Suppose that you have a 2 planet system: A sun type star (mass 210^30 kg), an Earth type planet 1 AU from the sun (weight 610^24 kg), and a Jupiter type planet (mass 2*10^27 kg) that is 1000 AU away from the sun.
The distance between the Earth type planet the center of the star could be nearly constant.
The distance between the Earth type planet and the barycenter would not be nearly constant -- it would not "orbit" the barycenter in a circular orbit.
I may be wrong and I would be very happy if someone corrected me.
(Note: I think the barycenter would be about 5 AU from the star!)
Suppose that you have a 2 planet system: A sun type star (mass 210^30 kg), an Earth type planet 1 AU from the sun (weight 610^24 kg), and a Jupiter type planet (mass 2*10^27 kg) that is 1000 AU away from the sun.
The distance between the Earth type planet the center of the star could be nearly constant.
The distance between the Earth type planet and the barycenter would not be nearly constant -- it would not "orbit" the barycenter in a circular orbit.
I may be wrong and I would be very happy if someone corrected me.
(Note: I think the barycenter would be about 5 AU from the star!)