Salviati: ... it is necessary that we declare ourselves as to whether or not you and I have the same concept of this center. Therefore tell me what and where this center is and what you mean.
Simplicio: I mean by "center" that of the universe, of the world; that of the stellar sphere, that of the heavens.
Salviati: I might reasonably dispute whether there is in nature such a center, seeing that neither you nor anyone else has so far proved whether the universe is finite and has a shape, or whether it is infinite and unbounded.
(From the third day of the Dialogue)
Galileo's project, ultimately, was not merely to demonstrate that the earth goes around the sun. That was just one instance of a much larger vision, which was fundamentally epistemological. By throwing off the shackles of received wisdom, and setting out to discover the universe as it revealed itself, he freed his imagination to conceive of a universe far grander and more wonderful than the church fathers could encompass. In this respect, it was in fact the one we know today -- unbounded and with no center. His telescope could not resolve the nebulae into galaxies, but he had an idea that the stars were suns, and the sun a star.
It is astonishing that nearly 400 years later, the implications of this insight are still so threatening to most Americans that they do not accept it. We are, after all, nothing special. We are not the principal interest of the almighty lord of creation, and the fate of our planet is of no consequence to the universe. It matters only to us and to the creatures with which we share it. If we could just abandon the delusions of religion, we might have a better shot at not screwing it up.