How can you prove that the sum of the forces of gravity on a group of objects would be the same as the force of gravity on an object with mass M equal to the sum of the masses of the objects and located in their center of gravity?
This is a necessary condition to prove that such an object would behave the same as the center of gravity of the group of objects.

Question

How can you prove that the sum of the forces of gravity on a group of objects would be the same as the force of gravity on an object with mass M equal to the sum of the masses of the objects and located in their center of gravity?
This is a necessary condition to prove that such an object would behave the same as the center of gravity of the group of objects.

anonymous · Answer

Hm, thank you for the answer, but I find the diagrams hard to understand :P. First why are there two equal and oppsite forces on CM? Let me draw the scenario I imagine.Scenario 1|dw:1347551404105:dw| Scenario 2 |dw:1347551673559:dw| In the first scenario F1, F2, etc are the forces acting on each of the objects, including the forces within the system and other forces outside the system. In scenario 2, F_CM is the force acting on the object shown. What I want to prove is that the sum of F1, F2, F3, etc is equal to F_CM