SIMBAD references

We study the perturbations of a relatively close third star on a tidally distorted eccentric eclipsing binary. We consider both the observational consequences of the variations of the orbital elements and the interactions of the stellar rotation with the orbital revolution in the presence of dissipation. We concentrate mainly on the effect of a hypothetical third companion on both the real, and the observed apsidal motion period. We investigate how the observed period derived mainly from some variants of the O-C relates to the real apsidal motion period. We carried out both analytical and numerical investigations and give the time variations of the orbital elements of the binary both in the dynamical and the observational reference frames. We give the direct analytical form of an eclipsing O-C affected simultaneously by the mutual tidal forces and the gravitational interactions with a tertiary. We also integrated numerically simultaneously the orbital and rotational equations for the possible hierarchical triple stellar system AS Camelopardalis. We find that there is a significant domain of the possible hierarchical triple system configurations, where both the dynamical and the observational effects tend to measure longer apsidal advance rate than is expected theoretically. This happens when the mutual inclination of the close and the wide orbits is large, and the orbital plane of the tertiary almost coincides with the plane of the sky. We also obtain new numerical results on the interaction of the orbital evolution and stellar rotation in such triplets. The most important fact is that resonances might occur as the stellar rotational rate varies during the dissipation-driven synchronization process, for example in the case when the rotational rate of one of the stars reaches the average Keplerian angular velocity of the orbital revolution.