HaLevi you have it exactly backwards. The whole controversy is in trying to advance the notion that the earth doesn’t rotate, but the universe revolves around it. The orbit of the earth around the sun is not the issue. The question is does the earth revolve or does the sun rise and set in a real sense. It’s not a question of a yearly phenomenon but a daily one.
As far as centrifugal force and other measurements, the proponents of this theory explain that it is the combined gravitational force of the universe as it revolves around the earth that causes those effects, not centrifugal force. I have no idea if this makes sense or not.
The notion of whether the sun revolves around the earth or vice versa is another issue entirely, though also interesting it has nothing to do with einsteins relativity, only with the general notion that movements are relative to one’s perspective.