Originally posted by: Brucmack
Second: Unless Newton made a huge mistake, the earth exerts a gravitational force on the moon, and the moon exerts an exactly equal force on the Earth. (people have trouble with this fact. They can "repeat for every force there's an equal and opposite force" ad nauseum, but they don't believe it) Since this results in a net force on the earth, it would be wrong to say that the earth continues in a path, unaffected by the moon, while the moon simply revolves around the earth.
Yes, this is correct, and that's why we get tides. But that doesn't make the earth-moon pair a binary system. It's a simple matter of the weight ratio... The earth is so much more massive than the moon, the centre of mass of the system is actually inside the earth. So the earth can't orbit about that point. Sure, it gets pulled by the moon, but it's insignificant compared to the effect the earth has on the moon.
With a system like Pluto-Charon, they are much closer to being the same mass (I think Pluto's only about twice as massive?) This means that the centre of mass is between the two bodies, and they orbit about this point, making it a binary system. As such, Charon isn't a moon in the traditional sense, only because Pluto is considered a planet and Charon is a smaller object in the vicinity.