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After reading this question and seeing its image I thought about this question I'm going to publish.

Does the Sun have different unique orbits around the barycenter for its multiple planets?

If yes, how does it revolve around all of them? For this it has to exit one orbit and enter another.

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    $\begingroup$ There is just one barycenter - the center of mass of all combined bodies. There isn't a unique barycenter for the Sun-Mercury system, Sun-Venus system, etc. $\endgroup$
    – Jim421616
    Commented Sep 14, 2023 at 18:22
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    $\begingroup$ Those barycenters have exactly as much reality as the solar system barycenter has. They're all just calculated relative positions based on the positions and masses of the objects you choose to include in the calculation. $\endgroup$
    – notovny
    Commented Sep 14, 2023 at 21:15
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    $\begingroup$ Related question: astronomy.stackexchange.com/questions/44851/… $\endgroup$
    – Heopps
    Commented Sep 15, 2023 at 7:50

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There's only one barycenter for the solar system, which includes the impact from every planet, asteroid, comet, and space probe in the solar system. The path the sun takes around that barycenter is mostly a circle because the Sun-Jupiter interaction completely dominates the physics of the system, but it's a bit wobbly due to all the interacting forces of the other bodies (mostly Saturn).

You can calculate the location of the barycenter between the sun and any other body in the system, but the sun doesn't continually switch which one of those it's paying attention to. It has to obey all of them all the time, leading to a complicated wobbly path around the single Solar System barycenter.

But it doesn't stop there, because all those other bodies are pulling on each other as well -- even as Jupiter is pulling on the sun and Saturn is pulling on the sun, those two are pulling on each other, making their orbits wobble as well, which feeds back into the sun's wobble. It's an almost infinitely complex interaction of forces.

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Yes, each planet creates a different barycenter with the sun.

All these barycenters get added up. Like, if one pulls 1,000 miles left and another pulls 3,000 miles right, the sun actually moves 2,000 miles right. You add up the vectors.

the path that the sun is pulled due to all these forces makes it look almost random,

but it's really just the sum of a whole lot of very symmetric forces that change with time in a flower petal pattern.

This is how the sun's center gets dragged around by the gas giants:

enter image description here

The scale bar is the diameter of the sun (1,300,000 km).

Subtract Jupiter's contribution:

enter image description here

We observe that the other big planets, even added together, don't QUITE pull the barycenter outside the sun.

Here's the contribution of Uranus only. Note the scale change. The wiggles are due to the other gas giants perturbing Uranus (not the sun):

enter image description here

With a HUGE scale change (zoom in 1,000x), we see that Pluto only pulls the sun about 20 miles off center:

enter image description here

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    $\begingroup$ Beautiful answer! I seem to remember that Neptune has a bigger contribution than Uranus, and perhaps even Jupiter, because even though lighter, it's much further away, so the center of mass is further away from the Sun for Neptune than for Jupiter or Uranus? $\endgroup$
    – uhoh
    Commented Jul 31 at 22:15
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    $\begingroup$ @uhoh > Beautiful answer! == Why, THANK you, uhoh! [curtsies] $\endgroup$
    – Miss Understands
    Commented Jul 31 at 22:27

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