Binary Star Total Mass Calculator
Calculate the total mass of a binary star system using Kepler's third law from orbital period and semi-major axis.
Optionally find individual masses.
Binary star systems are pairs of stars orbiting their common center of mass. About half of all stars in the Milky Way are in binary or multiple systems.
Kepler’s Third Law (generalized):
(M₁ + M₂) = a³ / T²
Where:
- M₁ + M₂ = total system mass in solar masses
- a = semi-major axis of the relative orbit in AU
- T = orbital period in years
This elegant formula lets us “weigh” distant star systems without knowing anything else.
If the mass ratio q = M₁/M₂ is known:
M₁ = (M₁+M₂) × q / (1+q)
M₂ = (M₁+M₂) / (1+q)
Types of binary stars:
- Visual binaries: both stars resolved in telescopes (a > ~10 AU typically)
- Spectroscopic binaries: detected by Doppler velocity variations (small separation)
- Eclipsing binaries: transit each other, revealing radii and masses precisely
- Astrometric binaries: detected by the wobble of the visible star
Famous binary systems:
- Alpha Centauri AB: T = 79.9 years, a = 23.4 AU, total mass ≈ 2.0 M☉
- Sirius A+B: T = 50.1 years, a = 20.03 AU, total mass ≈ 3.1 M☉
- 61 Cygni: T = 659 years, a = 84 AU, total mass ≈ 1.3 M☉
Binary stars are essential for measuring stellar masses — the only direct method we have. Without binary systems, our knowledge of stellar structure and evolution would be far more uncertain.