I say the only viewpoint available that provides us with the truth is the center of mass. You go ahead be my guest and choose another but be ware: Your physics will not remain the same. Lets fix the coordinate system on the sun and watch the earth moving. The sun is truly immovable thus has no force on it because of Newton 2. Because of Newton’s gravity sun’s mass is also zero but also and earth’s force will be zero. So how can earth move relatively to the sun? It will probably dilate time and contract space in order to move! I'm off to Bermuda!