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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.
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.
Isaac Newton is the great mathematician and physicist who brought together the theories and discoveries of Copernicus, Kepler, and Galileo under his theory of motion, known as the laws of motion and universal gravitation. His work laid the foundation for classical mechanics and revolutionized our understanding of the physical world.
Isaac Newton.
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 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.