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  4. A planet of the sun is in a circular orbit around the sun, midway between the sun and the earth. Then

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Q. A planet of the sun is in a circular orbit around the sun, midway between the sun and the earth. Then

NTA AbhyasNTA Abhyas 2020Gravitation

Solution:

$T^{2} \propto \, r^{3}$
$\frac{T_{1}}{T_{2}}=\left(\frac{r}{r / 2}\right)^{3 / 2}$
$\frac{365 \, \text{days}}{T}=2\sqrt{2}; \, T=\frac{365}{2 \sqrt{2}} \, \text{days} \, \, \, \Rightarrow 129 \, \text{days}$