  Galactic short period double white dwarfs (DWD) are guaranteed gravitational
wave (GW) sources for the next generation of space-based interferometers
sensitive to low-frequency GWs (10^{-4}- 1 Hz). Here we investigate the
possibility of constraining the white dwarf (WD) properties through
measurements of apsidal precession in eccentric binaries. We analyze the
general relativistic (GR), tidal, and rotational contributions to apsidal
precession by using detailed He WD models. We find that apsidal precession can
lead to a detectable shift in the emitted GW signal, the effect being stronger
(weaker) for binaries hosting hot (cool) WDs. We find that in hot (cool) DWDs
tides dominate the precession at orbital frequencies above ~0.01 mHz (~1 mHz).
Analyzing the apsidal precession of these sources only accounting for GR would
potentially lead to an extreme overestimate of the component masses. Finally,
we derive a relation that ties the radius and apsidal precession constant of
cool WD components to their masses, therefore allowing tides to be used as an
additional mass measurement tool.
