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 distance between the satellite and the planet at closest and farthest points is:

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

Answer 1

The correct option is A $1:6$

By angular momentum conservation $m{r}_{min}{v}_{max}=m{r}_{max}{v}_{min}$


Given, $v_{min}=\frac{v_{max}}{6}$
$\therefore \frac{r_{min}}{r_{max}}=\frac{v_{min}}{v_{max}}=\frac{1}{6}$