Testing gravitational theories using eccentric eclipsing detached binaries

In this paper, we compare the effects of different theories of gravitation on the apsidal motion of a sample of eccentric eclipsing detached binary stars. The comparison is performed by using the formalism of the post-Newtonian parametrization to calculate the theoretical advance at periastron and compare it to the observed one, after having considered the effects of the structure and rotation of the involved stars. A variance analysis on the results of this comparison shows that no significant difference can be found due to the effect of the different theories under test with respect to the standard general relativity (GR). It will be possible to observe differences, as we would expect, by checking the observed period variation on a much larger lapse of time. It can also be noted from our results that f(R) theory is the nearest to GR with respect to the other tested theories.