Pluto and Charon

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The velocity vector of the center of mass of an isolated system, as measured in an inertial coordinate frame, cannot change except from an external influence.

As the planets in a Solar System move around and change places the velocity vector of the barycenter of that sytem will not change as observed from an inertial reference frame.

If you are basing your coordinate frame on one of the revolving planets then it is not an inertail frame and the barycenter will be seen to wobble all around.
Thanks Bill. I think I’m getting it, now.

In the seesaw case it is not an isolated system. As the four little people move around they are pushing the seesaw legs against the Earth and moving the Earth slightly.
The see-saw analogy won’t work because it fails to make the big guy move, unlike our solar system’s Sun. As the planets align opposite the Sun, the Sun will have moved farther from the barycenter, which remains fixed, thus balancing the system. We can see this in the Pluto-Charon animation, not that it’s accurate.
 
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