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 between sun and planet ?
i.e.,`T^2=Kr^3`
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)/(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

The required centripetal force for the rotation of a planet is provided by the gravitational force,
`therefore (mv^2)/r =(GMm)/(r^2) or, v^2=(GM)/r`
so, time period ,
`T=(2pi r)/v or, T^2=(4pi^2r^2)/(GM//r)=(4pi^2)/(GM)r^3=Kr^3`
Hence,`(4pi^2)/(GM)=K or, GMK=4pi^2`