I don't think this destroys your argument, but the barycenter of the Earth-Moon system is located, according to wikipedia [1], 4670 km from the center of the Earth.
Interestingly, both the Pluto-Charon and the Sun-Jupiter systems have barycenters above the surface of the primary body.
pluto-charon (imo) is a dual dwarf-planet system not planet and moon.
Sun Jupiter is my argument for why a planet shouldn't be defined only by barycenter location.
updated density: 13.55g/cc.
this is about the current density of the core of the earth now. It's about halfway between rhodium and mercury at STP, so not as horribly unlikely, but still pretty out there.
> Sun Jupiter is my argument for why a planet shouldn't be defined only by barycenter location.
But Jupiter doesn't sustain nuclear fusion so it can't be considered in the same category as the sun. If it was a red/brown dwarf, then we would be in a binary system and that'd be a different story entirely.
Interestingly, both the Pluto-Charon and the Sun-Jupiter systems have barycenters above the surface of the primary body.
[1] http://en.wikipedia.org/wiki/Barycentric_coordinates_(astron...