A satellite is in an elliptical orbit around a planet P.
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 :

  1. (1) $1: 6$

  2. (2) $1: 3$

  3. (3) $1: 2$

  4. (4) $3: 4$


Correct Option: 1

Solution:

(1) By angular momentum conservation

$r_{\min } v_{\max }=m r_{\max } v_{\min }$

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

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

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