QuestionJune 24, 2025

Which of the following properties must be measured to determine the masses of stars in a typical binary system? Choose one or more: A. the radii of the two stars B. the velocities of the two stars C. the average separation between the two stars D. the period of the orbits of the two stars

Which of the following properties must be measured to determine the masses of stars in a typical binary system? Choose one or more: A. the radii of the two stars B. the velocities of the two stars C. the average separation between the two stars D. the period of the orbits of the two stars
Which of the following properties must be measured to determine the masses of stars in a typical binary system? Choose one or more: A. the radii of the two stars B. the velocities of the two stars C. the average separation between the two stars D. the period of the orbits of the two stars

Solution
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Answer

C. the average separation between the two stars; D. the period of the orbits of the two stars Explanation 1. Identify Relevant Properties To determine the masses of stars in a binary system, we use **Kepler's Third Law**: P^2 = \frac{4\pi^2}{G(M_1 + M_2)}a^3, where P is the orbital period, a is the average separation, and M_1 and M_2 are the masses. 2. Analyze Each Option B. Velocities help determine mass through Doppler shifts but aren't directly used in Kepler's formula. C. Average separation (a) is needed for calculating masses using Kepler's law. D. Orbital period (P) is also required in Kepler's law to find the sum of the masses.

Explanation

1. Identify Relevant Properties<br /> To determine the masses of stars in a binary system, we use **Kepler's Third Law**: $P^2 = \frac{4\pi^2}{G(M_1 + M_2)}a^3$, where $P$ is the orbital period, $a$ is the average separation, and $M_1$ and $M_2$ are the masses.<br />2. Analyze Each Option<br /> B. Velocities help determine mass through Doppler shifts but aren't directly used in Kepler's formula.<br /> C. Average separation ($a$) is needed for calculating masses using Kepler's law.<br /> D. Orbital period ($P$) is also required in Kepler's law to find the sum of the masses.
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