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Question

If the distance between the Earth and the Sun was half of its present value, what will be the approximate number of days in a year on the Earth?

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Solution

Let the present time period of revolution of the earth be T1, i.e. 365 days
Let T2 be the time period of revolution when the distance between the Sun and the Earth is halved.
Let R1 be the present radius of revolution and R2 be the radius of revolution when the distance is halved.
R1=2R2
According to Kepler's law of period, R3T2TR32

T1T2=(R1R2)32=(R1R12)32=22
T2=T122=36522 days=129 days

Hence, the time period of revolution of the earth will be 129 days if the distance between the Earth and the Sun is halved.

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