Actually, I can design an Earth centric coordinate system that works just fine.
However, The Sun/Earth system actually revolves around a common center of mass that just happens to be located inside the Sun do the a vast disparagy in mass between the two objects..
But the Jupiter-Sun system CoM is sometimes just outside the Sun's surface.
However, The Sun/Earth system actually revolves around a common center of mass that just happens to be located inside the Sun do the a vast disparagy in mass between the two objects..
So you prefer the centre of mass of the Sun as an arbitrary frame of reference. That is no more or less valid than any other frame of reference.