Astronomy help with Kepler's 3rd law and Newton?

Why does Kepler's 3rd law work for the moons of Jupiter? Isn't his third law for planetary motion? Why did Newton derive his version of Kepler's 3rd law if Kepler's 3rd law already worked? I just don't understand why p^2=a^3 is the same as Newton's version which involves a constant and masses. show more Why does Kepler's 3rd law work for the moons of Jupiter? Isn't his third law for planetary motion? Why did Newton derive his version of Kepler's 3rd law if Kepler's 3rd law already worked?

I just don't understand why p^2=a^3 is the same as Newton's version which involves a constant and masses.
Update: Thanks for all the help guys
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