were obtained from direct observation of planetary motion but can be derived from Newton’s universal law.

You might want to look at:http://www.physicsclassroom.com/class/circles/Lesson-4/Kepler-s-Three-Laws

A quick example is as follows:the universal law is

##F={GMm}/R^2##

where ##M## is the mass of the Sun say ##m## of a planet and ##R## the radius of its orbit.

Now since ##F=ma## we can rewritte this as

##a={M}/R^2##

At this point we can apply dimensional analysis by noting that is a length divided by a time squared and thus must be given by

## a propto R/T^2##

where ##T## is the period of the orbit – the only thing we don’t know is the constant of proportionality (but that’s not part of Kepler’s law). So we have

## {GM}/R^2 propto R/T^2##

which dropping the unimportant constant ##GM## and rearranging gives

## T^2 propto R^3##.