Question:
A satellite is in an elliptical orbit around a planet $P$. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is :
Correct Option: 1
Solution:
(1) By angular momentum conservation
$r_{\min } v_{\max }=m r_{\max } v_{\min }$
Given, $v_{\min }=\frac{v_{\max }}{6}$
$\therefore \frac{r_{\min }}{r_{\max }}=\frac{v_{\min }}{v_{\max }}=\frac{1}{6}$