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

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