  The source of the gravitational-wave signal GW170817, very likely a binary
neutron star merger, was also observed electromagnetically, providing the first
multi-messenger observations of this type. The two week long electromagnetic
counterpart had a signature indicative of an r-process-induced optical
transient known as a kilonova. This Letter examines how the mass of the
dynamical ejecta can be estimated without a direct electromagnetic observation
of the kilonova, using gravitational-wave measurements and a phenomenological
model calibrated to numerical simulations of mergers with dynamical ejecta.
Specifically, we apply the model to the binary masses inferred from the
gravitational-wave measurements, and use the resulting mass of the dynamical
ejecta to estimate its contribution (without the effects of wind ejecta) to the
corresponding kilonova light curves from various models. The distributions of
dynamical ejecta mass range between $M_{ej} = 10^{-3} - 10^{-2} M_{\odot}$ for
various equations of state, assuming the neutron stars are rotating slowly. In
addition, we use our estimates of the dynamical ejecta mass and the neutron
star merger rates inferred from GW170817 to constrain the contribution of
events like this to the r-process element abundance in the Galaxy when ejecta
mass from post-merger winds is neglected. We find that if $\gtrsim10\%$ of the
matter dynamically ejected from BNS mergers is converted to r-process elements,
GW170817-like BNS mergers could fully account for the amount of r-process
material observed in the Milky Way.
