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xkcd #2898: Orbital Argument
(imgs.xkcd.com)
Alt text:
"Some people say light is waves, and some say it's particles, so I bet light is some in-between thing that's both wave and particle depending on how you look at it. Am I right?" "YES, BUT YOU SHOULDN'T BE!"
Same for earth and moon. The center is inside earth. But not that close to the center of the earth itself
Meanwhile, Pluto and Charon noticeably orbit each other, the barycenter being fully outside of Pluto's surface.
And Jupiter is so massive that its barycentre is (barely!) outside of the sun!