Advancing Double Star Studies in an Age of Space-Based Astrometric Missions

The astrometric study of double stars is over 200 years old, and historically it has been a driver of stellar astrophysics resulting in the determination of the properties of stars, as well as formation and evolution models. Modern, space-based astronomy, from missions such as HIPPARCOS and Gaia, has opened a new sophisticated avenue of binary star studies. These space missions give the astrometric measures of a double star, its angular separation in arcseconds and position angle in degrees, with precisions that are 3 to 4 orders of magnitude more precise than has been available todate from single-aperture ground observations. In this thesis, Paper 1 crossmatches the double stars from the first published catalogue of double stars in the southern hemisphere (the Dunlop Catalogue) with the Gaia Data Release 2 (Gaia DR2) from the Gaia space-based mission and estimates the accuracy of the measures in the Dunlop Catalogue. Overall position angles are within 70°'/separation', separations within 7%, and apparent visual magnitudes are within 1 mag. Paper 2 develops an iteration-based technique for the determination of the first order orbital elements for long period and under-sampled arcs. This technique is then applied to a sample of binary stars from the Dunlop Catalogue. Orbital elements with a mean period and semi-major axis of ~81,000 years and ~76' respectively, were calculated displaying a mean uncertainty of ~37%. Paper 3 confirms the presence of 14 optical double stars within the Dunlop Catalogue and presents and applies an upgraded technique for calculating their rectilinear elements. This upgraded technique results in a minimum one order of magnitude improvement in their one sigma uncertainties over the current method