Assume Earth and Mars move in circular orbits around the Sun, with the Martian orbit being $1.52$ ti

Question

Assume Earth and Mars move in circular orbits around the Sun, with the Martian orbit being $1.52$ times the orbital radius of the Earth. What is the approximate length of the Martian year in days?

Professor PC Thomas Classes · Answer

By Kepler's third law, $T^2 \propto R^3$. So, $T_M = T_E \left(\frac{R_M}{R_E}ight)^{3/2} = 365 	imes (1.52)^{3/2} \approx 684	ext{ days}$.