Answer to Question #276624 in Physics for Hutchii

Question

Solve the problem involving the third law of Kepler's planetary motion with complete solutions. Mars takes 1.88 years to complete one orbit around the sun. What is its average distance from the sun?

Answer 1

Let's apply the Third Kepler's Law of planetary motion:

$$\dfrac{P_M^2}{a_M^3}=\dfrac{P_E^2}{a_E^3},$$ $$a_M=\sqrt{\dfrac{P_M^2a_E^3}{P_E^2}},$$ $$a_M=\sqrt[3]{\dfrac{(1.88\ yr)^2\times(1.5\times10^{11}\ m)^3}{(1\ yr)^2}}=2.285\times10^8\ km.$$