Nobody believes that.  Even if you grant Newtonian physics, the earth would revolve around the barycenter of the solar system, and not the sun.  At times you'll have this barycenter outside the physical boundaries of the sun so that even the sun is rotating around this barycenter.

But I think this is a good question for a poll, what people believe about the cosmos.  I'll construct a poll here with the various permutations.