R

#### ramparts

##### Guest

Air resistance only applies above ground, right? Where there's, like, air. So if we're going to include in our problem a period of falling through the air (say we start at a height above h off the ground), we need to make our differential equation a piecewise one. The first piece applies for R<r<h and would take the Earth to be a point source, but factor in air resistance. The second piece, for 0<r<R, is as I stated in my last post (but with different initial conditions).

Now we need to work out the nature of our travel through the Earth. Have we drilled a shaft through it? I prefer to treat our observer as a small particle that can pass through rock and stuff, but more realistically, let's say we drilled a hole. It's possible air would come through and we would, in fact, have to include air resistance throughout the whole problem. Even if not, the hole would have to be tight enough that we'll certainly have to take friction into account. Can someone please look up the coefficients of dynamic friction for each mineral found in the Earth's surface and for human flesh?

This is a problem I never, ever want to have to solve :lol:

Now, while we're being ridiculous, I'd like to propose that our problem take the density of the Earth not to be constant, but to scale with sin^2(r)