A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is :

\(\sqrt{\frac{gR^2}{R+x}}\)

\(mg (1 + \frac{x}{R})^{-2} = \frac{mv^2}{R+x}\)

\(\Rightarrow v = \sqrt{g(R+x)\frac{R^2}{(R+x)^2}}\)

\(\Rightarrow v = \sqrt{\frac{gR^2}{R+x}}\)