In his book, Starry Messenger, published in 1610, Galileo wrote about his very important observations of the sky above. By use of a telescope he made himself, improving greatly on the models available in his day, he was able to see things that could never before be seen. His telescope was far more powerful than anything that had been available up to that point, and when coupled with his observational skills, proved to be a huge step forward in the field of astronomy.
By observing the moon, Galileo was able to see that the surface of the moon was not smooth or shaped as a perfect sphere like Aristotle thought it was. He noticed that the moon had many craters covering it, and even mountains. He made these observations by studying the terminator of the moon. He noticed that line was not perfectly straight like it would be if the moon was a perfectly smooth sphere.
In fact, there were many inconsistencies in the line that proved that this was not the case.
Another big discovery he talks about in his book is that of Jovian satellites. By use of his telescope, Galileo was able to discover four satellites revolving around the planet Jupiter. He did this by observing four stars by Jupiter that he thought were interesting. They were very small, but yet very bright. For this reason he kept watching them, and noticed their positions changing. This is how he discovered that they were in fact satellites or Jupiter.
This discovery was not only important because new bodies had been discovered, but it also showed that the Earth was not the only center of rotation in our universe, which was the popular view. This meant that our solar system was not geocentric, like Aristotle had...