallax, or shift of position, much as objects viewed from the window of a moving vehicle seem to move against the background. No such parallax had been observed, which required the stars to be extremely far away. Based on the apparent size of the stars as seen with the unaided eye, this meant that each star would have to be larger than the whole solar system, a conclusion that seemed absurd. Now, Galileo showed that in fact the apparent size of the stars was an artifact of the human eye, and that the stars were indeed evidently very far off, too far for parallax to be observable with the instruments of the time.
It is worth noting that Tycho, who died before the telescope was invented, had dealt with the problem of the lack of stellar parallax by proposing a compromise system with the earth at rest in the center of the universe, the sun traveling in an orbit about the earth, and the planets in turn orbiting the sun. Galileo rejected this compromise, both because it seemed physically implausible and because he considered that there could be no explanation for the tides if the earth were motionless.