  In general, it is difficult to measure distances in the Weil-Petersson metric
on Teichm\"uller space. Here we consider the distance between strata in the
Weil-Petersson completion of Teichm\"uller space of a surface of finite type.
Wolpert showed that for strata whose closures do not intersect, there is a
definite separation independent of the topology of the surface. We prove that
the optimal value for this minimal separation is a constant $\delta_{1,1}$ and
show that it is realized exactly by strata whose nodes intersect once. We also
give a nearly sharp estimate for $\delta_{1,1}$ and give a lower bound on the
size of the gap between $\delta_{1,1}$ and the other distances. A major
component of the paper is an effective version of Wolpert's upper bound on $
\langle \nabla \ell_\alpha,\nabla \ell_\beta \rangle$, the inner product of the
Weil-Petersson gradient of length functions. We further bound the distance to
the boundary of Teichm\"uller space of a hyperbolic surface in terms of the
length of the systole of the surface. We also obtain new lower bounds on the
systole for the Weil-Petersson metric on the moduli space of a punctured torus.
