If the distance between earth and the sun were half of its present value,then how many number of days will be there in a year?

Asked by nimmalavarshini | 5th Jun, 2020, 11:52: AM

Expert Answer:

According to Keplers third law of planetary motion, "the square of the period of revolution of a planet around the sun is proportional to the cube of the semi major axis of the ellipse".
Let T1 and R1 be original time period and radius of revolutions of Earth's orbit around Sun and
T2 and R2 be the time period and radius after the distance between Sun and Earth is halved.
begin mathsize 14px style Therefore space according space to space Kepler apostrophe straight s space law colon straight T subscript 1 squared space proportional to space straight R subscript 1 cubed straight T subscript 2 squared space proportional to space straight R subscript 2 cubed So colon straight T subscript 2 squared over straight T subscript 1 squared equals straight R subscript 2 cubed over straight R subscript 1 cubed straight T subscript 2 over straight T subscript 1 equals open parentheses straight R subscript 2 over straight R subscript 1 close parentheses to the power of 3 divided by 2 end exponent Given space straight R subscript 2 space equals straight R subscript 1 over 2 straight T subscript 2 over straight T subscript 1 equals open parentheses fraction numerator straight R subscript 1 over 2 over denominator straight R subscript 1 end fraction close parentheses to the power of 3 divided by 2 end exponent straight T subscript 2 over straight T subscript 1 equals open parentheses 1 half close parentheses to the power of 3 divided by 2 end exponent We space know space straight T subscript 1 space equals space 365 straight T subscript 2 equals open parentheses 1 half close parentheses to the power of 3 divided by 2 end exponent cross times 365 straight T subscript 2 space approximately equal to 129 space days end style

Therefore if the distance between the earth and the sun were half its present value,
the number of days in a year would have been 129 days

Answered by Shiwani Sawant | 5th Jun, 2020, 03:58: PM

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