Ten models for the solar system in the 1600's

Frontispiece of Riccioli's 1651 New
Almagest (Wikipedia)

In order to understand the debate around the Copernican heliocentric system and Galileo, it is important to understand the different alternatives that existed, once it was realized that the geocentric Ptolemaic system from antiquity no longer was correct. 

There were really three different classes of models:

• Geocentric - with the earth in the center and with roots in antiquity
• Geoheliocentric - with the earth in the center, and the sun orbiting the earth, but with most of the other planets orbiting the sun.
  If you don't understand why this class of models gained prominence in the first half of the 17th century, you cannot really understand the science of the Galileo conflict.
• Heliocentric - with the sun in the center, resembling our system today

And then there were variations of these. The ones I have identified are: