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Galileo realized quickly these characterizations were insufficient, and so began to explore how heaviness was relative to the different specific gravities of bodies having the same volume. He was trying to figure out what is the concept of heaviness that is characteristic of all matter. What he failed to work out, and this was probably the reason why he never published De Motu, was this positive characterization of heaviness. There seemed to be no way to find standard measures of heaviness that would work across different substances. So at this point he did not have useful categories to replace the Aristotelian ones.
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In March 1610, Galileo published the results of his observations under the title The Starry Messenger. Hundreds of copies were soon printed. Some philosophers such as Kepler, received his work with enthusiasm, but others such as Libri who taught philosophy at Pisa, were far less enthusiastic. Libri actually refused to even look through a telescope. Allegations were made that Galileo's observations were the result of illusions created by the telescope. This may seem a curious reaction, but it was well known that a single lens could distort and if this was the case, the combination of two lens could be regarded with even more suspicion.
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Later in 1623, Galileo argued for a quite mistaken material thesis. In The Assayer, he tried to show that comets were sublunary phenomena and that their properties could be explained by optical refraction. While this work stands as a masterpiece of scientific rhetoric, it is somewhat strange that Galileo should have argued against the super-lunary nature of comets, which the great Danish astronomer Tycho Brahe had demonstrated earlier.
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