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# 🌍 **Orbital Mechanics Simulator**

### Numerical Integration of Planetary Orbits (Euler & RK4)

This project simulates the **orbit of any planet** around the Sun using:

* **Euler Method**
* **Runge–Kutta 4th Order Method (RK4)**

All simulation parameters—including the selected planet, integration method, time settings, and colors—are controlled through a single **config.json** file.

The simulator computes:

* The full orbital trajectory
* The **aphelion** (farthest point from the Sun)
* The orbital **speed at aphelion**
* A customizable **3D visualization**

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📁 Project Structure

project/
│
├── main.py              # Entry point: loads config, runs integration, plots
├── utils.py             # Numerical methods, gravity, plotting, helpers
├── config.json          # User-editable settings (planets, colors, times)
└── README.md            # Documentation

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⚙️ Configuration (config.json)

All simulation settings are controlled through config.json.

✔ Example Layout (updated format)

{
  "planet": "Earth",
  "method": "rk4",

  "global_colors": {
    "sun": "yellow",
    "orbit": "white",
    "perihelion": "cyan",
    "aphelion": "magenta",
    "background": "dark_background"
  },

  "time_settings": {
    "time_step_hours": 1,
    "simulation_days": 365
  },

  "planets": {
    "Mercury": {
      "position_at_perihelion": 46.0,
      "velocity_at_perihelion": 58.98,
      "colors": {
        "orbit": "orange",
        "perihelion": "red",
        "aphelion": "purple"
      }
    },

    "Venus": {
      "position_at_perihelion": 107.5,
      "velocity_at_perihelion": 35.02,
      "colors": {
        "orbit": "gold",
        "perihelion": "white",
        "aphelion": "darkred"
      }
    },

    "Earth": {
      "position_at_perihelion": 147.1,
      "velocity_at_perihelion": 30.29,
      "colors": {
        "orbit": "tab:blue",
        "perihelion": "grey",
        "aphelion": "blue"
      }
    },

    "Mars": {
      "position_at_perihelion": 206.7,
      "velocity_at_perihelion": 26.50,
      "colors": {
        "orbit": "red",
        "perihelion": "yellow",
        "aphelion": "brown"
      }
    },

    "Jupiter": {
      "position_at_perihelion": 740.5,
      "velocity_at_perihelion": 13.1,
      "colors": {
        "orbit": "peru",
        "perihelion": "goldenrod",
        "aphelion": "saddlebrown"
      }
    },

    "Saturn": {
      "position_at_perihelion": 1357.6,
      "velocity_at_perihelion": 9.7,
      "colors": {
        "orbit": "khaki",
        "perihelion": "gold",
        "aphelion": "darkkhaki"
      }
    },

    "Uranus": {
      "position_at_perihelion": 2732.7,
      "velocity_at_perihelion": 6.8,
      "colors": {
        "orbit": "cyan",
        "perihelion": "lightcyan",
        "aphelion": "turquoise"
      }
    },

    "Neptune": {
      "position_at_perihelion": 4471.1,
      "velocity_at_perihelion": 5.4,
      "colors": {
        "orbit": "royalblue",
        "perihelion": "lightskyblue",
        "aphelion": "darkblue"
      }
    },

    "Pluto": {
      "position_at_perihelion": 4436.8,
      "velocity_at_perihelion": 4.7,
      "colors": {
        "orbit": "tan",
        "perihelion": "bisque",
        "aphelion": "sienna"
      }
    }
  }
}

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🧠 How to Use

1. Choose a Planet

Set the "planet" field:

"planet": "Mars"

2. Choose numerical method

"method": "euler"
# or
"method": "rk4"

3. Adjust time settings

"time_settings": {
  "time_step_hours": 1,
  "simulation_days": 365
}

4. Customize colors globally

"global_colors": {
  "sun": "yellow",
  "orbit": "white",
  "perihelion": "cyan",
  "aphelion": "magenta",
  "background": "dark_background"
}

5. Override colors per planet (optional)

Each planet can override the defaults.

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🪐 Units Used

To simplify the config:

• Distances: millions of km (10⁶ km)

  • Earth perihelion = 147.1

• Velocities: km/s

  • Earth perihelion velocity = 30.29

Internally the simulator:

• Converts distances → meters
• Converts velocities → meters/second

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🔢 Numerical Methods

✔ Euler Method

Simple but lower accuracy.

✔ RK4 Method

High precision, stable, ideal for orbital mechanics.

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📈 Output

The simulator generates a 3D visualization that includes:

• Planet's orbital path

• Sun position

• Perihelion marker

• Aphelion marker

• Title showing:

  • Distance at aphelion
  • Speed at aphelion
  • Numerical method used

Colors dynamically match your config.json.

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🚀 Running the Simulation

From terminal:

python3 main.py

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