Aaaah, so objects are attracted to a mutual center of mass! I always thought Little was simply attracted to Big.
I now understand your first answer, phyzguy. Thanks jtbell for clarifying that for me.
Can I beg your patience to let me re-coach my original question (How do objects communicate?):
I can accept Newton's Second Law and I can accept that objects must obey, but my question is how do objects announce their presence to each other?
Lets say two balls are placed on the floor in a low gravity environment. One ball is large enough that the smaller ball is attracted to a center of gravity that is inside the big ball (slightly off center). Given low enough outside resistance, these two will warble toward each other.
But what caused Newton's Second to happen? Did the big ball pick up an atom sized cell phone and ring the little ball? "Um, yea, listen dude... I just happened to look out my window and see you over. Not sure if you know it, but we're kinda close to each other. My density is X and volume is Y... I'm pretty sure I'm a lot bigger than you. So if you don't mind, I think you should go ahead and start rolling toward me before the physics cops come by and write us up."