Kepler's third law states that square of period revolution `(T)` of a planet around the sun is proportional to third power of average distance `i` between sun and planet i.e. `T^(2)=Kr^(3)`
here `K` is constant
if the mass of sun and planet are `M` and `m` respectively then as per Newton's law of gravitational the force of alteaction between them is `F=(GMm)/(r^(2))`, here `G` is gravitational constant. The relation between `G` and `K` is described as

Options

A. `GK = 4pi^(2)`
B. `GMK = 4pi^(2)`
C. K = G
D. `K = (1)/(G)`

Answer

B

Explanation

`T = (2pi r)/(v) = (2pi r)/(sqrt((GM)/(r ))`
`T^(2) = (4pi^(2))/(GM)r^(3)`
On comparing with given equation `T^(2) = K r^(3)`
We have `K = (4pi^(2))/(GM)`
`MGK = 4pi^(2)`