Galileo was a great defender of the heliocentric model. He was the first person who used a telescope to observe the sky. This was the first time that a person used an instrument to enhance one's observing capability.
Galileo made four major discoveries:

1. The mountain terrain on the Moon.

2. The sunspots.
       These two discoveries proved
        that the heaven is not perfect.

3. Four satellites orbiting around Jupiter.
       So, there are other 'centers' in the heaven.
       The four satellites are now called the
       Galilean satellites.

4. Venus goes through a full set of phases.
       This proved that Venus must orbit around the Sun,
       not the center of the epicycle.

The observed phases of  Venus prove that
Venus must orbit around the Sun, and that
Earth cannot be the center of the system.