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 :
Answer & explanation
Correct answer: option 1
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 = \(\frac{4 \pi^2}{GM}\)