Where is the Solar system's barycenter located? The solar system as a whole, Where is the center of the mass for the combined mass of the Sun, inner planets, and gas giants, is it inside the Sun? Is there an AU measured distance of it?
The solar system barycenter (SSB) is sometimes inside the Sun and sometimes outside. As an observer outside the solar system could detect with Doppler spectroscopy, the Sun is what's wobbling around.
The Sun's offset from the SSB is a vector sum of roughly:
- 0.00496 au ±5% away from Jupiter
- 0.00272 au ±6% away from Saturn
- 0.00083 au ±5% away from Uranus
- 0.00155 au ±1% away from Neptune
The other planets contribute much smaller amounts to the total. Each planet's contribution is proportional to the product of its mass and its orbital distance.
When these components add constructively as in 2020-2023, the center of the Sun can be as far as 2 R☉ away from the SSB. When they cancel as in 2029-2030, the center of the Sun is within 0.5 R☉ of the SSB. The solar radius R☉ is 0.00465 au, shown here with a dashed line.
The fact is, Sun can't exert any moment about the barycenter unless Sun and its planets may be resting on some solid object which may be physically resting on some fulcrum type of thing. Of course Sun wobbles about SSB but not due to balancing of moments. It wobbles due to a different reason. It occupies a place where the gravitational forces exerted by it on all planets get balanced which gives us an impression that it is revolving about SSB.