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.

If the mean radius of the Earth is R, its angular velocity is omega an

1.	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.
Answer» Solution :Let R the radiusof thegeostationaryorbit . Angularvelocity of revolution of a geostationarysatellite is same as the angularvelocity 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))`