  We propose a novel method for determining the ages of low-mass, pre-main
sequence stellar systems using the apsidal motion of low-mass detached
eclipsing binaries. The apsidal motion of a binary system with an eccentric
orbit provides information regarding the interior structure constants of the
individual stars. These constants are related to the normalized stellar
interior density distribution and can be extracted from the predictions of
stellar evolution models. We demonstrate that low-mass, pre-main sequence stars
undergoing radiative core contraction display rapidly changing interior
structure constants (greater than 5% per 10 Myr) that, when combined with
observational determinations of the interior structure constants (with 5 -- 10%
precision), allow for a robust age estimate. This age estimate, unlike those
based on surface quantities, is largely insensitive to the surface layer where
effects of magnetic activity are likely to be most pronounced. On the main
sequence, where age sensitivity is minimal, the interior structure constants
provide a valuable test of the physics used in stellar structure models of
low-mass stars. There are currently no known systems where this technique is
applicable. Nevertheless, the emphasis on time domain astronomy with current
missions, such as Kepler, and future missions, such as LSST, has the potential
to discover systems where the proposed method will be observationally feasible.
