  We show that the tropical projective Grassmannian of planes is homeomorphic
to a closed subset of the analytic Grassmannian in Berkovich's sense by
constructing a continuous section to the tropicalization map. Our main tool is
an explicit description of the algebraic coordinate rings of the toric strata
of the Grassmannian. We determine the fibers of the tropicalization map and
compute the initial degenerations of all the toric strata. As a consequence, we
prove that the tropical multiplicities of all points in the tropical projective
Grassmannian are equal to one. Finally, we determine a piecewise linear
structure on the image of our section that corresponds to the polyhedral
structure on the tropical projective Grassmannian.
