Question:
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?
Answer:
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
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