The simple summary of Copernicus's work is that he discovered that the earth goes around the sun, rather than the apparent case that the sun goes around the earth.
It is perhaps more correct to say that it is simpler to model the behavior of the solar system by putting the sun, immobile, at the center, with planets revolving around it. That's a statement about ideas, not about physics.
On the other hand, it's pretty clear that the sun goes around us. You just have to point to where it is over the course of a day, and I suppose if the earth was transparent we could verify that it does a complete circuit of us each time, rather than getting swallowed up by the goddess Nut at sunset...
Ptolemy's model of planetary motion was very complicated, and had no physical justification, but it was good enough to predict things like planetary positions and eclipses. Was it wrong?
Before you say Ptolemy was wrong, consider if you were at a museum where a simple mechanical model of the solar system showed the sun at the center, with rods extending outward with a planet on the end of each rod, rotating just like in real life. Suppose you picked up this (very sturdy and movable) model and held it by the earth. It would continue to turn, and it would continue to exactly model the relative positions of the sun and all the planets. And now you would have to say that in this model, the sun goes around the earth.
Finally, note that space is relative, and that in larger astronomical models the sun rotates around the galactic center of the Milky Way which in turn moves in some fashion with the Local Group which wanders through a patch of space as part of the Virgo Supercluster.
So to Joe Sixpack, the sun rotates around the earth; to Myron Physico, the earth rotates around the sun, to Aaron Astronut, the sun and earth are dancing to the music of gravity in an endless ballroom.
In every case, these are not physical facts but ways of thinking about physical facts, and they are not so much right or wrong as simply suitable for our needs and purposes, or not.