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)
$\frac{\mathrm{r}_{\min }}{\mathrm{r}_{\max }}=\frac{\mathrm{V}_{\min }}{\mathrm{V}_{\max }}=\frac{1}{6}$
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