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xkcd #2898: Orbital Argument
(imgs.xkcd.com)
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Except it's still inside the sun, so depending on how big you view the center of the sun it could still be wrong.
It's usually not inside the sun thanks to Jupiter's fat ass
So if the point is inside the sun, do we not consider the sun as orbiting that point? I would think it is still orbiting a point.
The sun isn't orbiting itself, though, so to say it's wrong is also wrong. The sun is orbiting a small point in space that is affected by the bodies around it. That the point is covered by the sun doesn't change that.