Earth Gravity

If you think about what we have previously learned about gravity, every bit of mass pulls on every other bit. So the dirt right under your feet is exerting gravity, and dirt on the other side of the globe is as well. But the r² term in that equation says that the stuff close to you pulls much harder. It seems that if you want to know how all the earth together pulls on you, you must sum the effects of each individual bit.

The problem is simpler if we can think of the earth (or whatever) as an onion of nested spherical shells, where each shell is about uniform density. This is a fair assumption because for any very large object, gravity itself will collapse the thing down into a sphere shape and roughly sort the material of the sphere with denser material closer to the center. The Shell Theorem, proved by the ubiquitous Issac Newton, says that for any one of these shells, for the purposes of calculating the gravitational effect of the whole, it is equivalent to assume all of the mass is at a point in the center. Now, as you add the shells together, each tells you to model it’s mass at the same center point, so it’s valid to do that for the whole solid sphere.

The interesting flip side of that theory is that at any point Inside a hollow shell, you will feel no gravity from the shell. At the center this is not surprising, it’s pulling you in all directions equally and it cancels out. And with some thought it makes sense when you’re near the edge (but still inside) also. If you consider the part of the shell that is pulling you generally out from the center, it’s small but close to you. The remainder pulling you in toward the center is much larger, but farther away, so the effects balance out.

So, if you were to tunnel down into the earth, the further you went the less gravity you would feel until weightlessness at the center. Similarly, the gravitational effect of the atmosphere on you is roughly cancelled out to zero, because you are inside that shell.

Some have held the theory that the earth actually is a hollow shell, and that others inhabit the interior face with their own atmosphere, and even their own small sun at the center. We see now one reason this is would not work well. The inhabitants of the interior would feel no gravity holding them to the ground, only a slight (about 2 oz) centrifugal force.  The gravitational effect of the atmosphere inside the hollow earth and the small sun would likely overcome that effect and cause everything to  drift up into the center.