  The class of tidal features around galaxies known variously as "shells" or
"umbrellas" comprises debris that has arisen from high-mass-ratio mergers with
low impact parameter; the nearly radial orbits of the debris give rise to a
unique morphology, a universal density profile, and a tight correlation between
positions and velocities of the material. As such they are accessible to
analytical treatment, and can provide a relatively clean system for probing the
gravitational potential of the host galaxy. In this work we present a simple
analytical model that describes the density profile, phase-space distribution,
and geometry of a shell, and whose parameters are directly related to physical
characteristics of the interacting galaxies. The model makes three assumptions:
that their orbit is radial, that the potential of the host is spherical at the
shell radii, and that the satellite galaxy had a Maxwellian velocity
distribution. We quantify the error introduced by the first two assumptions and
show that selecting shells by their appearance on the sky is a sufficient basis
to assume that these simplifications are valid. We further demonstrate that (1)
given only an image of a shell, the radial gravitational force at the shell
edge and the phase-space density of the satellite are jointly constrained, (2)
that combining the image with measurements of either point line-of-sight
velocities or integrated spectra will yield an independent estimate of the
gravitational force at a shell, and (3) that an independent measurement of this
force is obtained for each shell observed around a given galaxy, potentially
enabling a determination of the galactic mass distribution.
