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)

Given $R_1=R_e.$
$R_2=R_e+\frac{R_e}{2}=\frac{3}{2}{R}_e$
The orbital velocity of satellite is
$v_0=\sqrt{\frac{G{M}_e}{R}}$
$\Rightarrow v_0\propto \sqrt{\frac{1}{R}}$
Hence, $\frac{v_1}{v_2}=\sqrt{\frac{R_2}{R_1}}$
$=\sqrt{\frac{3R_e}{2R_e}}=\sqrt{\frac{3}{2}}$
$v_2=\sqrt{\frac{2}{3}}{v}_1$
$=\sqrt{\frac{2}{3}}{v}_o$ $(=v_1=v_o)$