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 3.84×10^{8}m 

The time period of the orbit of the moon, T = 27.3days = 2.36×10^{6}s 



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. 
