The distance between Sun and Earth is R . The duration of year if...

According to Kepler's Third Law – The Law of Periods,

${T}^{2} ∝ {R}^{3}$

where $T$ is time taken by the planet to go once around the sun and $R$ is the semi-major axis (distance) of the elliptical orbit.

$∴ {T}^{2} = {kR}^{3} \ldots$(i)

Where $k$ is a constant of proportionality.

When $R$ becomes $3$ times, let the time period be \left({T}^{'}\right)$.<br /><br />$∴ {\left({T}^{'}\right)}^{2} = k ( 3R{)}^{3} \ldots ( ii )$<br /><br />$∴ \dfrac{{T}^{2}}{{\left({T}^{'}\right)}^{2}} = \dfrac{1}{27}$<br /><br />So, time period will be$3\sqrt{3}yr.