Interesting stuff. I haven't seen anyone talk about the weight at the core. The pressure must be tremendous. But what about weight. Here's what I mean.

Imagine that you could make a little room, a hollow space, right at the exact center of the earth. Let's imagine that the room was the size of a bedroom in your house. If there happened to be a round rock in that room, and the rock was about 2 feet in diameter, how much would it weigh? Remember, all the mass and matter of the earth is pulling on the rock about equally from all directions. Probably the rock would be weightless.

Personally, I don't know how to picture gravity at the center of the earth. Whatever materials exist there must be compressed by the weight of the materials all around them so that they are somewhat condensed, making them denser than surrounding materials. The farther out you go, the less dense the material would be because it is under less pressure from the weight of the materials above it.

Density means more mass. The more the mass, the higher the gravity. Yet the gravity created by the center of the earth wouldn't be felt as much on itself as it would be by materials a bit further away from the center. Or would it?

Since nobody has been down there, and since we don't even have shafts that go more than a tiny fraction of the distance, there really is no telling what may be down there. Depending on how the earth formed, the whole thing just might be hollow, with the extreme pressures and densities within 1000 miles from the surface. And it just might be these densities that are misleading scientists into believing that the earth is solid all the way through.