An improved algorithm for the determination of the system parameters of a visual binary

Abstract

This paper presents a method for the determination of the system parameters of visual binaries from observed relative coordinates which is based on an algorithm previously proposed. This algorithm enforces rigorously all the available dynamical and geometrical constraints and obtains the definitive orbital parameters through a Jefferys-type least-squares adjustment. The iterations, carried out by a modified Marquardt algorithm, always converged. The method was used to estimate the sets of system parameters of the binary systems 51 Tau, Beta 738, and BD + 19 deg 5116. In addition to the data traditionally communicated, the covariane matrices of the system parameter sets, their efficiences, the correlation matrices of the original system parameter sets, and the set of natural parameters are given, together with their variances.