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  4. If the distance between the earth and the sun is half its present value, the number of days in a year would have been

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Q. If the distance between the earth and the sun is half its present value, the number of days in a year would have been

UPSEEUPSEE 2013

Solution:

According to Kepler's law of period
$ \frac{T_{1}}{T_{2}}=\left(\frac{R_{1}}{R_{2}}\right)^{3 / 2}=\left(\frac{R_{1}}{R_{1} / 2}\right)^{3 / 2}\left(\because R_{2}=\frac{R_{1}}{2}\right)$
$=(2)^{3 / 2}=2 \sqrt{2} $
$\therefore \, T_{2} =\frac{T_{1}}{2 \sqrt{2}}=\frac{365}{2 \sqrt{2}}$ days
$=129$ days