What was one effect of Copernicus' theory of a sun-centered solar system?
Apart from Earth being moved away from the center of Earth, Math got simpler.
Copernicus stated what ancients had already believed but no one dared to speak, because bible 'forbids' it. So, the contribution of Copernicus really is to push the leap forward of making people speak of what they observe than keep it with themselves, not matter how hard hitting and unrealistic is might sound.
In a way, it paved for the first modern scientific thought of Francis Beacon and the present day concept of 'Science', viz. Observation, Hypothesis, Experimentation, Confirmation cycle.