Note on Inversion Formula to Determine Binary Elements by Astrometry

TL;DR

This paper refines simplified astrometric methods for determining binary star elements by analytically solving for parameters like periastron time and ascending node, clarifying differences from other approaches.

Contribution

It extends previous simplified solutions by analytically determining additional binary parameters, enhancing the method’s completeness without iterative procedures.

Findings

Analytical expressions for remaining binary parameters derived.

Clarification of differences between simplified and other analytical methods.

Enhanced understanding of astrometric binary element determination.

Abstract

Simplified solutions to determine binary elements by astrometry were obtained in terms of elementary functions (Asada et al. 2004), and therefore require neither iterative nor numerical methods. In the framework of the simplified solution, this paper discusses the remaining two parameters of the time of periastron passage and the longitude of ascending node in order to complete the solution. We thus clarify a difference between the simplified solution and other analytical methods.