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

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.