A particular star in a binary star system orbits the other in an elliptical orbit with a semimajor axis of 3 AU and a period of 5 years.What is the sum of the masses of the two stars in the system?
A) 0.9
B) 1.1
C) 13.9
D) 0.07

Question

Quizplus · Accepted Answer

According to Kepler's third law, the square of the orbital period (P) is proportional to the cube of the semimajor axis (a) of the orbit, with the proportionality constant being the sum of the masses of the two stars (M1 + M2) in solar masses. The formula is P^2 = a^3 / (M1 + M2). Substituting the given values: 5^2 = 3^3 / (M1 + M2), we find M1 + M2 = 1.1 solar masses.

A Particular Star in a Binary Star System Orbits the Other