  In this paper I describe numerical calculations of the motion of particles in
a disk about a solar-mass object perturbed by a planet on a circular orbit with
mass greater than 0.001 of the stellar mass. A simple algorithm for simulating
bulk viscosity is added to the ensemble of particles, and the response of the
disk is followed for several planet orbital periods. A two-arm spiral structure
forms near the inner resonance (2-1) and extends to the planetary orbit radius
(corotation). In the same way for gaseous disks on a galactic scale perturbed
by a weak rotating bar-like distortion, this is shown to be related to the
appearance of two perpendicular families of periodic orbits near the resonance
combined with dissipation which inhibits the crossing of streamlines. Spiral
density enhancements result from the crowding of streamlines due to the gradual
shift between families. The results, such as the dependence of pitch-angle on
radius and the asymmetry of the spiral features, resemble those of
sophisticated calculations that include more physical effects. The morphology
of structure generated in this way clearly resembles that observed in objects
with well-defined two-arm spirals, such as SAO 206462. This illustrates that
the process of spiral formation via interaction with planets in such disks can
be due to orbital motion in a perturbed Keplerian field combined with kinematic
viscosity.}
