🌌 Three-Body Problem Lab
🌌 Three-Body Lab
Newton's exact laws. Provably unpredictable futures. Break a universe with 0.001.
Why "unsolvable"?
2 bodies: 12 unknowns, 10 conserved quantities → solvable. Always an ellipse.
3 bodies: 18 unknowns, still only 10 — Bruns (1887) proved no more exist. No formula can ever be written.
Chaos: nearby starts diverge as e^(λt). Press NUDGE and watch it happen to your own universe.
Integrator: velocity Verlet (symplectic) with adaptive substeps — same math as the video.
Three-Body Problem Simulator — Chaos & the Figure-Eight Orbit
This lab simulates the general three-body problem with a symplectic velocity Verlet integrator and adaptive substepping, in the same natural units (G=1) used in research papers. The NUDGE button forks a ghost universe whose starting position differs by just 0.001 and plots the live log-scale separation between the two — watch sensitive dependence on initial conditions (chaos) emerge in real time. Presets include the Pythagorean problem (Burrau 1913), the Moore/Chenciner–Montgomery figure-eight, Šuvakov–Dmitrašinović periodic orbits (butterfly, dragonfly, yarn), and a Trojan body riding Jupiter's L4 Lagrange point. Pause to drag bodies and velocity arrows and design your own system; an energy-drift readout verifies the integration stays honest.
What you can do in this simulation
- NUDGE button: fork a ghost universe (+0.001) and watch the log-scale separation plot climb — chaos, live
- 7 presets: Pythagorean Chaos, Figure-Eight, Butterfly, Dragonfly, Yarn, Trojan L4 Point, Random Chaos
- Pause & drag bodies and green velocity arrows to design your own three-body system
- Auto-tracking camera that never loses a body; adjustable speed (1–8x) and zoom
- Symplectic (velocity Verlet) integration with adaptive substeps and a live energy-drift readout
Concepts covered
three-body problem · chaos theory · sensitive dependence on initial conditions · Lyapunov exponent · figure-eight orbit · Lagrange points · symplectic integration
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