The velocity of a planet revolving around the sun at three different times of a year is shown in the figure. Which among the following alternatives is correct ?

v_{2} = \frac{v_{1} + v_{3}}{2}

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v_{1} = \frac{v_{2} + v_{3}}{2}

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v_{1} > v_{2} > v_{3}

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v_{1} < v_{2} < v_{3}

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Solution

The correct option is C $v_{1} > v_{2} > v_{3}$
Kepler's law states that angular momentum is conserved.
$L = c o n s t a n t$
$v_{1} r_{1} = v_{2} r_{2} = v_{3} r_{3}$
r is the position vector from one point to the sun.
As we can see from the ellipse:
$r_{3} > r_{2} > r_{1}$
Hence,
$v_{1} > v_{2} > v_{3}$
Option C is correct.

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