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In response to "I think there's some weird quirk of their sizes and orbit that place the centre of their system outside of Pluto's surface ... -- nm" by Beryllium

you are right good sir. Charon is about half Pluto's width and somewhere around one-eighth to one-tenth its mass, and with a center-to-center orbit -- (edited)

of roughly 20,000 km, the center of mass for this system is actually above Pluto’s surface.

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