Why Gravitational Forces are Calculated From the Centre?

When gravitational forces are measured they are calculated from the centre of the earth for example. I would like to see a mathematical proof that this is so.
- louis woolfson (age 87)
leeds

This is not very easy to show, but what you do is to divide the Earth first into spherical shells. And to calculate the total gravitational force between a shell and a point object at a certain distance by dividing the shell into infinitesimal elements (i.e. take an integral on the shell of infinitesimal thickness using the solid angle). You can see it in  .  Now, the derivation in that link proves you that you can consider each shell can be considered as a point mass at the center. Since the shells that make up a spherical planet are concentric, that implies the whole planet can be considered as concentrated at the center.

Tunc

(published on 03/01/2015)