Suppose there existed a planet that went around the Sun with an orbital period half that of the Eart

Question

Suppose there existed a planet that went around the Sun with an orbital period half that of the Earth. What would be its orbital radius as compared to that of the Earth ($R_E$)?

Professor PC Thomas Classes · Answer

According to Kepler's third law, $T^2 \propto R^3$. Thus, $\frac{R'}{R_E} = (\frac{T'}{T_E})^{2/3} = (\frac{1}{2})^{2/3} = (0.25)^{1/3} \approx 0.63$. Therefore, the orbital radius would be $0.63 R_E$.