How do binary star systems help astronomers measure stellar masses?

Binary star systems are the primary means by which astronomers directly determine stellar masses. Because these stars orbit a common centre of gravity, their motion is governed by gravitational laws that allow for the calculation of their masses.123

The method of calculation depends on the type of binary system:

• Visual Binaries: When the distance to the system is known, astronomers can directly measure the angular size of the orbit and the orbital period. Using Kepler’s third law, they can determine the sum of the masses. By observing the motion of each star relative to the center of gravity, they can also calculate the mass ratio, allowing for the determination of individual stellar masses.4
• Eclipsing Binaries: These systems provide the most comprehensive data. By analyzing the light curve and using the Doppler effect to measure the radial velocity of each star, astronomers can derive both the mass ratio and the orbital characteristics, leading to precise mass measurements.25
• Spectroscopic Binaries: If only one spectrum is observed, astronomers can derive a mass function to find a lower limit for the masses. If spectra from both members are visible, mass ratios can be determined.5