Question

Two satellites $A$ and $B$ go around the earth in circular orbits at heights of $R_{A}$ and $R_{B}$ respectively from the surface of the earth. Assuming the earth to be a uniform sphere of radius $R_{e},$ the ratio of the magnitudes of their orbital velocities is :-

• A. $\sqrt{\frac{R_{B}}{R_{A}}}$
• B. $\frac{R_{B} + R_{e}}{R_{A} + R_{e}}$
• C. $\sqrt{\frac{R_{B} + R_{e}}{R_{A} + R_{e}}}$
• D. $\left(\frac{R_{A}}{R_{B}}\right)^{2}$

Answer 1

Answer: (C)

since, orbital velocity is inversely proportional to the square root of the radius of the orbit,
$\frac{v_{A}}{v_{B}}=\sqrt{\frac{R_{B} + R_{e}}{R_{A} + R_{e}}}$