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The Hipparcos catalog and its Double and Multiple System Annex (DMSA) lists4099 components with individual proper motions and coordinates on the epoch1991.25. Many of these long-period binary stars are also present in the GaiaData Release 2 (DR2). Using the available relative positions and proper motionsseparated by 25.25 years, the equations of relative orbital motion can besolved for the two epoch eccentric anomalies, orbital period, and eccentricity.The method employs elimination of the linear Thiele-Innes unknowns andnonlinear optimization of the remaining condition equations. The quality ofthese solutions is compromised by the insufficient condition and modestprecision of the Hipparcos astrometric data, as revealed by Monte-Carlosimulations with artificially perturbed data points. The presence of multiplesystems and optical pairs can also perturb the results. Limited experimentswith artificial data indicate that useful estimates can be obtained with a25-year epoch difference for wide binaries with orbital periods up to $\sim500$ years. The prospects of this method dramatically improve with the proposednext-generation space astrometry missions such as Gaia-NIR and Theia,especially when additional conditions are included from astrometric orspectroscopic measurements. A ancillary catalog of cross-identification andastrometric information for 1295 double star pairs cross-matched in Gaia DR2and Hipparcos is published.

Two-epoch orbit estimation for wide binaries resolved in Hipparcos and Gaia