Determining the minimum sum of the component masses for a binary with a known parallax from observations of a short arc of its apparent motion

An inequality that allows the minimum sum of the component masses for a binary, M₀, to be determined was derived from simple geometric considerations. This quantity satisfies the observed orbital motion according to Newton's law with a known parallax. The M₀ value can be calculated if the apparent-motion parameters for the components, including the curvature of the observed short orbital arc, were determined from observations. We estimated M₀ for 14 Pulkovo program stars for which the apparent orbital arc covered with observations was no less than 10°. We compare M₀ with the masses estimated from the mass-luminosity relation. A significant mass excess was found for the star ADS 10329.