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Q.

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 $r_{1} a n d r_{2}$ respectively. The time-period of the planet is proportional to

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a

$r_{1}^{3 / 2}$

b

$r_{2}^{3 / 2}$

c

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

d

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

answer is C.

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Detailed Solution

According of Kepler’s law $T^{2} \propto a^{3}$

$a = s e m i m a j o r a x i s = (\frac{r_{1} + r_{2}}{2})$

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

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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 r1 and r2 respectively. The time-period of the planet is proportional to