These sorts of arguments all fail the most basic principle of relativity -- that any viewpoint is relative. One can argue that the earth orbits the moon or the reverse, but the best way to think about it is that the earth and moon orbit their common center of mass. And that common center of mass orbits the sun -- or, if you prefer, the earth/moon common center of mass and the sun' center of mass have another common center of mass, around which they mutually orbit.