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Q & A: Why gravitational forces are calculated from the centre?

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Most recent answer: 03/01/2015
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
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)

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