Lagrange (L4/L5) Accumulation of Stellar Dust

Overview: This applet simulates a star, a planet, and lots of massless dust.
The default parameters match those of the Sun and Jupiter (so an orbit takes 12 years and is slightly eccentric).
Initially, the dust is uniformly distributed in a circle around the star at the same radius as the initial radius of the planet (which starts at its apogee).
Each dust particle is given an initial small (0.01%) random out-of-plane displacement to make this a truly 3-D simulation.
Let the simulation run for several minutes (or all night!). You should then see an aggregration of dust near the L4 and L5 Lagrange points (i.e., same radius as the planet but 60 degrees ahead/behind in the orbit).

Controlling the Simulation:

• To start the simulation, press Start.
• FrameRotationRate sets a counterrotation of the "camera". Setting it to 0.51 will hold the planet's motion approximately constant.
• dt is the time increment in years (so 0.01 is approximately three days). Give a negative value for dt to run the simulation backwards.
• Warp: The most time consuming part of the simulation is painting the window. Parameter "warp" indicates how many simulation time steps are performed per repainting. Large warp factors make the simulation faster (up to a point).
• You can change FrameRotationRate, dt and/or warp at any time. Just type in a new value and hit the "Enter" key.
• n:The number of objects (star, planet, and n-2 dust particles). On my computer 10,000 gives reasonable performance. On slower computers, a smaller value may be prudent.
• m/M:The planet's mass as a fraction of Jupiter's mass.
• v/V:The planet's initial velocity as a fraction of Jupiter's ``true'' velocity.
• Show/Hide Trails: You can ask the simulator to leave dust trails by pressing this button.
• Show/Hide Dust: You can hide the dust with this button (useful if the star or planet become lost).
• +/-: These buttons are used to zoom in/out.