Two planets travel in circular orbits about a star. The period of planet A is T, while that of planet B is 3T. What is the ratio of their orbital radii, R_A/R_B? A) 0.33 B) 0.19 C) 0.48 D) 0.69

Question

Quizplus · Accepted Answer

The ratio of the orbital radius of two planets is given by: R_A/R_B=(T1^2/T2^2)^(1/3) where T1 and T2 are the periods of the planets. Substituting T and 3T for T1 and T2 respectively, we get: R_A/R_B=(T^2/9T^2)^(1/3)=1/3^(1/3)=0.48 Therefore, the answer is C.

Two Planets Travel in Circular Orbits About a Star