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.
Solution:
Kepler's law of planetary motion says,
$T^{2} \propto R^{3}$
$\frac{T_{\mathrm{m}}^{\mathrm{z}}}{T_{e}^{\mathrm{Z}}}=\frac{R_{\mathrm{m}}^{\mathrm{I}}}{R_{e}^{\mathrm{I}}}$
$\left(\frac{1.88}{1}\right)^{2}=\left(\frac{R_{m}}{R_{e}}\right)^{3}$
$\frac{R_{m}}{R_{e}}=\left(\frac{1.88}{1}\right)^{\frac{\mathrm{}}{\mathrm{s}}}=1.52$