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:
By angular momentum conservation
$\mathrm{r}_{\min } \mathrm{v}_{\max }=\mathrm{r}_{\max } \mathrm{v}_{\min }$.......(1)
Given $\mathrm{V}_{\min }=\frac{\mathrm{v}_{\max }}{6}$
from equation (i)
$\frac{r_{\min }}{r_{\max }}=\frac{v_{\min }}{v_{\max }}=\frac{1}{6}$
Ans. (1)