system
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human
Is the barycenter of the Sun and Jupiter also the center of their mutual orbit?

I know that the calculated barycenter of the Jupiter and the Sun places it just outside the Sun's surface. The calculation I've seen is just a mass x distance calculation and is exactly the same one that we use to balance an aircraft (find the CG). All the points on an aircraft are rigidly connected and so gravitational attraction of the various parts to each other, even it was substantial, doesn't change the center of mass. That's not true of the Sun and Jupiter in a mutual orbit. They are not rigidly connected together and their mutual gravitation attraction attenuates substantially with distance. Wouldn't this mean the center of mutual orbit would not be the same as the calculated barycenter?
gpt
With only the Sun and Jupiter they would orbit the barycenter, this is a direct consequence of conservation of momentum. With the other planets involved they don't move on perfect ellipses.

The position of the barycenter of the Solar System (relative to the Sun) largely depends on the relative position of Jupiter and Saturn. Currently they are close (and will come extremely close in our night sky in December), so the barycenter is outside the Sun. In a few years they are farther away and the barycenter will be inside the Sun again.