Hohmann Transfer Orbit Analysis

Overview

This script provides a comprehensive tool for calculating and visualizing orbital transfers around Earth. It specifically focuses on the most energy-efficient method of transferring a spacecraft between two circular orbits using minimal propulsive maneuvers.

Features

Precise Orbital Transfer Calculations

• Compute delta-v (velocity change) for departure and arrival burns.
• Calculate transfer orbit semi-major axis.
• Determine total transfer time.

Interactive Analysis

• User-friendly input for initial and final orbit altitudes.
• Detailed printout of transfer orbit parameters.

3D Visualization

• Graphical representation of Earth.
• Plotting of initial and final orbital trajectories.
• Visual understanding of the transfer orbit.

Dependencies

• numpy: Numerical computing library.
• matplotlib: Plotting and visualization.
• scipy: Scientific computing tools (specifically for constants).

Mathematical Foundations

The script leverages key celestial mechanics principles:

• Gravitational Parameter (μ): 398,600.4418 km³/s².
• Earth's Equatorial Radius: 6,378.137 km.

Transfer Orbit Calculations

• Semi-major axis computation.
• Orbital velocity calculations.
• Delta-v budget analysis.

Installation

1. Ensure you have Python 3.x installed.

2. Install required dependencies:

   pip install numpy matplotlib scipy

** Usage **

Run the script:

python hohmann_transfer.py

When prompted, input:

• Initial orbit altitude (in kilometers).
• Final orbit altitude (in kilometers).

The script will:

• Calculate transfer parameters.
• Display detailed transfer information.
• Generate a 3D orbit visualization.

Example Output

Hohmann Transfer Orbit Details:
Initial Orbit Altitude: 500.00 km
Final Orbit Altitude: 35,786.00 km
Transfer Orbit Semi-Major Axis: 23,093.07 km
Delta-V (Departure Burn): 1.80 km/s
Delta-V (Arrival Burn): 2.44 km/s
Total Delta-V: 4.24 km/s
Transfer Time: 12.54 hours

Visualization

The 3D plot will show:

• Earth's spherical representation.
• Initial orbit trajectory.
• Final orbit trajectory.
• Transfer orbit path.

Limitations

• Currently supports transfers around Earth.
• Assumes circular orbits.
• Does not account for extremely complex gravitational interactions prior to insertion.

Contributing

License

This project is open-sourced under the MIT License. See the LICENSE file for details.