  Given a simple closed curve $\gamma$ on a connected, oriented, closed surface
$S$ of negative Euler characteristic, Mirzakhani showed that the set of points
in the moduli space of hyperbolic structures on $S$ having a simple closed
geodesic of length $L$ of the same topological type as $\gamma$ equidistributes
with respect to a natural probability measure as $L \to \infty$. We prove
several generalizations of Mirzakhani's result and discuss some of the
technical aspects ommited in her original work. The dynamics of the earthquake
flow play a fundamental role in the arguments in this paper.
