Body behaves as Particle under Gravitation
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Theorem
A body of finite volume under a gravitational force behaves identically to a point mass under the same gravitational force.
Proof
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Historical Note
The fact that a Body behaves as Particle under Gravitation was proved by Isaac Newton after considerable work.
Some sources suggest that it took Newton some $20$ years to resolve this, and this is what explains the delay in publishing his work.
Its truth justifies the mathematical derivation of Newton's Law of Universal Gravitation.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.25$: Kepler's Laws and Newton's Law of Gravitation