7 Conclusions

We derive updated apsidal motion elements for two eccentric eclipsing binaries by means of an O-C diagram analysis. Both systems analysed here present important relativistic contributions to the total apsidal motion.

Concerning TV Cet, we have detected apsidal motion at a rate $\dot{\omega}_{\rm obs} = 0.000\,30 \pm 000\,08$ deg cycle^-1. A substantial fraction of this ($\sim$80%) is due to the contribution from general relativity and our measurement is consistent with theory. The difference between theoretical and observed values of the internal structure constants is caused probably by the relatively high uncertainty of the observed rate of apsidal motion.

In the case of V451 Oph, our resulting orbital eccentricity and the period of apsidal motion is in a good agreement with elements previously obtained by Khaliullin & Kozyreva (1984) and Clausen et al. (1987). A few more times of minimum added over the next decade will make V451 Oph one of the best investigated systems in the observational check of stellar structure models. Nevertheless, the scatter of O-C values seems to be relatively high for the detached eclipsing system. Substracting the influence of apsidal motion, the O-C₂ diagram in Fig. 4 can be plotted. From this diagram, no other phenomenon (i.e. presence of a third body in the system) can be simply derived. The differences from the zero line are substantially larger than the standard errors of many observed times of minimum.

A small group of triple eccentric eclipsing binaries presenting apsidal motion and light-time effects, is given in Table 4. These excellent labratories of celestial mechanics deserve a continuous monitoring. More high-accuracy timings of these systems are necessary in the future in order to enlarge the time span for a better analysis of the apsidal motion, especially in TV Cet, where the light-time effect is only poorly determined.

Acknowledgements

This investigation was supported by allocation of SAAO observing time, in part by the Grant Agency of the Czech Reublic, grant No. 205/99/0255 and by the research plan J13/98: 113200004 Investigation of the Earth and the Universe. MW wishes to thank Dr. David Kilkenny, SAAO, for help with the photometric data reductions. We are also thankful to Mr. Wilhelm Kleikamp, BAV, for sending his original data of TV Ceti, and to Dr. Valentina Kozyreva, SAI, Moscow, for supplying us with her photoelectric measurements of V451 Oph. RD wishes to thank the Emilia Guggenheim-Schnurr Foundation for financial support. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA's Astrophysics Data System Bibliographic Services.