Few Observation Binary Orbit Solver (FOBOS) from two (or more) astrometric observations

Abstract: We have developed a new, fast method of estimating the orbital properties of a binary or triple system using as few as two epochs of astrometric data. FOBOS (Few Observation Binary Orbit Solver) uses a flat prior brute force Monte Carlo method to produce probability density functions of the likely orbital parameters. We test the code on fake observations and show that it can (fairly often) constrain the semi-major axis to within a factor of 2-3, and the inclination to within $\sim$20$^{\circ}$ from only two astrometric observations. We also show that the 68 and 95 per cent confidence intervals are statistically reliable. Applying this method to triple systems allows the relative inclination of the secondary and tertiary star orbits to be constrained. FOBOS can usually find a statistically significant number of possible matches in CPU minutes for binary systems, and CPU hours for triple systems.