Quote Originally Posted by OngBonga View Post
But they're still orbitting each other. It's not like they were orbitting something that was where the x is, and now it's gone.
They're orbiting each other PLUS a thing at x.

That thing at x is many orders of magnitude smaller than the combined center of mass at x.

EDIT: So if you take away the thing at x, you really haven't changed much of anything.