Moment Approach for Determining the Orbital Elements of an Astrometric Binary with Low Signal-to-noise Ratio

TL;DR

This paper proposes a moment-based method to determine the orbital elements of low signal-to-noise ratio astrometric binaries, including close systems and planet-wobbled stars, using only astrometric observations.

Contribution

It introduces an exact solution approach using second and third moments of projected positions to estimate orbital elements from noisy astrometric data.

Findings

Effective for low SNR astrometric binaries

Applicable to close binaries and planet-induced wobbles

Provides a potential estimation of true orbits

Abstract

A moment approach for orbit determinations of an astrometric binary with low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period such as Cyg-X1 and also at a star wobbled by planets. As an exact solution to the nonlinearly coupled equation system, the orbital elements are written in terms of the second and third moments of projected positions that are measured by astrometry. This may give a possible estimation of the true orbit.