The theory of heliocentric is a theory that the sun is the center of the unvierse but that the planets moved in perfect circles which was incorrect but he had an idea.
The theory of geocentric was first created but had been disproved it also came from the scientific revolution.
The trial of Galileo was big trial set by the church because they believed in geocentric theory and Galileo tried to proven the heliocentric theory was correct. Galileo confirmed that the Copernican system was corrrect and it was worthed a fight for those who didnt want to believe it. It seemed as disrespect to the churches so they took him to trial.