I offer this, from memory: If you look up the JPL ephemerides of the planets, you will not find the earth! but rather, the obscure designation EMB, or Earth Moon Barycenter. So we may say that the earth and moon have been officialy recognized, ipso facto, as a double planet, as indeed they may be legitimately regarded. So I say, welcome Pluto and the Moon, to planethood!
The barycenter is below the surface of the earth.
Not a double planet.
Any two bodies where one orbits the other have a barycenter; this comes up once in a while, it reminds me of the “is a tomato a fruit or a vegetable” thing. The Earth:Moon mass ratio is something like 100:1. While the mass of Saturn’s moon Titan is something less than twice that of our Moon, Saturn’s mass is many times that of the Earth. The only planet:moon ratio in the Solar System that is known to be closer is that of Pluto and its moons.
Wikipedia’s partly nuts here:
> In cases where one of the two objects is considerably more massive than the other, the barycenter will typically be located within the more massive object. Rather than appearing to orbit a common center of mass with the smaller body, the larger will simply be seen to “wobble” slightly. This is the case for the Earth–Moon system, where the barycenter is located on average 4,671 km from Earth’s center, well within the planet’s radius of 6,378 km. When the two bodies are of similar masses, the barycenter will be located between them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, Jupiter and the Sun, and many binary asteroids and binary stars.
Jupiter isn’t similar in mass to the Sun, as another page notes:
https://en.wikipedia.org/wiki/Planetary_mass#Planetary_mass_and_planet_formation
> The largest planet, Jupiter, is 0.09% the mass of the Sun, while the Earth is about three millionths (0.000003%) of the mass of the Sun.
Earth is about 1/318th the mass of Jupiter (the number is easy for me to remember, because 318 was the displacement of a very common V8 engine Chrysler used for decades), Jupiter (it sez there) is less than 1/10th of 1/100th, or 1/1000th the mass of the Sun.