Question

A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities of satellites are $ 3\times 10^4 \, m/s $ and $ 1 \times 10^3 \, m/s $ respectively. What is the minimum distance of satellite from planet is maximum distance if $ 4 \times 10^4\, km $

• A. $ 4 \times 10^3\, km $
• B. $ 3 \times 10^3\, km $
• C. $ 4/3 \times 10^3 \,km $
• D. $ 1 \times 10^3\,km $

Answer 1

Answer: (C)

If no external torque acts on a system, then angular momentum of the system does not change.
ie, If $\tau=0$
$\Rightarrow \frac{d L}{d t} =0$
$\therefore L=$ constant
Hence,
$m v_{\max } r_{\min } =m v_{\min } r_{\max }$
$\Rightarrow r_{\min } =\frac{v_{\min } \times r_{\max }}{v_{\max }}$
$=\frac{1 \times 10^{3} \times 4 \times 10^{4}}{3 \times 10^{4}}$
$=\frac{4}{3} \times 10^{3}\, km$