A New Algorithm in Computations of Binary Stars' Observational Quantities and Its Application

摘要

The determination of the orbital parameters of binaries is an important constituent of fundamental astronomy. It is the only reliable way to determine the stellar mass, which is crucial for the studies of stellar dynamics and evolution. And the orbital parameters can be used to compute the motions of component stars, which could improve the population of reference stars in the bright star catalogue reference frame. However, the previous studies on the determination of binaries' orbital parameters adopted some approximations in the computation of observational quantities. According to the statistical results of hundreds of binaries with bright component stars, it could be found that the approximations in the variation of the tangent plane and the prospective effect of the reference plane have made the deviations of computed observational quantities become larger than the present observational precision (1 mas). In this paper, a new algorithm based on the two-body model and the rigorous relation of solid geometry for computing observational quantities is presented. This new algorithm has been verified by fitting the simulation and actually-observed data. And the fitting results show that the fitted parameters solved by the new algorithm usually have a higher confidence than that solved by the approximate algorithm. Therefore, the new algorithm has certain improvements in the determination of the orbital parameters of binaries, especially, for the wide binaries nearby the solar system.