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# A planet moves around the sun. At a given point P,it is closet from the sun at a distance $d_1$ and speed $v_1$ At another point Q when it is farthest from the sun at a distance $d_2$, its speed will be

$a)\;\large\frac{d_1^2v_1}{{d_2}^2} \\ b) \; \large\frac{d_2v_1}{d_2} \\ c) \;\large\frac{d_1v_1}{d_2}\\ d) \large\frac{{d_2}^2 v_1}{{d_1}^2}$

Angular momentum of the planet remains constant
$mv_1d_1=mv_2d_2$
$=>v_2=\large\frac{v_1d_1}{d_2}$
Hence b is the correct answer.
edited Apr 1, 2014 by meena.p