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https://github.com/jman4162/three-body-problem-simulator
A Python-based simulation and visualization of the three-body problem, exploring chaotic gravitational interactions using numerical methods and interactive plots.
https://github.com/jman4162/three-body-problem-simulator
astrodynamics astrophysics chaos-theory gravity gravity-simulation numerical-methods physics physics-education physics-simulation science three-body-problem three-body-simulation
Last synced: 24 days ago
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A Python-based simulation and visualization of the three-body problem, exploring chaotic gravitational interactions using numerical methods and interactive plots.
- Host: GitHub
- URL: https://github.com/jman4162/three-body-problem-simulator
- Owner: jman4162
- License: mit
- Created: 2024-12-07T21:21:42.000Z (about 1 month ago)
- Default Branch: main
- Last Pushed: 2024-12-07T21:35:51.000Z (about 1 month ago)
- Last Synced: 2024-12-07T22:24:08.804Z (about 1 month ago)
- Topics: astrodynamics, astrophysics, chaos-theory, gravity, gravity-simulation, numerical-methods, physics, physics-education, physics-simulation, science, three-body-problem, three-body-simulation
- Language: Jupyter Notebook
- Homepage:
- Size: 62.5 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Three-Body Problem Simulation in Python
This repository demonstrates how to simulate and analyze the **three-body problem** using Python. The three-body problem involves predicting the motion of three massive bodies under their mutual gravitational attraction. It is a fascinating problem in physics and mathematics, often exhibiting chaotic behavior and sensitivity to initial conditions.
---
## Features
- **Mathematical Overview**: Detailed explanation of the equations of motion governing the three-body problem.
- **Numerical Integration**: Implementation using Python's `scipy.integrate.solve_ivp` to solve the coupled ordinary differential equations (ODEs).
- **Visualization**: Interactive plots of the trajectories of the three bodies.
- **Example Simulation**: Includes a simplified simulation of the Sun-Earth-Moon system.
---
## Requirements
Ensure you have Python 3.8+ installed along with the following packages:
- `numpy`
- `scipy`
- `matplotlib`
To install the dependencies, use:
```bash
pip install numpy scipy matplotlib
```
---
## Repository Contents
- **`three_body_problem.py`**: The main Python script containing the implementation of the simulation.
- **`README.md`**: This file, providing an overview of the project.
- **`example_plot.png`**: A sample visualization of the three-body trajectories.
---
## Usage
1. Clone this repository:
```bash
git clone https://github.com/jman4162/three-body-problem.git
cd three-body-problem
```
2. Run the simulation script:
```bash
python three_body_problem.py
```
3. View the plotted trajectories of the three bodies in a 2D plane.
---
## Highlights of the Implementation
### Mathematical Background
The motion of the three bodies is governed by Newton's laws of gravitation and motion. For bodies with masses $m_1$, $m_2$, and $m_3$, the equations of motion are expressed as:
$$
\mathbf{a}_1 = -G m_2 \frac{\mathbf{r}_1 - \mathbf{r}_2}{|\mathbf{r}_1 - \mathbf{r}_2|^3} - G m_3 \frac{\mathbf{r}_1 - \mathbf{r}_3}{|\mathbf{r}_1 - \mathbf{r}_3|^3}.
$$
(Refer to the `three_body_problem.py` script for more details.)
### Numerical Integration
The simulation uses Python's `solve_ivp` function to integrate the ODEs over time. Adaptive time-stepping methods ensure accuracy and efficiency.
### Visualization
The script generates a plot of the trajectories of the three bodies in a 2D plane using Matplotlib. Example:
---
## Example: Sun-Earth-Moon System
The repository includes an example simulation where:
- The Sun, Earth, and Moon are modeled as point masses.
- Initial conditions are chosen to approximate their real-world positions and velocities.
---
## Customization
You can customize the following parameters in `three_body_problem.py`:
- **Masses**: Modify `m_sun`, `m_earth`, `m_moon`.
- **Initial Conditions**: Change the starting positions and velocities of the bodies.
- **Time Span**: Adjust the duration of the simulation (`t_span`).
---
## Learning Objectives
By exploring this repository, you will:
- Gain insights into the physics of the three-body problem.
- Learn how to use Python to numerically solve ODEs.
- Understand the sensitivity and chaotic nature of multi-body gravitational systems.
---
## Contributing
Contributions are welcome! If you find bugs, want to add features, or improve the code, please open an issue or submit a pull request.
---
## License
This project is licensed under the MIT License. See `LICENSE` for details.
---
## Acknowledgments
This project is inspired by the fascinating problem of multi-body dynamics in classical mechanics. The numerical methods and visualization techniques used are based on modern computational tools in Python.