Marcus, you are right that gravity would steadily decrease as you burrowed deeper and deeper into the Earth. A math teacher just explained it to me. The thing is, the mass that is above you would pull you in the opposite direction of the mass that is beneath you, and the deeper you burrowed, the more mass would be above you.
If we could compress the Earth, so that it still contained the same mass but had a smaller radius, then gravity would pull at you more strongly when you were standing on its surface than it does today. Or so I really believe anyway. I think that, in math-speak, you would say that a smaller Earth with the same mass would have a steeper gravity well.
Gravity as a function of mass and distance is a
really tricky business. Imagine, for example, that we could shrink the Sun into a black hole. If this happened, the Sun would get an incredibly steep gravity well, pulling everything inside that ventured too close, and crushing every hapless incoming morsel into nothingness. But the Earth would not be pulled inside. Why not? Well, because we are not pulled inside today, and the Sun's total gravity would not increase if it became a singularity. We are in a stable orbit around the Sun, and that wouldn't change if the Sun turned into a black hole.
Imagine what would happen if the innermost core of the Earth became a black hole. I
believe that the black hole core of the Earth would start eating up the rest of the Earth, but because this black hole would be extremely tiny, it would only be able to swallow tiny morsels at a time. In other words, the inner black hole would inexorably eat away at the Earth, but it would take a long time before it affected the surface of the Earth, where we live.
On the other hand, a black hole Earth would never be able to swallow the Moon, because the Moon is too far away from the Earth, in a stable orbit around it. Or so I believe at least, but as you've seen, I've been wrong before! So if I got this wrong too, I'd appreciate it if anyone cared to enlighten me!
Ann
