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A planet is moving in an elliptical path around the sun of shown speed of planet in position P and Q are $v_1$ and $v_2$ respectively with $SP= r_1\;and SQ=r_2$ then $v_1/v_2$ is equal to

$a) \; \frac{r_1}{r_2} \\ b) \;\frac{r_2}{r_1} \\ c) \;constant \\ d)\; \bigg(\frac{r_1}{r_2}\bigg)^2$

The angular momentum of planet about sun is constant.
ie $mvr \sin \theta$= constant
where $\theta$ is the angle between radius vector and velocity vector
At P and Q $\theta=90^{\circ}$
and $m-$ mass of planet is constant.
$\therefore \; vr= constant$
$\large\frac{v_1}{v_2}=\frac{r_2}{r_1}$
Hence b is the correct answer.

edited Mar 14, 2014 by meena.p