Q 11-07-164JEE MainJEE Main 2020 (6 Sep, Shift 1)Easy
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 the closest and farthest points is:
Answer: (A) $1:6$
At the closest and farthest points the velocity is perpendicular to the radius, so conservation of angular momentum gives $r_1v_1 = r_2v_2$:
$$\frac{r_{\text{closest}}}{r_{\text{farthest}}} = \frac{v_{\text{farthest}}}{v_{\text{closest}}} = \frac16$$
Solution by Sreeraj P, M.Sc Physics