Question

A satellite orbiting the earth in a circular orbit of radius $R$ completes one revolution in $3h$. If orbital radius of geostationary satellite is $36000km$, orbital radius of satellite is

• A. $6000km$
• B. $9000km$
• C. $12000km$
• D. $15000km$

Answer 1

Answer: (B)

$9000km$

For satellites, the centripetal force for rotation is provided by the gravitational force acting on them. So, we have:

$\frac{GmM}{R^2}=\frac{m{v}^2}{R}\Rightarrow v=\sqrt{\frac{GM}{R}}\Rightarrow T=\frac{2\pi R}{v}=\frac{2\pi }{\sqrt{GM}}{R}^{\frac{3}{2}}\Rightarrow \frac{T_1}{T_2}=\frac{R_1^{1.5}}{R_2^{1.5}}$

We have, $T_2=3hr{T}_1=24hr{R}_1=36000km$

Therefore, $R_2=\frac{R_1{T}_2^{\frac{2}{3}}}{T_1^{\frac{2}{3}}}=36000\times {\left(\frac{3}{24}\right)}^{\frac{2}{3}}=\frac{36000}{4}=9000km$