Physics - Gravitation Question with Solution | TestHub

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

$\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }{T}^2\propto R^3$

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.

$\therefore T^2={k R}^3 \dots$(i)

Where$k$is a constant of proportionality.

When$R$becomes$3$times, let the time period be$\left(T^{\text{'}}\right)$.

$\therefore {\left(T^{\text{'}}\right)}^2=k(3R{)}^3 \dots (\mathrm{i}\mathrm{i})$

$\therefore \frac{T^2}{{\left(T^{\text{'}}\right)}^2}=\frac{1}{27}$

So, time period will be$3\sqrt{3} \mathrm{yr}$.