That's a rather unsatisfactory way to define moon-hood, because it doesn't depend on any essential features of the two bodies. Replace Earth with something of the same mass but more dense, and the Moon gets promoted to planet, even though its size, shape, and orbit don't change? Yuck!
I believe the center of mass for the earth moon system is something like 3000 km from the center of the earth (in a moonward direction). Just for reference, the radius of the earth is 6300 km.
The density of the earth is ~5.52g/cc, and halving the radius of the earth will increase the density by 8 which gives a density of 44.16 g/cc or 44,160 kg/m^3, which is about twice the density of osmium and a third as dense as the center of the sun.
In other words, the scenario you imagine is not practically possible in a system where one body is much larger than the other (if they're both about the same size, then it a dual planet system).
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.
i believe the center of mass is inside the sun if you look at each planet-sun pair individually. IOW, 2 body to n-body kind of messes this definition up.
also, by inside the sun do you mean inside the corona?
This rule is for when both bodies are the "same" type.
There are three types:
Black hole -> Sun -> planet/moon
Two suns are a binary sun if they orbit a COM outside both. Same for two planet/moons.
A sun around a black hole is not a binary sun, but we've never named such a thing (except maybe galaxy).
A small sun around a large one with the COM inside the larger one should have a special name, but we never gave that a name either since we've never seen one.
A planet around a black hole is a planet, since it's not the same type as the other one.
the event horizon (schwarzschild radius) of the sun is 3km.
i don't think planethood should be defined based on whether the barycenter of the system is within the orbited object, but I do think that's a pretty good definition for determining whether two objects are a planet moon pair or dual planets.
but in case you con't want to follow, here's a summary:
dual planet system (eg pluto charon): barycenter lies outside of either object
planet with moon (eg earth and moon): barycenter lies within the radius of the planet
planet: "(a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit[1]." [2]
as for why planethood shouldn't be determined by barycenter location alone:
"If the definition of a double- or binary-star system is used as a comparison, and it depended only on the location of the barycenter, then any revolving body with a barycenter beneath a star's surface would be a planet, and any body with a barycenter lying outside the surface of the star would be another star. In the Solar System, all of the major planets would be planets under this definition except one. The Sun–Jupiter barycenter is the only center of mass that lies outside the surface of the Sun. Therefore, since Jupiter is not a star, the difficulty faced by astronomers to derive a reality-based definition of double planet begins to become clear." [3]
[1]: meaning it has become gravitationally dominant, and there are no other bodies of comparable size other than its own satellites or those otherwise under its gravitational influence.
there's a major error in their calculation in that they didn't do that in 3 dimensions, and they assumed that all planets always lie on the same radius from the sun. do the math again with jupiter and saturn on opposite sides and use 3 dimensions, and the CoM should go back into the sun.
Also, Jupiter and Saturn make up most of the mass of the planets (1.8986×10^27 kg and 5.6846×10^26 = 2.46x10^27) where the total mass of the planets is 2.67×10^27 kg.
As long as Jupiter and Saturn are aligned with the sun the barometric center of the solar system will be outside of the sun, and they would align once every 12 years or so, so this does happen from time to time.
