I was thinking that any solid -- such as a planet -- can be replaced by a point at its center with equal mass, and its neighbors -- such as a moon -- wouldn't n

I was thinking that any solid -- such as a planet -- can be replaced by a point at its center with equal mass, and its neighbors -- such as a moon -- wouldn't notice. But that's not entirely true.... For instance, replace the earth with an equal size ball of styrofoam, and place two super-dense basketball-sized masses, one in Californis and the other in Africa (I.e. on the opposite sides of the globe.) And, assume, the entire system is the same mass as our earth, assume the 'center of mass' is at the core of the styrofoam planet, and assume the styrofoam is magically able to keep our two Neutron-star-dense basketballs in place. Phew.... Now, the moon probably wouldn't notice s thing. From its point of view, it will 'feel' the same attraction as it would from our planet. But, something much closer -- such as a mile or two of water -- would definitely bunch up around the basketballs and would not form a sphere around the center of our imagine planet. Is that right?