N-Body Gravitational Simulation 🌌

A stunning Python-based interactive simulation of the N-body gravitational problem, featuring real astronomical data and multiple numerical integration methods. Watch the dance of planets, trace historic space missions, and explore the cosmos! 🚀

✨ Key Features

Feature	Description
🎮 Interactive 3D Visualization	Dynamic real-time animation with adjustable speed
🌍 Real Astronomical Data	Accurate planetary positions from NASA
🧮 Multiple Integration Methods	Choose from Euler, RK2, RK4, or advanced symplectic methods
🛸 Historic Space Missions	Simulate Voyager trajectories
⚡ High Performance	Optimized calculations with NumPy

🚀 Quick Start

Prerequisites

Python 3.8 or higher
pip (Python package installer)

Installation

1. Clone the repository:

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

2. Install dependencies:

pip install -r requirements.txt

Running the Application

Development Mode

python src/main.py

Production Mode

For production deployment, we use Gunicorn as our WSGI server:

1. Make the production script executable:

chmod +x run_production.sh

2. Create logs directory:

mkdir logs

3. Run the application:

./run_production.sh

The application will be available at http://localhost:8050

🎯 The Science Behind It

The Core Equation

$\vec{a}i = G \sum{j \neq i} \frac{m_j(\vec{r}_j - \vec{r}_i)}{|\vec{r}_j - \vec{r}_i|^3}$

Parameter	Description
🔰 G	1.4872e-34 AU³/(M☉·day²) - Gravitational constant
⭐ $m_j$	Mass in solar masses (M☉)
📏 $\vec{r}$	Position in astronomical units (AU)

🧮 Numerical Methods

Method	Equation	Characteristics
Euler	$y_{n+1} = y_n + h f(t_n, y_n)$	✅ Fast computation ✅ Minimal memory ⚠️ Basic accuracy
RK4	$y_{n+1} = y_n + \frac{h}{6}(k_1 + 2k_2 + 2k_3 + k_4)$	✅ High accuracy ✅ Stable ⚠️ Computationally intensive
Verlet	$\vec{r}_{n+1} = \vec{r}_n + \vec{v}_n\Delta t + \frac{1}{2}\vec{a}_n\Delta t^2$	✅ Energy conservation ✅ Long-term stability ⚠️ Ideal for orbits
Adams-Bashforth	$y_{n+1} = y_n + \frac{h}{24}(55f_n - 59f_{n-1} + 37f_{n-2} - 9f_{n-3})$	✅ Efficient ✅ High accuracy ⚠️ Best for smooth systems

📚 Included Scenarios

Scenario	Features
🌞 Solar System	• Complete planetary system • Major moons and asteroids • Accurate orbital parameters
🛸 Space Missions	• Voyager 1 & 2 trajectories • Historic planetary encounters • Mission timeline recreation
☄️ Cometary Orbits	• Halley's Comet simulation • Planetary perturbations • Long-term orbital evolution

🔧 Configuration

The production server can be configured through run_production.sh:

• Port: 8050 (default)
• Workers: 4 (default)
• Timeout: 120 seconds
• Log files location: logs/ directory

📝 License

This project is licensed under the GNU License - see the LICENSE file for details.