/sci/ - Science & Math

>>9648890
The reason underlying it is quite mathematical, but the basic result is that you feel no gravitational force from the inside of a spherical shell of matter.

When you go deep into the earth, the contributions to the gravitational force you feel then are the contribution from the sphere of matter deeper than you, and the contribution from the shell of matter outside of you. So if you dig down to a depth d (see figure), then the sphere of matter you're outside of is of radius R-d if R is the radius of the earth. Since the spherical shell of matter around you of thickness d doesn't exert a force on you, then you are only feeling gravitational force due to the smaller sphere, which contains less matter than the entire sphere, and is hence less massive, so exerts a smaller force on you.

In addition, I would add that to get some intuitive understanding of why a spherical shell exerts no force on you if you're inside it, imagine you dug down to the centre of the earth. There's equal amounts of mass above you, below you, to the left, to the right, etc. So whatever gravitational force each bit of matter would exert on you is cancelled out by a force in the opposite direction from a piece of matter opposite to it.