Heliocentricity has nothing to do with Galileo or the 'conflict between science and the Church'. Christian scientists discovered using advanced mathematics the concept of heliocentricity long before Galileo took the credit. Copernicus, a Catholic monk, devised a system to explain why the earth rotated around the Sun; much of what he theorized was wrong. He waited 20 years to publish his work out of fear of academic reaction [sound familiar?], who were invested in the Ptolemaic concept of geocentricity and Luther's Protestants who following Luther's condemnation of the theory, were violently opposed to Copernicus. The violence against Copernicus by both Protestants and academics was indeed quite virile and hostile.
It was Kepler, another Christian, and ironically a Lutheran, who developed the math to explain elliptical orbits, and whose theory merged with real observations on planetary motions. He formed his math 10 years before Galileo stepped onto his soapbox. Galileo never quoted nor corresponded with Kepler though he must have known of his work. It is Kepler whose mathematical detail provides a thorough support for heliocentricity.
Galileo contributed nothing, but invective and the addled notion that tides, which arise from the gravitational pull of the moon, 'proved' that the earth revolved around the Sun. The 2 have nothing to do with each other, a fact that Jesuit astronomers had proven for 30 years during Galileo's lifetime. Apparently Galileo was either too ignorant or too careless a scientist to bother with well-known facts widely circulated during his day.
“Many people wrongly believe Galileo proved heliocentricity. He could not answer the strongest argument against it, which had been made nearly two thousand years earlier by Aristotle: If heliocentrism were true, then there would be observable parallax shifts in the stars’ positions as the earth moved in its orbit around the sun. However, given the technology of Galileo’s time, no such shifts in their positions could be observed. It would require more sensitive measuring equipment than was available in Galileo’s day to document the existence of these shifts, given the stars’ great distance. Until then, the available evidence suggested that the stars were fixed in their positions relative to the earth, and, thus, that the earth and the stars were not moving in space—only the sun, moon, and planets were.” link
There was precious little science, but lots of earnest slander in Galileo's works. Galileo also propounded without evidence, that the Sun was the center of the entire universe ! He provided no math or evidence to support his assertion.
The Galileo myth is just another tired Atheist-Protestant piece of puff propaganda. Banal, untrue but entirely convenient for cult members who dearly want to believe that only Atheism promotes science [such as abiogenesis, mud-to-men, life on the moon, life on venus and mars, Communism, Marxism, Nazi evolutionary theology etc.].