The heliocentric solar system of Copernicus was attacked for several reasons:
1) He had proposed an idea but gave no suggestion on how to prove the idea.
2) He proposed that our Earth was moving through space. If that were true, then we on Earth should detect ourselves moving. But we don't.
3) Furthermore, any such movement would result in a change in the star background over time. Since no such movement was detected, the Earth could not be moving.
4) On philosophical grounds, as it was pointed out that Copernicus had arrived at his ideas through mathematics. At the time, it was believed that math was purely intellectual, with no real connection to the real world; thus, one could not connect the two.
For sixty years after the publication of Copernicus' work, the above were the main objections to his ideas. Only after decades of minimal controversy, people attacked his ideas over a seeming contradiction with Scripture.