The mean radius of earth is $R$, its angular speed on its own axis is $\omega$ and the acceleration

Question

The mean radius of earth is $R$, its angular speed on its own axis is $\omega$ and the acceleration due to gravity at earth's surface is $g$. What will be the radius of the orbit of a geostationary satellite?\

Professor PC Thomas Classes · Answer

(a) : $\frac{G M m}{r^{2}}=m \omega^{2} r \Rightarrow r^{3}=\frac{G M}{\omega^{2}}=\frac{g R^{2}}{\omega^{2}}$\ $	herefore \quad r=\left(g R^{2} / \omega^{2}ight)^{1 / 3}$.