What would be the average duration of year if the distance between the Sun and the Earth becomes thrice the present distance.

Explanation

Let `r_1` = Present distance between the Earth and Sun
T = 365 days.
If` r_2 = 3r_1` to find `T_2 = `?
According to Kepler’s law of period
`T_1^2 prop r_1^3 `and `T_2^2 prop r_2^3`
`(T_2^2)/(T_1^2) = (r_2^3)/(r_1^3)`
` therefore T_2/T_1 = (r_2/r_1)^(3//2)`
` = ((3r_1)/(r_1))^(3//2)`
` therefore T_2/T_1 = sqrt27`
` T_2 = T_2 xx sqrt27`
` = 365 xx sqrt27`
= 1897 days