  We model the Comet Shoemaker-Levy 9 - Jupiter impact plumes to calculate
synthetic plume views, atmospheric infall fluxes, and debris patterns. Our
plume is a swarm of ballistic particles with one of several mass-velocity
distributions (MVD). The swarm is ejected instantaneously and uniformly into a
cone from its apex. Upon falling to the ejection altitude, particles slide with
horizontal deceleration following one of several schemes. The model ignores
hydrodynamic and Coriolis effects. We adjust plume tilt, opening angle, and
minimum velocity, and choose MVD and sliding schemes, to create impact patterns
that match observations. Our best match uses the power-law MVD from the
numerical impact model of Zahnle and Mac Low, with velocity cutoffs at 4.5 and
11.8 km/sec, cone opening angle of 75 degrees, cone tilt of 30 degrees from
vertical, and a sliding constant deceleration of 1.74 m/sec^2. A
mathematically-derived feature of Zahnle and Mac Low's published cumulative MVD
is a thin shell of mass at the maximum velocity, corresponding to the former
atmospheric shock front. This vanguard contains 22% of the mass and 45% of the
energy of the plume, and accounts for several previously-unexplained
observations, including the large, expanding ring seen at 3.2 microns by
McGregor et al. and the ``third precursors'' and ``flare'' seen near 300 and
1000 sec, respectively, in the infrared lightcurves. We present synthetic views
of the plumes in flight and after landing and derive infall fluxes of mass,
energy, and vertical momentum as a function of time and position on the
surface. These fluxes initialize a radiative-hydrodynamic atmosphere model
(Paper II of this series) that calculates the thermal and dynamical response of
the atmosphere and produces synthetic lightcurves.
