Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T² = Kr³ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = GMm/r² , here G is gravitational constant. The relation between G and K is described as :

GMK = 4\(\pi ^ 2\)

T = \(\frac{2\pi r}{v}\)

v = \(\sqrt{\frac{GM}{r}}\)

⇒ \(T^2 = \frac{4 \pi^2 r^3}{GM}\)

comparing with : T² = Kr³

K = \(\frac{4 \pi^2}{GM}\)