  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.
