Investigation of the correlation between the angle of inclination and eccentricity in the problem of determining the orbits of binary stars from observations covering short arc of visible orbit

Two methods of determining the orbit of a wide binary star are compared. The Apparent Motion Parameters (AMP) method is applicable to limited number of stars, since it requires the use of not only positional observations of stars in the sky plane, but also additional data on radial velocities, parallaxes and masses of stars. The Thiele-Innes method gives a reliable result if the arc is large enough for the observations to cover different phases of relative positions components of a binary star in orbit. We considered 96 orbits calculated by the AMP method and 825 orbits calculated by the Thiele-Innes method. As a result, it is obtained that for stars with an orbital period over 2000 years by the Thiele-Innes method, we have a correlation between the angle of inclination and eccentricity, which should not be. Using the AMP method, we obtain independent elements of the orbit. Also in the work, the question of the existence of a predominant direction in the inclination of the orbit relative to the plane of the Galaxy is considered. No preferential direction was revealed on this observational material.