Dusk disk

Perturbation of a Stellar/Planetary Dust Disk by a Planet/Moon
Joachim Köppen Kiel July 2016

This computes the evolution of dust particles in a disk circling a central body, such as the Sun and stars (for protoplanetary disks) or Saturn (for its rings), but perturbed by a planet or a moon, respectively. Initially, the particles are on individual circular orbits, uninfluenced by any neighbouring particles. Only the gravitational field of the central body and the smaller 'planet' act on the particles.
One may choose the outer edge of the disk, in units of the orbital radius of the planet, the mass ratio of planet and the central body, and whether all dust particles are launched from the same azimuth or with random azimuths. The maximum number of particles is 1000. As this quickly fills up the plot, it is convenient to clear the plot from time to time.
If the speed of the planet is taken differet from the circular speed, its orbit will be elliptic. Then the time step must be chosen sufficiently small that the orbit does not show any precession, which is due to the numerical accuracy of the simulation!
When one likes to see the long-term behaviour, one may not plot every time step, but choose a high number of time steps between plotting.
In a simple static x-y representation one sees the orbits as viewed from above. Choosing the co-rotating view - in which the planet always remains in the same spot - reveals the Lagrange points, in particular L4 and L5, in which some particles get trapped - as the Trojan asteroids which accompany Jupiter.