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Question

# 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:

A

64.5 days

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B

129 days

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C

182.5 days

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D

730 days

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Solution

## The correct option is B 129 days 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, R3∝T2⟹T∝R32 ∴T1T2=(R1R2)32=(R1R12)32=2√2 ⇒T2=T12√2=3652√2 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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