Which of galileo's theories drew fire from the catholic church and led to his house arrest? objects of different weights fall at the same speed. the sun is at the center of the solar system and the planets move around it. the time taken to swing through one complete cycle depended on the length of the pendulum. ocean tides are caused by earth's rotation and revolution.

The Sun is at the center of the solar system and the planets move around it.

Explanation:

During the Middle Ages, it was believed that the Earth remained motionless, occupying the center of a universe subject to uniform circular motion where Earth was the only world. All this because the only accepted idea was that of Ptolemy.  

Until the Polish astronomer Nicolaus Copernicus proposed that the Earth annually orbits the Sun and rotates once a day on its own axis.  He also dared to affirm that the other planets also orbited the Sun as a fixed point. This meant the Earth was no longer unique, nor did it occupy the center of the known universe.  

On the other hand, Galileo observed Venus with his telescope and found out it presented phases (such as those of the moon) together with a variation in size; observations that are only compatible with the fact that Venus rotates around the Sun and not around Earth.

These observations and discoveries were presented by Galileo to the Catholic Church (which supported the geocentric theory at that time) as a proof that completely refuted Ptolemy's geocentric system and affirmed Copernicus' heliocentric theory.

It is important to note, this was the main reason for Galileo to be arrested.