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

Gravitation

Solution:

According to law of conservation of angular momentum
$mv_1d_1 = mv_2d_2$
$mv_1d_1 = mv_2d_2$
$\therefore v_2 = \frac{d_1v_1}{d_2}$