What would be the duration of the year if the distance between the sun and the Earth were to become half the present distance ?

Explanation

Data : ` T_(1) =1 " Year " = 365 " days" r_(2) = 1/2 r_(1)`
`T^(2) = ((4pi^(2))/(GM))r^(3) " " therefore T_(1)^(2) prop r_(1)^(3) and T_(2)^(2) prop r_(2)^(3)`
` ((T_(2))/T_(1))^(2) = (r_(2)/r_(1))^(3) " " therefore (T_(2)/365)^(2) = (1/2)^(3) = 1/8 " " therefore T_(2)/365 = 1/sqrt8`
` T_(2) = 365/sqrt8 = 129 "days" `
The new duration of the year would be 129 days.