How Kepler derived that T^2 is proportional to r^3

[parsa418]

How did Kepler exactly prove that the period squared is proportional to the radius cubed? If he didn't prove it. Then how is it proven?

 

[Mapes]

How did Kepler exactly prove that the period squared is proportional to the radius cubed? If he didn't prove it. Then how is it proven?

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Deriving_Kepler.27s_third_law"

 

[nasu]

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Deriving_Kepler.27s_third_law"

Kepler did not derive any of his laws from the law of gravity.
He found it by experiment, using the observation data of the planetary motions to find the relative distances and the periods of the orbital motions and then looking for a relationship between these quantities.
Newton's law came later and it was supported by the fact that it can explain the laws that Kepler found by "experiment".