2590 binary stars in Hipparcos and Gaia DR2

Many of these long-period binary stars are also present in Gaia Data Release 2 (DR2). Using the available relative positions and proper motions separated by 24.25yr, the equations of relative orbital motion can be solved for the two epoch eccentric anomalies, orbital period, and eccentricity.

This method employs elimination of the linear Thiele-Innes unknowns and nonlinear optimization of the remaining condition equations. The quality of these solutions is compromised by the insufficient condition and modest precision of the Hipparcos astrometric data, as revealed by Monte Carlo simulations with artificially perturbed data points. The presence of multiple systems and optical pairs can also perturb the results.