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Important Geographical Explorations

A planet move...

Question

A planet moves around the sun. At a given point $P$ , it is closest 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

A

\frac{d_{2} v_{1}}{d_{1}}

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B

\frac{d_{1} v_{1}}{d_{2}}

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C

\frac{d_{2}^{2} v_{1}}{d_{1}^{2}}

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D

\frac{d_{1}^{2} v_{1}}{d_{2}^{2}}

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Solution

The correct option is B $\frac{d_{1} v_{1}}{d_{2}}$
As we know from Kepler's law of planter motion, angular momentum of the planet about sun remains constant.
$m v_{1} d_{1} = m v_{2} d_{2}$
$v_{2} = \frac{d_{1} v_{1}}{d_{2}}$
Hence, final answer is (c).

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