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Three-Body Problem Simulation

This repository contains Python implementations of the Three-Body Problem, a classical problem in celestial mechanics that involves predicting the motion of three bodies under mutual gravitational attraction. The simulations are available in both 2D and 3D versions.

Features

  • 2D Simulation: Visualizes the orbits of three bodies in a 2D plane.
  • 3D Simulation: Adds depth and realism by simulating the bodies in three-dimensional space.
  • Custom Initial Conditions: Modify mass, velocity, and starting positions for different scenarios.
  • Animated Trajectories: Real-time visualization using matplotlib.animation.

🛠 Installation

  1. Clone this repository: 
    git clone https://github.com/yourusername/three-body-simulation.git
cd three-body-simulation
  2. Install the required dependencies: 
    pip install numpy matplotlib scipy
  3. Run the simulation: a. 2D Version: 
    python three_body_2d.py
    b. 3D Version: 
    python three_body_3d.py

📜 How It Works

Equations of Motion

The system is governed by Newton's law of universal gravitation:

$$ F = \frac{G m_1 m_2}{r^2} $$

For each body, acceleration is computed as:

$$ a = \frac{F}{m} $$

Where G is the gravitational constant, 𝑚 is mass, and 𝑟 is the distance between bodies.

Integration Method

The code uses scipy.integrate.solve_ivp with the RK45 method to numerically solve the system of differential equations.

🎮 Usage

Changing Initial Conditions

You can modify the starting positions and velocities of the bodies inside the Python files:

initial_conditions = [
    -1, 0, 0, 0, -0.5, 0,  # Body 1
    1, 0, 0, 0, 0.5, 0,    # Body 2
    0, 1, 0, 0.5, -0.5, 0  # Body 3
]
masses = [1, 1.5, 2]  # Different masses

Adjusting these values can create different orbital behaviors.

📌 Todo / Future Improvements

  1. Add energy conservation checks.
  2. Implement a GUI for user-friendly interaction.
  3. Optimize performance for longer simulations.

💡 References

  1. Newtonian Mechanics & Three-Body Problem: Wikipedia
  2. matplotlib animations: Matplotlib Do

📜 License

This project is open-source and licensed under the MIT License. 📩 Feel free to contribute and improve this simulation!