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 $\tau =0$
$\Rightarrow \frac{dL}{dt}=0$
$\therefore L=$ constant
Hence,
$m{v}_{\max }{r}_{\min }=m{v}_{\min }{r}_{\max }$
$\Rightarrow r_{\min }=\frac{v_{\min }\times r_{\max }}{v_{\max }}$
$=\frac{1\times 10^3\times 4\times 10^4}{3\times 10^4}$
$=\frac{4}{3}\times 10^{3}km$