  Apsidal motion is the precession of the line of apsides in the orbit of a
binary star due to perturbations from General Relativity (GR), tides, or
third-body interactions. The rate of precession due to tidal effects depends on
the interior structures of the stars, and as a result, binaries in which this
precession occurs are of great interest. Apsidal motion is observed through the
analysis of eclipse times, which reveal small changes in the average interval
between successive primary and secondary eclipses, taking all available
observed times of eclipse and yielding an estimate of the apsidal rate. Given
that this is a single observed quantity, various degeneracies are unavoidably
present. Ideally, one would have a model that predicts eclipse times given the
orbital and stellar parameters. These parameters for a given binary could then
be computed using least squares, provided a suitably large number of eclipse
times. Here we use the eclipsing light curve (ELC) program as such a model. The
Newtonian equations of motion with additional force terms accounting for GR
contributions and tidal distortions are integrated, yielding precise sky
positions as a function of time. Times of mid-eclipse and instantaneous orbital
elements are computed as a function of time. In this paper, we outline the
method and compare numerically computed apsidal rates with standard formulae
using a set of 15 binaries based on real systems. For our simulated systems,
the derived apsidal rates agree with the standard formula.
