If the distacne between the earth and the sun gets doubled then what would be the duration of the year

Options

A. 2.828 years
B. 3.285 years
C. 1.234 years
D. 5.234 years

Explanation

Given `r_(2)-2r_(1)` and time pero9d `T_(1)=365` days
According too kepler third law `T_(1)^(2) prop r_(1)^(3)` and `T_(2)^(2) prop r_(2)^(3)`
`therefore (T_(2)^(2))/(T_(1)^(2))=(r_(2)^(3))/(r_(1)^(3))` or `(T_(1)^(2))=(r_(2))/(r_(1))`
`rarr T_(2)=T_(1)xx2xx1.414=2.828` years