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.

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🛠 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
   

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📜 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.

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🎮 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.

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📌 Todo / Future Improvements

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

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💡 References

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

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📜 License

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