Question

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

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

Answer 1

Answer: (C)

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

Answer 2

Given $R_1 = R_e.$ $R_2=R_e+\frac{R_e}{2}=\frac{3}{2}R_e$ The orbital velocity of satellite is $v_0=\sqrt{\frac{GM_e}{R}}$ $\Rightarrow v_0\propto\sqrt{\frac{1}{R}}$ Hence, $\frac{v_1}{v_2}=\sqrt\frac{R_2}{R_1}$ $=\sqrt\frac{3R_e}{2R_e}=\sqrt{\frac{3}{2}}$ $v_2=\sqrt{\frac{2}{3}}v_1$ $=\sqrt{\frac{2}{3}}v_o$ $(=v_1=v_o)$