The time taken by Mars to revolve round the sun is $1.88~years$. Find the approximate ratio of the a

Question

The time taken by Mars to revolve round the sun is $1.88~years$. Find the approximate ratio of the average distance between Mars and the sun to that between the earth and the sun.

Professor PC Thomas Classes · Answer

According to Kepler's third law, $T^2 \propto R^3$. The ratio of distances is $\frac{R_M}{R_E} = (\frac{T_M}{T_E})^{2/3}$. Given $T_M = 1.88~years$ and $T_E = 1~year$, we get $\frac{R_M}{R_E} = (1.88)^{2/3} \approx 1.52$.