Question

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

Answer 1

According to Kepler's laws of planetary motion, the time period of revolution of a planet about the Sun is directly proportional to the cube of the distance between their centres.
i.e., T² $\propto$ R³
$$\begin{gathered} \Rightarrow \frac{T_m^2}{T_e^2}=\frac{R_m^3}{R_e^3} \\ \Rightarrow {\left(\frac{R_{\mathrm{m}}}{R_{\mathrm{e}}}\right)}^3={\left(\frac{1.88}{1}\right)}^2 \\ \therefore \frac{R_{\mathrm{m}}}{R_{\mathrm{e}}}={\left(1.88\right)}^{2/3}=1.52 \end{gathered}$$