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  4. A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r 2. If v 1 and v 2 are the linear velocities at these points respectively, then the ratio ( v 1/ v 2) is:

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Q. A planet moving along an elliptical orbit is closest to the sun at a distance $r_{1}$ and farthest away at a distance of $r _{2}$. If $v _{1}$ and $v _{2}$ are the linear velocities at these points respectively, then the ratio $\frac{ v _{1}}{ v _{2}}$ is:

AIPMTAIPMT 2011Gravitation

Solution:

According to the law of conservation of angular momentum
$L_{1} =L_{2}$
$m v_{1} r_{1} =m v_{2} r_{2} $
$\Rightarrow v_{1} r_{1}=v_{2} r_{2} $
or $ \frac{v_{1}}{v_{2}}=\frac{r_{2}}{r_{1}}$