Two planets,A and B,are in orbit around the same star.If A has a period of 12 days and an orbit radius of 1.63·10⁵ km,and B has a radius of 3.26·10⁵ km,what is the period of B in days?

Question

Quizplus · Accepted Answer

According to Kepler's Third Law, the period (P) of a planet's orbit is related to its distance from the star (R) by the equation P^2 = (4π^2/GM)R^3, where G is the gravitational constant and M is the mass of the star. Assuming that the mass of the star is the same for both planets, we can set up a ratio between the periods of A and B as follows:

(PB/PA)^2 = (RB/RA)^3
(PB/12)^2 = (3.26x10^5/1.63x10^5)^3
PB/12 = (2)^(3/2)
PB = 12x(2)^(3/2) = 12x(2^(1/2))(2^(1/2))
PB = 12x(2)^(1/2)x(2)^(1/2)
PB = 12x2 = 24

Therefore, the period of planet B is 24 days, which corresponds to answer choice B.

Two Planets,A and B,are in Orbit Around the Same Star