Textbooks all say that the center of gravity of an object is the point at which all it's gravitaional effects appear to be concentrated. But that seems to depend on who's checking. (see atachment) Imagine a small mass M some distance from the Earth. That mass is attracted simultaneously by all the particles that make up the Earth. At first blush you would think that since the Earth is symetrical, they would average out and the center of gravity is at the geometric center. But that cannot be right. The gravitaional attraction between M and each particle is an inverse square law. That means that particles that are symmetrically each side of the Earth's center do not average to the center. So as far as M sees it, the center of gravity must be closer to m than the center point, right? I would have thought this would be a major effect on how M would orbit the Earth. Seems to me that the mass M would see the CG as a ring. The CG would follow M around a circular path around the center point. What am I missing?