Question

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. $T^2=K{r}^3$ where 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 $F=\frac{GMm}{r^2}$ , here G is gravitational constant

The relation between G and K is described as:

• A. K=1/G
• B. GK=4π²
• C. GMK = 4π²
• D. K = G

Answer 1

The correct option is C

GMK = 4π²

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

$T=2\pi \frac{r}{\sqrt{\frac{GM}{r}}}=2\pi \frac{r^{\frac{3}{2}}}{\sqrt{GM}}{T}^2=\frac{4{\pi }^2}{GM}{r}^3=K{r}^3$

$\therefore K=\frac{4{\pi }^2}{GM}$

$GMK=4{\pi }^2$