Question

The orbital velocity of an artificial satellite in a circular orbit very close to Earth is $v$. The velocity of a geosynchronous satellite orbiting in a circular orbit at an altitude of $6 R$ from Earth's surface will be

• A. $\frac{v}{\sqrt{7}}$
• B. $\frac{v}{\sqrt{6}}$
• C. $v$
• D. $\sqrt{6} v$

Answer 1

Answer: (A)

For a satellite, $\frac{m v^{2}}{R}=\frac{G M m}{R^{2}} ; v^{2}=\frac{G M}{R}$
$\left(\frac{v_{2}}{v_{1}}\right)^{2}=\left(\frac{R_{1}}{R_{2}}\right) \Rightarrow \left(\frac{v^{\prime}}{v}\right)^{2}=\left(\frac{R}{R+6 R}\right)$
$\Rightarrow v^{\prime}=\frac{v}{\sqrt{7}}$