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Kepler's third law states that square of...

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

A

`GMK = 4 pi^(2)`

B

`K = G`

C

`K = (1)/(G)`

D

`GK = 4 pi r^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
As time period of revolution
`T = (2pi r)/(upsilon) = (2pi r)/(sqrt(GM)) sqrt(r ) [:' upsilon = sqrt((GM)/(r ))]`
`T = (2 pi r^(3//2))/(sqrt(GM))`, squaring both sides we get
`T^(2) = (4 pi^(2) r^(3))/(GM) = kr^(3)` (Given),
`:. K = (4pi^(2))/(GM)` or `GM K = 4pi^(2)`
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