By studying the radial velocity curves of two visible stars in an edge-on binary system, we determine that the mass of Star A is 3 times the mass of Star B. We also observe their period to be 8 years and the semimajor axis of their relative orbit to be 4 au. What are the masses of these stars?

Question

Quizplus · Accepted Answer

Using Kepler's third law and the given information, we can find the total mass of the system. The formula for Kepler's third law in this context is $P^2 = \frac{4\pi^2}{G(M_A + M_B)}a^3$, where $P$ is the period, $a$ is the semimajor axis, $M_A$ and $M_B$ are the masses of the stars, and $G$ is the gravitational constant. Given that $P = 8$ years and $a = 4$ AU, and knowing that $M_A = 3M_B$, we can solve for the total mass of the system in solar masses. The total mass comes out to be $1 M_{\odot}$, with Star A being $0.75 M_{\odot}$ and Star B being $0.25 M_{\odot}$.

By Studying the Radial Velocity Curves of Two Visible Stars