Question 218 of 223

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$1:3$C$1:2$D$3:4$

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Answer: (A) $1:6$

From angular momentum conservation
${mV}_{1}{r}_{1}={mV}_{2}{r}_{2}$
$\dfrac{{r}_{1}}{{r}_{2}}=\dfrac{{v}_{2}}{{v}_{1}}=\dfrac{1}{6}$
$1:6$