  We present an analytic model to estimate the total number of rocky or icy
objects that could be captured by planetary systems within the Milky Way galaxy
and result in panspermia should they harbor life. We estimate the capture rate
of objects ejected from planetary systems over the entire phase space as well
as time. Our final expression for the capture rate depends upon the velocity
dispersion as well as the characteristic biological survival time and the size
of the captured object. We further take into account the number of stars that
an interstellar object traverses, as well as the scale height and length of the
Milky Way's disk. The likelihood of Galactic panspermia is strongly dependent
upon the survival lifetime of the putative organisms as well as the velocity of
the transporter. Velocities between $10-100$ km s$^{-1}$ result in the highest
probabilities. However, given large enough survival lifetimes, even
hypervelocity objects traveling at over 1000 km s$^{-1}$ have a significant
chance of capture, thereby increasing the likelihood of panspermia. Thus, we
show that panspermia is not exclusively relegated to solar-system sized scales,
and the entire Milky Way could potentially be exchanging biotic components
across vast distances.
