Question

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

• A. $\left(\sqrt{\left(\frac{2}{3}\right)}\right)v_0$
• B. $\frac{2}{3}{v}_0$
• C. $\frac{3}{2}{v}_0$
• D. $\sqrt{\left(\frac{3}{2}\right)}{v}_0$

Answer 1

Answer: (A)

$\left(\sqrt{\left(\frac{2}{3}\right)}\right)v_0$

$v=\sqrt{\left(\frac{GM}{r}\right)}$ where $r$ is radius of the orbit of the satellite.
here $r=R_e+h=R_e+\frac{R_e}{2}=\frac{3}{2}{R}_e$
So, $v=\sqrt{\frac{2GM}{3R_e}}=v_0\sqrt{\frac{2}{3}}$
where $v_0$ is the orbital velocity of the satellite, which is moving in circular orbits of a radius, $r=R_e$