A Comparison of Three Approaches to Determining Orbits of Visual Double Stars Based on Observations of Their Short-Arced Orbits

Using model examples and the results of actual published observations, three methods currently used at the Pulkovo Observatory are compared: (1) The Thiele–Innes element method, developed by I.S. Izmailov. Unlike the classical Thiele–Innes method, suitable for short-period doubel stars, in this case the orbital period, eccentricity, and periastron passage moment are determined using a Monte Carlo method with subsequent refinement. No additional data are required. (2) The apparent motion parameter (AMP) method, proposed by A.A. Kiselev in 1980. This is a direct method in which the initial parameters obtained from high-precision homogeneous positional observations are held constant, while remote heterogeneous observations serve as self-checks for the resulting solution. Additional parameters are also used: parallax, radial velocities, and masses. Two solutions or a family of orbits are obtained over a short arc, from which a single solution can sometimes be selected. The method requires an individual approach for each specific star. (3) The AMP2 method, according to I.S. Izmailov’s algorithm, in which the initial parameters are not fixed, but are refined iteratively over all observations using fixed radial velocity observations. The advantage of this method is the ability to determine stellar orbits and masses on a large scale. The results of model studies are compared with those of published catalogs. This article is partially based on a paper presented at the Modern Stellar Astronomy 2025 conference.