If earth be at one half of its present distance from the sun, how many days will there be in a year?

If earth be at one half of its present distance from the sun, how many

1.	If earth be at one half of its present distance from the sun, how many days will there be in a year?
Answer» By Keplers laws of planetary motion, we know that T2 is proportional to R3\xa0Hence, T12 / R13 \xa0= T22 / R23 \xa0\xa0(T2 / T1 )2 = (R2 \xa0/ R1 )3\xa0By the given problem, R2 is half of R1 R2 = R1/ 2Hence,\xa0(T2 / T1 )2 = (R1/ 2 R1 )3 = 1/8Substituting T1 as 1 yearT22 \xa0= 1/8 (1)2 = 1/8 (365 days)2T2 =129days