# N-Body Gravity Simulation

Explore celestial mechanics, chaos theory, and energy conservation through interactive N-body simulation. Use RK4 integrator for accurate multi-body gravity system simulation, observe orbital evolution, chaotic phenomena, and gravity assist effects.

> Canonical page: https://elysiatools.com/en/visualizations/n-body-gravity

- **Category:** Physics

## Overview

Interactive N-body gravity simulation exploring celestial mechanics, chaos theory, and energy conservation through accurate physics simulation. Features RK4 (4th-order Runge-Kutta) integrator for high-precision numerical integration of Newton's law of universal gravitation F = G·m₁·m₂/r². Interactive canvas: click and drag to add celestial bodies with custom mass and initial velocity. Real-time visualization includes orbital trails with fading effect showing trajectory history, velocity vectors with directional arrows, body sizes proportional to mass, and color-coded bodies by mass index. Energy conservation tracking with real-time plot displaying kinetic energy, potential energy, and total energy to verify numerical accuracy. Preset astronomical scenarios: Earth-Moon-Sun system (demonstrating stable hierarchical orbits), binary star system (two equal-mass stars orbiting common center of mass), chaotic three-body (random initial conditions showing unpredictable chaotic behavior), and gravity assist slingshot (spacecraft maneuver using planetary gravity for acceleration). Comprehensive physics controls: time speed adjustment (0.1x - 5x), trail length control (0 - 500 points), velocity vector toggle, trail display toggle, energy plot toggle, mass slider for new bodies (10 - 1000 units), and clear all function. Real-time statistics display: body count, total energy with conservation percentage, maximum velocity in system, simulation time elapsed, and center of mass calculation. Educational content sections: Theory (Newton's universal gravitation law, N-body problem explanation, chaos theory connection with butterfly effect, energy conservation principles, Kepler's laws and orbital mechanics), History timeline (Newton's Principia 1687, Lagrange points 1772, Poincaré's chaos discovery 1890, modern applications in space missions), and Guided Experiments (create stable orbit tutorial, three-body chaos demonstration, gravity assist maneuver, orbital resonance exploration). Technical features: O(n²) force calculation optimized for <100 bodies, softening parameter to prevent singularities, canvas-based rendering with 60 FPS, dark space theme with glowing body effects, responsive design for all screen sizes, and comprehensive i18n support (zh, en, es, fr, de, ru, pt). Perfect for astronomy enthusiasts, physics students studying classical mechanics and chaos theory, and anyone interested in orbital dynamics and gravitational systems.

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