Saying that the earth orbits the sun is actually a bit more than just a choice in reference frame. When you have two bodies (or more, although it gets more comp

Saying that the earth orbits the sun is actually a bit more than just a choice in reference frame. When you have two bodies (or more, although it gets more complicated) orbiting where one is significantly larger you can end up with a center of mass of the two objects (barycenter) which will be inside of the larger object. So from either reference frame the barycenter can determine that the smaller object is orbiting larger object. So while it's true that you can work the equation from either reference frame defining each as orbiting the other, the center of mass will more than likely lie in or closer to one or the other, and with that you can define which is orbiting the other canonically.