So I've followed and understood the proof that inside a thin hollow shell the gravitational potential is constant and hence the force is zero, but when applying it to a problem (namely "how does the force depend on the distance for an object dropped through the Earth in a narrow tunnel") I'm slightly confused:
The solution stated that only the sphere of mass "below" the falling object exerts a gravitational force. Is this because we have broken up the whole planet into 2 parts:
Above the momentary position (that is, all the mass that is farther away from the center of the earth then the object)
Below the momentary position ( The sphere with radius = position from the center)
so the "above" can be thought of as a bunch of thin hollow shells and hence it doesn't exert force, and the below part as regular ball of mass ?