Question

The orbital velocity of an artificial satellite in a circular orbit of a height $R$ above earth's surface is $v$ ($R$ is radius of earth). The orbit velocity of a satellite orbiting at an altitude $2R$ above the earth's surface will be:

• A. $v/2$
• B. $\frac{3}{2}v$
• C. $\frac{2}{3}v$
• D. $\sqrt{\frac{2}{3}}v$

Answer 1

Answer: (D)

$\sqrt{\frac{2}{3}}v$

Orbital velocity $=\sqrt{\frac{GM}{r}}$

Where $r$ is the distance of satellite from the centre of earth.

$V=\sqrt{\frac{GM}{2R}}$

$V^1=\sqrt{\frac{GM}{3R}\times \frac{2}{2}}$

$V^1=\sqrt{\frac{2}{3}}\sqrt{\frac{GM}{2R}}$

$V^1=\sqrt{\frac{2}{3}}V$