Question

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius, the orbital velocity will be

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

Answer 1

The correct option is C $\sqrt{\frac{2}{3}}v$

The orbital velocity of a satellite in circular orbit of radius $R$ of a planet having mass $M$ is given by $$v=\sqrt{\frac{GM}{R}}$$ $\Rightarrow v\propto \frac{1}{\sqrt{R}}$

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{R_2}{R_1}}$

Given,
Let, the radius of the earth be $R$ so, $R_1=R$

For a satellite orbiting at an altitude of half the earth's radius, $R_2=R+\frac{R}{2}$

$\Rightarrow v_2=\sqrt{\frac{R}{R+\frac{R}{2}}}v$

$\therefore v_2=\sqrt{\frac{2}{3}}v$

Hence, option (c) is the correct answer.

Key Concept: The orbital velocity of a satellite is given by $$v=\sqrt{\frac{GM}{r}}$$