Answer to Question #276628 in Physics for Hutchii

Question

Solve the problem involving the third law of Kepler's planetary motion with complete solutions. The mean distance of an object A from the Sun is 19.6 x 10^9 km and the mean distance of object B from the Sun is 57.9 x 10^8 km. The period of Earth's revolution is 1 year, what is the period of objects B's revolution?

Answer 1

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

$$\dfrac{P_B^2}{a_B^3}=\dfrac{P_E^2}{a_E^3},$$ $$P_B=\sqrt{\dfrac{P_E^2a_B^3}{a_E^3}},$$ $$P_B=\sqrt{\dfrac{(1\ yr)^2\times(57.9\times10^8\ km)^3}{(1.5\times10^8\ km)^3}}=240\ yr.$$