A browser-based three-body gravitational simulator that visualizes how simple Newtonian gravity produces complex and chaotic motion.
This project uses an adaptive Runge–Kutta–Fehlberg (RKF45) integrator to solve the classical three-body problem in normalized astronomical units, with real-time rendering and numerical diagnostics.
- Adaptive RKF45 (4th/5th order) numerical integration
- Normalized Newtonian gravity (G = 1)
- Multiple well-known scenarios:
- Figure-eight orbit (Chenciner–Montgomery)
- Burrau’s Pythagorean three-body problem
- Star–planet–moon system
- Lagrange L4/L5 configuration
- Real-time diagnostics:
- Total energy
- Relative energy drift (ΔE / E₀)
- Adaptive timestep (dt)
- Step acceptance rate
- Interactive controls:
- Time scaling
- Error tolerance
- Pause / resume
- Preset switching
- Particle trails with fading for orbit visualization
- Classical Newtonian gravity in 2D
- Point masses with configurable mass ratios
- No relativistic corrections
- Optional numerical softening for close encounters (used internally for stability)
The simulator emphasizes short-term numerical accuracy and transparency, allowing users to observe both stable and chaotic dynamics as well as numerical error growth.
The system is integrated using the Runge–Kutta–Fehlberg (RKF45) method with adaptive timestep control:
- 4th- and 5th-order solutions are compared each step
- Local truncation error determines timestep acceptance
- Timestep increases or decreases dynamically based on error
This approach provides high accuracy for short-to-medium time spans, while making numerical drift visible rather than hiding it.