Physics textbooks frequently mention Galileo and the Tower of Pisa Experiment. They might also mention that the story may be apocryphal but all too often leave the impression that the experiment would have worked if only it had been done. While the truth of the matter is that he likely did tower experiments while he was in Pisa (1589-1592) and his purpose would be to see if objects of different sizes but the same density would fall at the same rate and that objects of the same size but different densities fell at rates proportional to their densities. In 1638, almost 50 years later, he published, Two New Sciences in which he discusses "tower" experiments predicting among other things that a lead ball and an ebony ball of the same size would be separated by less than 4 inches after a fall of 100 m. This and other stories are often associated with his (much) earlier tenure at Pisa.
Galileos writings, both early and late on falling objects generally turn out to be inaccurate. In some cases very much so. How can this have happened? Some historians claim that Galileo actually never did experiments, that he was a theorist. Others would maintain that the 'tower' type experiments reported in "Two New Sciences" were just "Thought Experiments". Galileo was without a doubt a close observer of nature so that raises the question as to why he could be so far off in his descriptions. One possible explanation follows.
Galileo reportedly experimented on both pendulums and balls on inclined planes. Galileo was well aware of air resistance but may well have based his feeling for it magnitude on these experiments. At the low speeds used in these experiments air resistance would be proportional to the speed and would be much less in its effect on motion than the air resistance encountered in falling bodies which varies as the speed squared.
One thing is clear if Galileo did do the Tower of Pisa Experiment at the time he was at Pisa he would not been trying to prove what he discusses in "Two New Sciences".
