Nicolaus Copernicus's scientific ideas regarding the universe and specifically the idea of heliocentrism were at odds with the generally accepted ideas of his time. It was difficult for people to accept these new ideas, made even more difficult by the Catholic Church's powerful opposition to them for some time.
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Galileo had such a hard time showing his theories on the universe to the people because if he showed his opinion or said it he would be put in house arrest.
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Arguably, Copernicus' biggest obstacle was the church. The church supported the Ptolemaic view that the universe consisted of 10 concentric spheres with Earth at the center and heaven outside. Questioning this philosophy meant upsetting the church, which had the authority to capture Copernicus. He thus kept the idea of heaven outside the universe, but made a heliocentric conception nonetheless.
Actually, no one challenged his theory. In fact the next real astronomer, to even come back to his theory was Galileo, who came around fifty years later. There were absolutely no challenges to his theory, but between the fifty years of Copernicus's death, and Galileo proving Copernicus right, his theory was shunned, and the church passed a law that saying his name was illegal.
Galileo did not have his own theory. He was a supporter of Copernicus's heliocentric theory and an opponent of the geocentric Ptolemaic theory. Eventually both theories were rejected in favour of Kepler's theory. But Kepler's theory uses the heliocentric idea from Copernicus's theory.
Galileo did not propose a heliocentric theory, he agreed with Copernicus and his heliocentric theory. The Catholic church, at the time, disagreed and they held a huge amount of power and put him on trial.
Nicolaus Copernicus was the Polish scholar who published a heliocentric theory in his treatise 'On the Revolution of the Heavenly Spheres' in 1543. This theory proposed that the Sun, rather than the Earth, was the center of the universe, leading to significant changes in our understanding of the cosmos.
Yes, Galileo and Newton built upon Copernicus' heliocentric theory of the universe by providing further evidence and support through their own observations and laws of motion. Galileo's telescopic observations confirmed Copernicus' model, while Newton's laws of motion and universal gravitation explained the physical principles behind the heliocentric system.