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##.
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