Astronomy
How Binary Star Systems Help Measure Stellar Masses
Quick fact
About half of all stars in the Milky Way are part of binary or multiple systems, making this mass-measurement technique one of the most widely used in astronomy.
Why this is interesting
Did you know that most stars are not alone but have companions? Binary star systems are nature’s gift to astronomers—they provide a direct way to weigh stars, something that is impossible for isolated stars.
Read the full explanation
Understanding How Binary Star Systems Help Measure Stellar Masses
Imagine two dancers twirling around a shared center point. In a binary star system, two stars orbit their common center of mass. By watching their dance from Earth, we can measure two key properties: the time it takes to complete one orbit (the orbital period) and the size of their orbit (the semi-major axis). With these measurements and Kepler's third law—adjusted by Newton to include gravity and masses—we can calculate the total mass of the two stars combined. If we can also see both stars moving, or if we detect their speeds via the Doppler effect, we can determine how much mass belongs to each star individually. This is the most reliable way astronomers have to find the masses of stars.
A deeper explanation
The underlying principle is Newton's form of Kepler's third law: P² = (4π² / G(M₁+M₂)) × a³, where P is the orbital period, a is the semi-major axis of the relative orbit, G is the gravitational constant, and M₁+M₂ is the total mass. By observing P and a, we solve for the total mass. To separate the masses, we need additional information: in visual binaries where both stars are resolved, the ratio of their distances from the center of mass gives the mass ratio (M₁/M₂ = r₂/r₁). In spectroscopic binaries, we measure radial velocity curves; if both spectra are visible, we get the mass ratio from the velocity amplitudes. If only one spectrum is visible (single-lined binary), we derive the 'mass function' which provides a lower limit on the companion mass. For eclipsing binaries, the inclination of the orbit is known from the light curve, allowing full solution for both masses. These techniques have given us empirical stellar masses, which in turn underpin the mass-luminosity relation and our understanding of stellar evolution. Without binary systems, our knowledge of stellar masses would be far less certain.