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A binary mass function combines the observed orbital period $P$ and radial velocity semi-amplitude $K_1$ of a visible member of a spectroscopic binary. For a circular Kepler orbit, $K_1=2\pi a_1\sin i/P$, where $a_1$ is the visible star's orbital semimajor axis about the centre of mass and $i$ the orbital inclination. The centre of mass relation $a_1=a{M}_2/(M_1+M_2)$ and Kepler's third law $4{\pi }^2{a}^3=G(M_1+M_2)P^2$ eliminate the unobserved separation:It has units of mass. The right side is at most $M_2$, so $f(M)\le M_2$ is a strict observational lower bound on the unseen companion's mass within this model. If $M_1$ is independently estimated, setting $\sin i=1$ and solving the equation gives a stronger minimum companion mass. An unknown orbital inclination generally prevents a unique pair of stellar masses from being inferred from one velocity curve alone.

For an eccentric Kepler orbit with measured orbital eccentricity $e$, the radial-velocity semi-amplitude is $K_1=2\pi a_1\sin i/[P\sqrt{1-e^2}]$, so the observable expression becomes $f(M)=P{K}_1^3(1-e^2{)}^{3/2}/(2\pi G)$. A fitted semi-amplitude, rather than an arbitrary instantaneous radial velocity, is required. This is why an unseen companion can be constrained dynamically even when its own spectral lines are absent.

A binary star consists of two stars bound by gravity and moving around their shared astronomical barycenter. In a sufficiently isolated pair, a Kepler orbit approximates their relative motion. Combining the orbital period $P$ and relative semi-major axis $a$ gives the total mass through Kepler's third law, $M_1+M_2=4{\pi }^2{a}^3/(G{P}^2)$.

A resolved orbit supplies angular information; a spectroscopic binary supplies line-of-sight velocities; an eclipsing binary supplies geometric information through its light curve. Combining these can determine individual masses and stellar radii. Close pairs also exchange matter through binary mass transfer, altering their subsequent stellar evolution and sometimes reversing which component is more massive.

An inference of a compact object's gravitating mass from specified tracers and a dynamical or radiation model. Resolved stellar or gas orbits, spectroscopic binary dynamics, and reverberation mapping supply complementary approaches with different distance, geometry and equilibrium assumptions. A short variability timescale constrains size but is not a unique mass measurement.

Equal radial velocity amplitudes imply equal stellar masses. Under the circular, edge-on eclipsing binary interpretation, each star moves at $K=100\mathrm{km}{\mathrm{s}}^{-1}$, and the relative speed is $2K$. ThusUsing $P=5.45$ days givesMore generally, spectroscopic binary amplitudes determine $a\sin i=P(K_1+K_2)\sqrt{1-e^2}/(2\pi )$ and $(M_1+M_2){\sin }^{3}i=P(K_1+K_2{)}^3(1-e^2{)}^{3/2}/(2\pi G)$. Thus these numerical masses and separation use $e=0$, $\sin i=1$; eclipses alone imply high inclination rather than its exact value.