Center of mass and planetary motion

[aaaa202]

Why is it that for instance the Earth and the moon orbit their common center of mass? I mean surely the moon feels a gravitational force as though the mass of the Earth were concentrated at its center? If yes, what is that then makes it orbit around their center of mass rather than this point. I do realize that the Earth will also feel a gravitational force from the moon, but I still don't really see it. Can you explain this intuitively and do any of you have a link that might explain it well?

 

[mathman]

http://en.wikipedia.org/wiki/Two-body_problem

The above is the whole story.

 

[Drakkith]

Imagine a dad swinging his little girl around in a circle. He has to lean backwards a little bit in order to avoid falling over. The "center of mass" for this scenario is no longer inside either of the two people, just like it isn't exactly in the middle of the Earth or the Moon. The article mathman linked will explain it in detail.