Question

The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to

• A. 81 years
• B. 27 years
• C. 729 years
• D. $\sqrt[3]{81}$ years
• E. 9 years

Answer 1

Answer: (B)

Given,
Semi-major axis of the orbit of saturn $=g{r}_E$
Where, $r_E=$ semi major axis of earth
According to Kepler's law,
$T^2\propto r^3$
Let the time period of revolution of saturn around the sun is $T_s$
$\therefore \frac{T_S^2}{T_E^2}={\left(\frac{9r_E}{r_E}\right)}^3$
$T_S^2=T_E^2(9{)}^3$
$T_S=\sqrt{T_E^2(9{)}^3}$
$=9^{3/2}\times 1$ year
$\approx 27$ years