Masses for Binary Stars

The determination of masses in binary systems generally uses Kepler's third law, modified to include the effect of the center of mass,

and the "seesaw equation" for the center of mass illustrated in the right figure. In these equations subscripts "1" and "2" distinguish the two stars, P is the orbital period, m denotes masses, R is the total average distance between the stars, and d is the distance from the center of mass.

Solving for the Mass

of the binary system. Then, if we know enough about the orbits to determine the respective distances from the center of mass d₁ and d₂, the equations in the top right figure can be used to determine the individual masses of the two stars.

Binary Masses with Limited Information

In practical mass determination, we often have insufficient information to apply the preceding method. This is typically because of some combination of two problems:

We may not be able to map the orbits exactly. This is obviously true if the binary is astrometric and we see only one star.

Even if the orbits can be mapped, they correspond to the two-dimensional projections on the celestial sphere of the true three-dimensional orbit and further information may be required to construct the true orbit.

In these instances, we often can determine only the sum of the masses rather than the individual masses, or we may only be able to place limits on the masses rather than actually determine them. In the case of astrometric binaries, we can often find limits or estimates for masses if certain assumptions are made about the system. For example, we may be able to estimate the mass of the primary indirectly from systematics of its luminosity and spectral type.