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Apsidal motion is the precession of the line of apsides in the orbit of abinary star due to perturbations from General Relativity (GR), tides, orthird-body interactions. The rate of precession due to tidal effects depends onthe interior structures of the stars, and as a result, binaries in which thisprecession occurs are of great interest. Apsidal motion is observed through theanalysis of eclipse times, which reveal small changes in the average intervalbetween successive primary and secondary eclipses, taking all availableobserved times of eclipse and yielding an estimate of the apsidal rate. Giventhat this is a single observed quantity, various degeneracies are unavoidablypresent. Ideally, one would have a model that predicts eclipse times given theorbital and stellar parameters. These parameters for a given binary could thenbe computed using least squares, provided a suitably large number of eclipsetimes. Here we use the eclipsing light curve (ELC) program as such a model. TheNewtonian equations of motion with additional force terms accounting for GRcontributions and tidal distortions are integrated, yielding precise skypositions as a function of time. Times of mid-eclipse and instantaneous orbitalelements are computed as a function of time. In this paper, we outline themethod and compare numerically computed apsidal rates with standard formulaeusing a set of 15 binaries based on real systems. For our simulated systems,the derived apsidal rates agree with the standard formula.

Modeling Apsidal Motion in Eclipsing Binaries using ELC