Let me extend this comparison a little more. I wrote:
It is a shame [Tycho Brahe] he never got a chance to use a telescope. If he had, he would have known instantly what he was seeing despite the problems with the early instruments.
Furthermore, if Tycho had seen Galileo's initial setup, he would have been disgusted. (He was never one to hide his opinions.) I expect his reaction would have been similar to that of a modern-day expert at Los Alamos or MIT looking at an early cold fusion experiment. Compared to Tycho's instruments, the mounting, aiming, and data collection capabilities of Galileo's early telescope was an amateur joke. Plus, as I said, people would aim the telescope at one bright visible star, and they would sometimes see two stars, or none. So it was no surprise that experts in astronomy doubted the initial reports of satellites orbiting Jupiter. Fortunately for Galileo, the Pope -- who was a good friend -- supported him, and quickly supplied major government funding for improved instrumentation.
The popular version of the story, in which the Pope's emissaries "refused to look" and did not support Galileo, is completely incorrect and backwards. He only got in trouble with the ecclesiastical establishment years later.
Galileo used lousy equipment because he was in a mad rush to publish quickly before others got a chance. He first circulated a cryptic poem to establish priority without letting on exactly what he had discovered. Then as I recall, he published a deliberately incomplete and misleading report so that others would not replicate too quickly. He was a piece of work -- a nasty backstabber who was always willing to steal credit, deny an obvious fact for political expediency, or produce a second-rate obsolete instrument on a huge government military grant (a telescope for harbor defense). However, he was a brilliant scientist, and he improved the science of optics by leaps and bounds in a matter of months.
By the way, Galileo's proof that all bodies fall in the gravitational field with the same acceleration was not experimental. He never dropped anything off the Tower of Pisa. It was a pure "thought experiment," like Einstein's early work in special relativity. He asked a simple question: "If a large body falls faster than a small one, what happens when you chain the two together? Do they fall at the average speed? Does the lighter one retard the heavy one?" Everyone could see that was absurd.
- Jed

