https://github.com/scorleos773/three-body-problem-simulator

Three-Body Problem Simulation - A Python-based simulation of the Three-Body Problem with both 2D and 3D visualizations. Uses `matplotlib` and `scipy` to model gravitational interactions and animate orbital trajectories. 🚀🔭
https://github.com/scorleos773/three-body-problem-simulator

differential-equations matplotlib mplot3d newtonian-mechanics numerical-integration numpy orbital-mechanics python runge-kutta-methods scipy-integrate three-body-problem three-body-simulation

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Three-Body Problem Simulation - A Python-based simulation of the Three-Body Problem with both 2D and 3D visualizations. Uses `matplotlib` and `scipy` to model gravitational interactions and animate orbital trajectories. 🚀🔭

• Host: GitHub
• URL: https://github.com/scorleos773/three-body-problem-simulator
• Owner: SCORLEOs773
• License: mit
• Created: 2025-02-11T11:08:23.000Z (3 days ago)
• Default Branch: main
• Last Pushed: 2025-02-11T11:39:39.000Z (3 days ago)
• Last Synced: 2025-02-11T12:25:24.252Z (3 days ago)
• Topics: differential-equations, matplotlib, mplot3d, newtonian-mechanics, numerical-integration, numpy, orbital-mechanics, python, runge-kutta-methods, scipy-integrate, three-body-problem, three-body-simulation
• Language: Python
• Homepage:
• Size: 17.6 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# 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:

   ```sh

   git clone https://github.com/yourusername/three-body-simulation.git

   cd three-body-simulation

2. Install the required dependencies:

   ```sh

   pip install numpy matplotlib scipy

3. Run the simulation:

      a. 2D Version:

      ```sh

      python three_body_2d.py

      ```

      b. 3D Version:

      ```sh

      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:

```sh

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!