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xkcd #2898: Orbital Argument
(imgs.xkcd.com)
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It's called a barycenter, kids, a common center that both objects circle around. That common center happens to be inside the sun, but that's a topic for next week's class in this semester's AP Astrophysics program.
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!
Goddammit, Barry.
Always trying to compromise
I don't think the barycentre is inside the sun? Wikipedia says on the barycentre article:
The Jupiter-Sun barycentre in outside the sun.
The Earth-Sun barycentre is inside the sun.