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

Explanation

`(F) = (GMm)/(r^(2)) = m omega^(2) r`
`omega^(2) = (GM)/(r^(3))`
`(4 pi^(2))/(Kr^(3)) = (GM)/(r^(3))`
`(4 pi r^(2))/(Kr^(3)) = (GM)/(r^(3))`
`GMK = 4 pi^(2)`