Relativity is wrong...

I found wikipedia's article on centre of mass interesting as it had some interesting animations modelling the orbits of different celestial bodies, including this one of the sun and earth (note the sun is the larger object): Now both objects are orbiting the barycentre (red cross), since the mass of both objects interact with each other, but that this centre of gravity still lies within the sun. Of course there are other planets in the solar system which also influence the movement of the sun, and I found this page what effect the other planets have.You say the earth is motionless, but if the entire universe is orbiting it, then surely this combined mass would cause the earth to develop an orbit even more eccentric than the suns? It would no longer lie at the centre of the universe (as per your definition of heliocentric).