Stability of triple star systems with highly inclined orbits

It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose values are in disagreement with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity. Although many theoretical scenarios have been demonstrated to bring calculations into line with observations, all have seemed unlikely for various reasons. In particular, it has been established that the hypothesis of a third star in an orbit almost perpendicular to the orbital plane of the close binary system can explain the anomalous motion at least in some cases. The stability of triple star systems with highly inclined orbits has been in doubt, however. We have found conditions that allow the long-term stability of such systems, so that the third-body hypothesis now seems a likely resolution of the apsidal motion problem. We apply our stability criteria to the cases of AS Cam and DI Her and recommend observations at the new Keck interferometer, which should be able to directly observe the third bodies in these systems.