  How do galaxies move relative to one another? While we can examine the motion
of dark matter subhalos around their hosts in simulations of structure
formation, determining the orbits of satellites around their parent galaxies
from observations is impossible except for a small number of nearby cases. In
this work we outline a novel approach to probing the orbital distributions of
infalling satellite galaxies using the morphology of tidal debris structures.
It has long been understood that the destruction of satellites on near-radial
orbits tends to lead to the formation of shells of debris, while those on less
eccentric orbits produce tidal streams. We combine an understanding of the
scaling relations governing the orbital properties of debris with a simple
model of how these orbits phase-mix over time to produce a `morphology metric'
that more rigorously quantifies the conditions required for shells to be
apparent in debris structures as a function of the satellite's mass and orbit
and the interaction time. Using this metric we demonstrate how differences in
orbit distributions can alter the relative frequency of shells and stream
structures observed around galaxies. These experiments suggest that more
detailed modeling and careful comparisons with current and future surveys of
low surface brightness features around nearby galaxies should be capable of
actually constraining orbital distributions and provide new insights into our
understanding of structure formation.
