Oh one more FYI, Alpha Cent is actually a Triple star not a double, well probably its not 100% sure that proxma is actually in orbit about the A&B stars.
And if you postulate a Earth centered system you still have to explain the orbits of the other planets (remember them) which from the point of view of a fixed Earth are just strange. Oh and the Coriolis force, and the phases of Venus, and stellar parallax, and orbital dynamics.