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In this paper I describe numerical calculations of the motion of particles ina disk about a solar-mass object perturbed by a planet on a circular orbit withmass greater than 0.001 of the stellar mass. A simple algorithm for simulatingbulk viscosity is added to the ensemble of particles, and the response of thedisk is followed for several planet orbital periods. A two-arm spiral structureforms 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 perturbedby a weak rotating bar-like distortion, this is shown to be related to theappearance of two perpendicular families of periodic orbits near the resonancecombined with dissipation which inhibits the crossing of streamlines. Spiraldensity enhancements result from the crowding of streamlines due to the gradualshift between families. The results, such as the dependence of pitch-angle onradius and the asymmetry of the spiral features, resemble those ofsophisticated calculations that include more physical effects. The morphologyof structure generated in this way clearly resembles that observed in objectswith well-defined two-arm spirals, such as SAO 206462. This illustrates thatthe process of spiral formation via interaction with planets in such disks canbe due to orbital motion in a perturbed Keplerian field combined with kinematicviscosity.}

Spiral structure generated by major planets in proto-planetary disks: the role of periodic orbits near resonance