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:

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

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

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

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

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Solution

The correct option is B $\frac{d_{1} v_{1}}{d_{2}}$
Planets movie in elliptical orbits around the sun and their angular momentum is constant.
i.e $\frac{L}{2 m} =$ constant

$\Rightarrow \frac{m v r}{2 m} =$ constant; where $m$ is the mass of the planet, $v$ is the linear speed of the planet, and $r$ the distance between planet and sun.
$\Rightarrow v_{1} r_{1} = v_{2} r_{2}$
$\Rightarrow v_{1} d_{1} = v_{2} d_{2}$
$\Rightarrow v_{2} = \frac{v_{1} d_{1}}{d_{2}}$

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A planet moves around the sun. At a given point P, it is closest from the sun at a distance d1, and has a speed v1 . At another point Q, when it is farthest from the sun at a distance d2, its speed will be:

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: