If the distance between the earth & the sun were half its present value, the number of days in a year would have been

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Solution

According to Kepler's law, $T^{2} \propto R^{3}$
where $R$ is the radius of orbit and $T$ is the time period.
$∴ {(\frac{T_{2}}{T_{1}})}^{2} = {(\frac{R_{2}}{R_{1}})}^{3}$
or ${(\frac{T_{2}}{T_{1}})}^{2} = {(\frac{R_{1} / 2}{R_{1}})}^{3} = \frac{1}{8} = 0.125$

Since $T_{1} = 365 days$ (in 1 year),
$T_{2} = 129 days$

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If the distance between the Earth and the Sun were half its present value, the approximate number of days in a year on the Earth would have been:

If the distance between the earth and the sun were reduces to half its present value, Then the number of days in one year would have been

T^{2} \propto R^{3}

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