The elliptical orbits of the planets are very
nearly circular. 

Here we will assume circular obits for simplicity. 






Applying Newton's law of gravitation to the situation shown here, we have 







this force gives the planet its centripetal acceleration so we
can also write 



These two equations lead us to 



Remembering that 



gives the following equation 



which is a statement of Kepler's third law as everything on the right hand
side is constant. 



This can be considered as further evidence to support the inverse square law
of gravitation. 
