Question

A satellite moves in an elliptical orbit about a planet. The maximum and minimum velocities of the satellite are $3 \times 10^{4} \,m / s$ and $1 \times 10^{3} \,m / s$, respectively. If the minimum distance of the satellite from the planet is $\frac{m}{n} \times 10^{3} \,km$ then find $(m-n)$.
(The maximum distance of the satellite from the planet is $4 \times 10^{4} \,km$.)

Answer 1

By conservation of angular momentum,
$m v_{\max } d_{\min }=m v_{\min } d_{\max }$
$d_{\min }=\frac{v_{\min } d_{\max }}{v_{\max }}=\frac{1 \times 10^{3} \times 4 \times 10^{4}}{3 \times 10^{4}}$
$=\frac{4}{3} \times 10^{3} km$