Mountains on the Moon
In 1610, Galileo published "The Starry Messenger," which included observations of mountains and valleys on the moon. Aristotelian ideas at the time stated that heavenly bodies were smooth, spherical bodies. The similarities between features on the Earth and moon would also contribute to Galileo's belief that the same kind of matter and natural motion existed in the heavens as on Earth.
Moons of Jupiter
Also published in "The Starry Messenger" were Galileo's observations of four moons orbiting the planet Jupiter. Galileo used these moons to support the Copernican heliocentric (sun-centered) model over the Ptolemaic geocentric (Earth-centered model). These moons established that not all heavenly bodies orbit the Earth and that the moon orbiting the Earth was not unique.
Phases of Venus
"Letters on the Sunspots," published in 1612, included observations on the planet Venus. Venus, he had observed, underwent phases. Galileo argued that these phases resulted from Venus' closer orbit around the sun than the Earth, providing further evidence for the heliocentric model.