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. That means T^2 = Kr^3here 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

Kepler's third law states that square of period of revolution (T) of a

1.	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. That means T^2 = Kr^3here 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
Answer» `GK = 4pi^2` `GMK = 4pi^2` `K=G` `K = 1/G` SOLUTION :`implies` HINT : `T = (2pi)/OMEGA = (2pir)/v "" [ :. omega = v/r]` `:. T = (2pir)/sqrt(GM) xxsqrtr "" [ :. v = sqrt((GM)/r)]` `:. T = (2pi) / sqrt(GM) .r^(3/2)` `:. T^(2)= (4pi^2)/(GM) .r^3` COMPARING this equaotion with equation `T^2 =Kr^3` `:. K = (4pi^2)/(GM)` `:. GMK = 4pi^2)`