The correct answers to these open questions are the following.
Why might the Church be concerned about a heliocentric explanation of the universe?
Because in those Middle Ages times, the Catholic Church was so powerful and forced people to believe only what the church said. The high clergy of the church punished people who dared to think otherwise under the justification that no human could be against the will of God. Those were the obscure and horrible times of the inquisition.
The Church saw the heliocentric view of the solar system as a challenge to its authority because the heliocentric view, if correct, might mean God did not put humans at the center of the universe. And that would mean losing its power.
That is why the church was concerned about scientific theories such as the Heliocentric Theory, developed by Nicolaus Copernicus.
The church did not want the scientific method to explain the natural phenomena that had been attributed to the glory of God. And that was exactly what science did, to prove the church wrong with ideas such as that it was the Earth and other planets the ones that revolved around the Sun.
