If the mean radius of the Earth is R, its angular velocity is `omega` and the acceleration due to gravity at the surface of the Earth is g, then what will be the cube of the radius of the orbit of a geostationary satellite.

Explanation

Let r the radius of the geostationary orbit . Angular velocity of revolution of a geostationary satellite is same as the angular velocity of rotation of the Earth .
`mromega^(2) = (GMm)/(r^(2))`
` r^(3) = (GMm)/(momega^(2)) xx (R^(2))/(R^(2)) = (GM)/(R^(2)) ((R^(2))/(omega^(2))) " " [ g = (GM)/(R^(2))] `
` r^(3) = (gR^(2))/(omega^(2))`