Question

if the distance between the earth and the sun where half it's present value, the number of days in a year would have been ​

Answer 1

By Keplers laws of planetary motion, we know that T2  is proportional to R3

Hence, T12 / R13  = T22 / R23  

(T2 / T1 )2 = (R2  / R1 )3

By the given problem, R2 is half of R1 R2 = R1/ 2

Hence,

(T2 / T1 )2 = (R1/ 2 R1 )3 = 1/8

Substituting T1 as 1 year

T22  = 1/8 (1)2  = 1/8 (365 days)2

T2  =129days