Technically, yes.
You ever see the olympic sport where they spin around with a rope and a weight at the end?
The person would be the sun, and the planet would tend to be the planet. The person spinning does move slightly around, they aren’t perfectly center.
Same thing tends to happen with stars and planets, they all orbit each other but the one with the most mass tends to ‘swing’ the other planets more. Like with the sun, it’s pretty damn big and heavy, and if you watch an orbit simulation, the sun wiggles a little around an axis, it doesn’t stay perfectly centered
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