Re: What happens to an apple falling through a hole in the earth?

The question has to do with what will happen to the apple in the following schematic.

First, there is an answer previously posted to the MadSci Network which provides some information:
one

Second, as this previous answer says, the earth is spinning, and the apple, even though it will start down the tunnel that goes through the center of the earth, will eventually hit the eastern wall of the tunnel due to its angular momentum. If it could go down the tunnel and not bang into the side walls, it would oscillate back and forth (up and down) in the tunnel until frictional losses due to the air caused it to eventually settle at the center of the earth.

You may be wondering why the apple would oscillate (let's neglect air resistance and the sides of the tunnel for just a moment for this discussion). Gauss's law of gravitation (which is similar to Gauss's law of electrostatics) says that, for a spherically symmetrical mass, only the mass inside a spherical shell contributes any net gravitational acceleration. That is, if you could actually go inside the earth, and if the earth were 100% spherically symmetric in the distribution of its material, at the very center of the earth the net gravitational acceleration is zero!! So the apple would accelerate down the hole until it reached the center of the earth (although the magnitude of the acceleration would continually decrease to zero the closer it approached the center), and then the acceleration would slow it to a stop just as it got back to the surface on the other side. Neglecting air resistance and the angular momentum, the apple would do this forever (well, okay, after a while the apple would rot).

There is a good treatment of this question in the famous Halliday and Resnick textbook of physics ("Physics", David Halliday and Robert Resnick, published by John Wiley and Sons). I have a very old copy (1960), in which chapter 16 discusses gravity. Section 16-6 discusses spherical distributions of mass, and in that section there is actually an example (Example 3) which talks about a particle moving in a tunnel through the earth.

Well, I sure hope this helps!!

John Link, MadSci Physicist