Numerical experiments concerning the determination of the orbits of close visual doubles considering second order terms in the observing errors
The errors in the observed distances and position angles of narrow visual binaries are non-negligible in comparison to the apparent semi-major axes of these objects. The conventional least squares algorithm, which is based on condition equations made linear in the observation errors will therefore not lead to those orbital elements which minimize the sum of the squares of the observation errors. The authors assumed several sets of orbital elements, computed ephemerides from them, added observing errors of known dispersion to the computed locations and applied a least squares routine to this material to recover the elements from which the ephemerides were computed. This was first done in the conventional way with condition equations that are linearized in the observing errors, and next with condition equations that consider second order terms in the observing errors following an algorithm worked out by the authors. The results show that the consideration of second order terms in the observing errors always lead to recovered elements that are considerably close to the true ones than those computed by the conventional, first order approach.