Q:

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

- louis woolfson (age 87)

leeds

A:

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)*