Multiple planets (binary, etc)

A somewhat silly numerical experiment...

One point that sometimes comes up is that the Earth may be regarded as a binary planet. This paper proposes a criterion for planets, Λ>1 where

Λ≈1.7×10¹⁶(M_p/M_⊙)²a^-3/2

With the units of a being AU. So if we define a binary planet as one with a satellite which if it were in independent solar orbit, would also be a planet, what happens?

Satellites which would be planets

Earth
Moon (Λ≈23)

Jupiter
Io (Λ≈2.9)
Ganymede (Λ≈7.9)
Callisto (Λ≈4.2)

(Europa just misses qualifying, with Λ≈0.83)

Saturn
Titan (Λ≈2.6)

So perhaps Earth-Moon and Saturn-Titan are double planets, and Jupiter-Io-Ganymede-Callisto is a quadruple?

Λ seems to me to be a bit arbitrary. I would to define a double planet as two objects that would, if the other companion was missing, be classifiable as a planet, and whose orbit is such that the barycenter is outside the radius of the more massive object. (i.e. Pluto/Charon... if both objects qualified as a planet).

Just to clarify here: Λ is a parameter which reflects the likelihood that it would cause a small body in a sufficiently similar orbit to be deflected out of the neighbourhood within a Hubble time.

I wouldn't go for the "saturn, titan" or the "jupiter, io, ganyemede, callisto" not based on mass but based on size relative to the plent it is orbiting.

With the moon/earth system and pluto/charon system it makes alot of sense. However with saturn and titan it doesn't at all even if titan could be classified as a planet itself otherwise. I see where your coming from but......I dunno....maybe if uranus or neptune were a sattelite to saturn or jupiter it might make sense......