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Testing the Inverse Square Law of Gravitation
Evidence to support Newton's inverse square law of gravitation can be found in Kepler's third law of planetary motion.  
Here we consider the orbital motion of the moon around the earth to obtain similar confirmation.
 
The distance between the centre of the earth and the centre of the moon is about 60 times the radius of the earth.  
The acceleration due to gravity at the surface of the earth is 9.8ms-2  
   
If the inverse square law is correct, then, at a distance 60 times further away from the centre of the earth, the acceleration due to gravity should be  
 
The moon experiences a centripetal acceleration due to the force of gravity.  
The magnitude of this acceleration is given by  
 
   
The radius of the moon's orbit, r, is about 3.84108m  
The time period of the orbit of the moon, T = 27.3days = 2.36106s  
   
Using these last two figures we find that the speed of the moon in its orbit is about 1023ms-1  
So, using the equation for centripetal acceleration, above, gives  
 
   
The fact that these two figures for acceleration are the same provides convincing evidence that Newton's inverse square law of gravitation is a good theory.  
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