DAp.1.05 — Coordinate System Issues in Binary Star Computations

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Aug 4th at 6:00 PM until 6:00 PM

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Author(s): George H. Kaplan1

Institution(s): 1. U.S. Naval Observatory (contractor)

It has been estimated that half of all stars are components of binary or multiple systems. Yet the number of known orbits for astrometric and spectroscopic binary systems together is less than 7,000 (including redundancies), almost all of them for bright stars. A new generation of deep all-sky surveys such as Pan-STARRS, Gaia, and LSST are expected to lead to the discovery of millions of new systems. Although for many of these systems, the orbits may be undersampled initially, it is to be expected that combinations of new and old data sources will eventually lead to many more orbits being known. As a result, a revolution in the scientific understanding of these systems may be upon us.
The current database of visual (astrometric) binary orbits represents them relative to the “plane of the sky”, that is, the plane orthogonal to the line of sight. Although the line of sight to stars constantly changes due to proper motion, aberration, and other effects, there is no agreed upon standard for what line of sight defines the orbital reference plane. Furthermore, the computation of differential coordinates (component B relative to A) for a given date must be based on the binary system’s direction at that date. Thus, a different “plane of the sky” is appropriate for each such date, i.e., each observation. However, projection effects between the reference planes, differential aberration, and the curvature of the sky are generally neglected in such computations. Usually the only correction applied is for the change in the north direction (position angle zero) due to precession (and sometimes also proper motion). This paper will present an algorithm for a more complete model of the geometry involved, and will show that such a model is necessary to avoid errors in the computed observables that are significant at modern astrometric accuracy. The paper will also suggest where conventions need to be established to avoid ambiguities in how quantities related to binary star orbits are interpreted.