Gravity - Effective distance of center of earth

[John Davis]

To calculate the force of gravity from a distant body we assume the body is a point mass and it is therefore relatively easy to determine its effective distance. On the surface of the earth, the same formula is used and we use the radius of the Earth as the effective distance, thus we assume the Earth is a point mass at a distance of about 4000 miles.
But a cubic mile of Earth that is only 1 mile below the surface has a much greater effect than a cubic mile of Earth that is nearly 8000 miles below the surface. So how is it valid to assume the Earth is a point mass when we are so close to it?

 

[FunkyDwarf]

its because given uniform density you get cancelation of the affect on either side of the line of symmetry.

this is a proof of using Newtons law of gravity as a point mass for the Earth from my mechanics lectures

http://members.iinet.net.au/~housewrk/pointmass.jpg

 

[Doc Al]

But a cubic mile of Earth that is only 1 mile below the surface has a much greater effect than a cubic mile of Earth that is nearly 8000 miles below the surface. So how is it valid to assume the Earth is a point mass when we are so close to it?

Realize that a uniform spherical shell of mass m produces the same gravitational field as a point mass of mass m located at the center of the sphere. (This is one of Newton's shell theorems.) But that shell of Earth 1 mile below the surface is only one mile away from you at the near side--the other side is about 8000 miles away.

 

[FunkyDwarf]

yeh he's right, sorry i should have mentioned that :P
clever mr mentor :)