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Kepler's Law

A planet of m...

Question

A planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distance of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The time period of the planet is proportional to

A

r_{1}^{2 / 5}

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B

{(r_{1} + r_{2})}_{1}^{3 / 2}

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C

{(r_{1} - r_{2})}_{1}^{3 / 2}

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D

r^{3 / 2}

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Solution

The correct option is A ${(r_{1} + r_{2})}_{1}^{3 / 2}$
Kepler's third law:
Square of the time period $T$ is directly proportional to cube of semi-major axis i.e mean distance of the planet $\frac{r_{1} + r_{2}}{2}$
$T^{2} \propto {(\frac{r_{1} + r_{2}}{2})}^{3}$

$T \propto {(r_{1} + r_{2})}^{3 / 2}$

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