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 ?

• A. $(R^2 g / {\omega}^2 ) ^{1/3}$
• B. $(R g / {\omega}^2 ) ^{1/3}$
• C. $(R^2 {\omega}^2 /g ) ^{1/3}$
• D. $(R^2 g / \omega) ^{1/3}$

Answer 1

Answer: (A)

$(R^2 g / {\omega}^2 ) ^{1/3}$

Answer 2

$\frac{ GM m }{r^2} = m {\omega}^2 r \Rightarrow r^3 = \frac{GM}{ {\omega}^2} = \frac{ g R^2}{{\omega}^2}$
$\therefore \, \, \, \, r = ( g R^2 / {\omega}^2 ) ^{1/3}$