If the distance between the earth and the sun doubles, what would be the duration of the year?

1032 days

\(\text{According to ques : }a' = 2 a\)

... where a is the semi-major axis of the elliptical orbit traced by earth and a' is the new semi-major axis if the distance between the sun and the earth gets doubled .

\(\text{Time period : } T^2 \propto a^3\)

\(\Rightarrow [\frac{T'}{T}]^2 = [\frac{a'}{a}]^3\)

\(\Rightarrow [\frac{T'}{T}]^2 = [\frac{2a}{a}]^3\)

\(\Rightarrow [\frac{T'}{T}]^2 = 8\)

\(\Rightarrow T' = \sqrt{8}*T\)

\(\Rightarrow T' = \sqrt{8}*365 \text{ days}\)

T' = 1032.7 days