A three-dimensional orbit for the binary star Alpha Andromedae

Stars that are both spectroscopic and optical binaries present a means to determine simultaneously the masses of the components and the distance of the system independent of trigonometric parallax. Alpha Andromedae (Alpheratz) represents such a system and, moreover, the primary is the brightest of the mercury-manganese stars. An orbit, based on 42 interferometric observations and 378 radial velocities, is calculated to solve for 10 parameters: the six coefficients of the apparent ellipse, the constant of areal velocity, the systemic velocity, and the semiamplitudes. From these, one calculates the orbit of the binary, its period and time of periastron passage, the masses of the components, and the distance of the system. The dynamical parallax does not differ greatly from the trigonometric parallax found from Hipparcos.