Binary Star Orbit

Calculate the total mass of a binary star system from orbital period and semi-major axis using Kepler's Third Law.

Inputs

Orbital Period

years

Semi-Major Axis

Tab to move between fields

Results

Total System Mass

1 M☉

Orbital Velocity

29.79 km/s

Each Star (if equal)0.5 M☉

Period365.25 days

Separation499 light-sec

Orbital Energy-443,669,318.18

How to Use This Calculator

Enter the Orbital Period (years) of the binary system — obtainable from long-term radial velocity or astrometric monitoring.
Enter the Semi-Major Axis (AU) of the relative orbit, derived from angular separation at known distance or interferometry.
Read Total System Mass (M☉) computed via Kepler's Third Law (M = a³/P²).
If the stars have equal mass, Each Star mass is half the total; use the mass ratio from spectroscopy for unequal pairs.
Use Orbital Velocity (km/s) and Separation (light-sec) to contextualize the system's compactness.

How the result changes with Semi-Major Axis

Semi-Major Axis	Total System Mass	Orbital Velocity
1,000	1,000,000,000 M☉	29,785.68 km/s
3,500	42,875,000,000 M☉	104,249.87 km/s
6,500	274,625,000,000 M☉	193,606.91 km/s
9,000	729,000,000,000 M☉	268,071.1 km/s

What each input means

Orbital Period: Orbital period of the binary pair in years (e.g., Alpha Centauri AB = 79.9 yr)
Semi-Major Axis: Semi-major axis of the relative orbit in AU (e.g., Alpha Centauri AB = 23.4 AU)

How this is calculated

Formula

M = a³ / P² (Kepler's Third Law)

Worked example, using the default values

Identify Input Parameters
Orbital Period = 1, Semi-Major Axis = 1 = 2 input(s) provided
Calculate Total System Mass
Total System Mass = m
1 = 1
Calculate Orbital Velocity
Orbital Velocity
29.79 = 29.79
Calculate Each Star
Each Star
0.5 = 0.5
Calculate Period
Period
365.25 = 365.25

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