I may have some confusion with the terms "pressure" and "gravity" here. If hypothetically we could sink towards the centre of the Earth, say with our feet pointing towards it, as we start to sink intuitively pressure on top of us would gradually increase, as it does when we sink into the ocean dephts. As for the force of gravity, when we are at the surface all of it pulls us towards the center, but it would gradually reduce, and once in the very centre we would not feel any gravity at all, since an equal amount of mass would be pulling us in every direction towards the outside (towards the surface). Now, I intuitively attribute pressure to the force of gravity, when in the depth of the ocean we have the pressure of the water on top because it is being pulled towards the centre by the Earth's gravity. If the net effect of gravity at the center is zero, it seems that pressure should also be zero, since the stuff just around us is being pulled away towards the outside as much as is being pulled towards us in the opposite direction. There's no reason it should still be pulled towards the center since at the center there is no mass, the mass is now in the sphere surrounding us so the stuff is being pulled outwards equally in every direction. It seems that as we get deeper and deeper, we would experience an increase of pressure but a decrease in gravity, and at some point in the voyage things would start to reverse and pressure would start decreasing until becoming zero at the center. And yet I guess that the center is the most dense point, so what is wrong with my reasoning?