Yes, but it’s mostly shifting because of Jupiter. It’s just so dang heavy. Like, a couple times heavier than every other planet put together. I don’t have the brain wattage to do the cool math right now, but a quick google search says that while the barycenter of the solar system does depend on all the planets, more often than not, it is outside the sun
xkcd #2898: Orbital Argument ( imgs.xkcd.com )
xkcd.com/2898...
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