Question

The ratio of the orbital speeds of two satellites of the earth if the satellites are at heights $6400$ km and $19200$ km from the surface of the Earth. (Radius of the earth $=6400$ km.) :

• A. $\sqrt{2}:1$
• B. $\sqrt{3}:1$
• C. $2:1$
• D. $3:1$

Answer 1

The correct option is A $\sqrt{2}:1$

Orbital Speed is given by: $V\propto \frac{1}{\sqrt{R}}$
Hence, $\frac{V_1}{V_2}=\sqrt{\frac{R_2}{R_1}}$
$\frac{V_1}{V_2}=\sqrt{\frac{19200+6400}{6400+6400}}$
$\frac{V_1}{V_2}=\sqrt{2}$

Hence, the orbital speeds are in the ratio $\sqrt{2}:1$