Kepler's third law Definition and 52 Threads

How did Kepler come about to conclude that his third law is Radius3/Period2? How did he derive this equation?

Hi, I just got my physics test back and am hoping I can be helped with two questions. My instructor gave it back at the end of class leaving no time for going over it. 1) Suppose the period of the moon in its orbit about the Earth were 41.1 days and the moon were 768,000 km from earth...