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Mechanics

Testing the Inverse Square Law of Gravitation

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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 (approximately) 60 times further away from the centre of the earth, the acceleration due to gravity should be

9·8/60² = 2·72 × 10-3 ms-2
   
The centripetal acceleration of the moon is given by

The radius of the moon’s orbit is r = 3·84 × 108 m

The time period of the moon’s orbital motion is T = 27·3 days.

Using these figures we find that the centripetal acceleration of the moon is

2·72 × 10-3 ms-2

As the centripetal acceleration of the moon is provided by gravity, we can conclude that the inverse square law is a good theory.

 

© David Hoult 2008