Stephen Hawking has this to say,...
So which is real, the Ptolemaic or Copernican system? Although it is not uncommon for people to say that Copernicus proved Ptolemy wrong, that is not true. As in the case of our normal view versus that of the goldfish, one can use either picture as a model of the universe, for our observation of the heavens can be explained by assuming either the Sun or the Earth to be at rest. Despite its role in philosophical debates over the nature of our universe, the real advantage of the Copernican system is simply that the equations of motion are much simpler in the frame of reference in which the sun is at rest.
Stephen Hawking, (from his book) The Grand Design, page 41-42, published in 2010