Galileo argued in favor of heliocentric theory

 He taught geometry and astronomy till 1610. During that period, Galileo made several discoveries in science, combining geometry and astronomy.  

Galileo made first telescope with a convex lens and a concave eyepiece. On 7th January 1610, he discovered the three moos of the Jupiter with his telescope, on 13th January; he discovered the fourth moon also. He published an article in which he gave an account of all his observations. In 1616, he discovered the Saturn and its rings. He reported that moon was just like the earth, with mountains and craters. He observed the Milky Way and found that it was a constellation of millions of stars that looked like clouds. In 1612, he observed the Neptune although he did not say anything in particular.

In 1611, Galileo gave a demonstration of his telescope at the Jesuit Collage of Rome. The four moons of the Jupiter were seen with his telescope.

In his article, Galileo argued in favor of heliocentric theory, which caused a great opposition. It was believed that Galileo committed the heresy of speaking against the Holy Bible. Several priests denounced Galileo for his opinions on the movement of the Earth. In 1616, Galileo was handed a warning and was ordered not to favor heliocentric theory.