Church Clashes
Galileo made discoveries that shocked church officials, leading many to refuse to look through his telescope because of the belief that the devil manipulated the telescope. His conflicts with the church eventually led to the church forcing him to recant and spend the rest of his life under house arrest. Copernicus was encouraged more by the church to study the universe than Galileo had been, even though he was somewhat discouraged because the clergy saw his theories as disagreeing with the Bible. Copernicus delayed the publishing of "On the Revolutions," a six-book series on astronomy. The first book of "On the Revolutions" explained Copernicus' most significant contribution, the heliocentric view of the universe. The delay resulted from the time-consuming astronomical observations and mathematical proofs needed to complete the book. Copernicus did not have as much access to the same quality telescope that Galileo had access to, but he did build his own outdoor observatory in 1513.
Sun
Copernicus said the retrograde motion of planets comes from an illusion created by the Earth's motion. He mentioned how the Earth makes a daily rotation, and an annual revolution of its center, and an annual revolution of its inclination. All these make the sun appear as if it moves.
Unlike Copernicus, Galileo was able to study the sun directly with his telescope. He discovered that sunspots were on the sun. By looking at the sun, Galileo eventually went blind. Galileo also discovered the sun rotated, which made the rotation of the Earth seem less surprising. His discoveries violated the view of the church that the heavens never changed.
Moons
Galileo noticed the four brightest moons rotating around Jupiter. This discovery showed that objects could rotate around larger objects, which rotated around even bigger objects, which refuted an argument against the Copernican System. The argument against the Copernican System was that if the Earth orbited around the sun and the moon orbited around the Earth, the Earth would leave the Moon behind as it moved around its orbit. The fact that Venus had phases also verified the Copernican System.
Physics
Galileo discovered the concept of inertia, the idea that an object in a state of motion will remain in motion until an external force acts upon it. Galileo realized that objects in motion stop their motion because there is hidden frictional force acting upon it. Copernicus mostly focused on astronomy and did not perform work directly on physics.