It is often more useful to consider the time taken for a complete orbit, the orbital period T.
Since the distance around an orbit is equal to the circumference 2πr, it follows that:

$v = \frac{{2\pi r}}{T}$

We can substitute this in the equation for ${v^2}$.
This gives:

$\frac{{4{\pi ^2}{r^2}}}{{{T^2}}} = \frac{{GM}}{r}$

and rearranging this equation gives:

${T^2} = \left( {\frac{{4{\pi ^2}}}{{GM}}} \right){r^3}$ 

or ${\sqrt {\frac{{4\pi {r^3}}}{{GM}}} }$

This equation shows that the orbital period T is related to the radius r of the orbit. The square of the period is directly proportional to the cube of the radius $({T^2} \propto {r^3})$. This is an important result. It was first discovered by Johannes Kepler, who analysed the available data for the planets of the Solar System. It was an empirical law (one based solely on experiment) since he had no theory to explain why there should be this relationship between T and r. It was not until Isaac Newton formulated his law of gravitation that it was possible to explain this fact.