The Earth/Moon system does not qualify as a binary planet because it does not meet the L4/L5 instability threshold. In a system of two orbiting masses, the larger needs to have at least 25x the mass of the smaller for the system to have stable L4/L5 points. Earth is ~80x more massive than the Moon, allowing the system to have stable L4/L5 points, and is therefore a satellite system.
The Moon being classified as a Moon despite qualifying as a binary planet. :(
The Earth/Moon system does not qualify as a binary planet because it does not meet the L4/L5 instability threshold. In a system of two orbiting masses, the larger needs to have at least 25x the mass of the smaller for the system to have stable L4/L5 points. Earth is ~80x more massive than the Moon, allowing the system to have stable L4/L5 points, and is therefore a satellite system.
Quick diagram for anyone wondering
L4 and L5 get unstable if the masses orbiting each other are too similar
It lacks the je ne se quois of a binary planet. It just doesn’t have the right atmosphere for it, you know.
The barycenter between the Earth and Luna is well within the surface of the Earth. There is no definition where it counts as a binary system