The period of revolution of a planet in its orbit
 

Let us suppose the orbit to be circular so that r = a. Then expression (1)

(1)

becomes
(2)
But
V = 2πa/T
where T is the time it takes the planet to describe its circular orbit. Hence,
(3)
Although it will not be proved here, the expression (3) holds even when the orbit is elliptical, a being the semi-major axis of the orbit.