Quote "Imagine drilling a hole to the centre of the earth. As you go deeper, the gravity increases until you get near the centre.
At the centre, you'd be pulled in all directions, so would feel no net gravity, just like in a black hole (perhaps)."

Does the force you experience increase as you approach the centre? I'd have thought that the forces from rock outside your radius would balance out and then you'd be left with the forces from the sphere between you and the centre. Hmm, so its mass is proportional to the cube of its radius and you feel a force proportional to the mass and inversely proportional to the radius squared. So the gravitational force you feel drops roughly linearly as you approach the centre. Does that make sense?