I was thinking about writing a section about that.
Summarily, I would say that by Galileo's time it was already widely believed that the Earth was a globe, largely based on Greek knowledge. The debate was whether the Earth was in motion and moving in the Solar System or whether the Earth was the center of it all. They got it right that the planets were revolving around the Sun, because that is the most natural inclination when you see Mercury and Venus following the sun in the sky, and moving to either side of it.
See this Dance of the Planets animation where Mercury, Venus, and Mars follow the Sun, appearing to travel to either side of it at different times:
http://www.davidcolarusso.com/astro/In that sense, I would agree that the Solar System is Heliocentric (Sun centered). The Earth just isn't a planet in the Solar System. The Solar System sits above the Earth.
I have seen other FE'ers disagree that the planets move around the Sun. Mercury, Venus, and Mars would need to seem to be moving back and fourth around the Sun for another reason, in that case.