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 :

• A. 1 : 6
• B. 3 : 4
• C. 1 : 3
• D. 1 : 2

Answer 1

Answer: (A)

By angular momentum conservation
$r_{\min }{v}_{\max }=r_{\max }{v}_{\min }\dots (i)$
Given $v_{\min }=\frac{v_{\max }}{6}$
from equation (i)
$\frac{r_{\min }}{r_{\max }}=\frac{V_{\min }}{V_{\max }}=\frac{1}{6}$