In his observations of the Moon, Galileo observed that the line separating lunar day from night (the terminator) was smooth where it crossed the darker regions of the moon, but quite sinuous where it crossed the brighter areas. From this observation, he deduced that the darker regions are flat, low-lying areas, while the brighter regions are rough and covered with mountains. Based on the distance of sunlit mountaintops from the terminator, he estimated that the lunar mountains were at least 4 miles in height. This contradicted Aristotelean cosmology, which held that since the heavens were more perfect than the earth, the heavenly bodies must be perfectly smooth spheres.
In observing the stars, Galileo reported that he saw at least 10 times as many stars through the telescope as with the naked eye, and he published star charts of the belt of Orion and the Pleiades showing some of the newly observed stars. Also, when he observed some of the "nebulous" stars in the Ptolemaic star catalogue, he saw that rather than being cloudy, they were made of many small stars. From this, he deduced that the nebulae, and the Milky Way itself, were collections of stars too small and close to be resolved into individual stars by the naked eye.
In the last portion of Sidereus Nuncius, Galileo reported his discovery of four objects that appeared to form a straight line of stars near Jupiter. He gave illustrations of the relative positions of Jupiter and its moons as they appeared nightly from late January through early March of 1610. From the fact that they changed their relative positions from night to night, but always appeared in the same straight line near Jupiter, he deduced that they were four bodies in orbit around Jupiter.
At the time of its publication, Galileo was a mathematician at the University of Padua, and he had recently received a lifetime contract for his work at building more powerful telescopes. He desired to return to Florence, and in hopes of gaining patronage there, he dedicated Sidereus Nuncius to Cosimo II de' Medici, fourth Grand Duke of Tuscany, and he named the four moons of Jupiter he had discovered the "Medicean stars." Since then, his effort at naming the moons has failed, for today they are referred to as the "Galilean moons."