Orbit Determination and Statistical Study of Visual Binaries

The determination of visual binary orbits is the problem of computing orbital elements of a binary from a set of observed positions. There are several methods of orbit computations, and they fall into two categories namely geometrical methods and analytical methods. The firsts are quicker but lead to fewer certain values of the elements. About 60 to 80 orbits are computed each year throughout the world. More than half are improvements of former orbits. Of the 800 or 900 orbits now published, only a few score have definitive elements. The reasons for this difficulty beside the errors in the measures are : 1- The lack of existing orbit determination algorithms that can deal with what we call it ”extreme cases” of visual binary orbits like for examples ,parabolic orbits, hyperbolic orbits, quasi parabolic orbits and others. So the determination of these orbits will certainly increases the available orbital elements. 2- Three observations (necessary and sufficient data for orbit determination may define a (possible empty ) set of Keplerian orbits whose corresponding apparent orbits pass through those points.