MATLAB Code Implementation for Orbital Six Elements (Keplerian Elements)

This MATLAB program provides comprehensive calculation and analysis of orbital six elements, also known as Keplerian elements, which are fundamental parameters for describing celestial object motion in space. The six parameters include: semimajor axis (a), eccentricity (e), inclination (i), right ascension of the ascending node (Ω), argument of perigee (ω), and mean anomaly (M). The program implements robust algorithms to convert position and velocity vectors (r and v) into Keplerian elements using mathematical transformations. Key functions include vector normalization, cross product calculations for angular momentum determination, and trigonometric solutions for orbital parameter extraction. The implementation follows standard astrodynamics formulas, ensuring numerical stability through proper singularity handling near circular and equatorial orbits. For practical applications, the code features: - Input validation for position/velocity vectors - Coordinate system transformations between ECI and orbital frames - Time-dependent parameter calculations using Kepler's equation solvers - Visualization tools for orbital trajectory plotting This MATLAB implementation serves critical roles in satellite tracking systems, space mission planning, trajectory optimization, and orbital mechanics research. The modular code structure allows easy customization for specific mission requirements, such as adding perturbation models for higher accuracy or integrating with ground station data. The program's architecture supports batch processing of multiple satellites and includes error handling for edge cases. With comprehensive documentation and commented code, users can readily adapt the algorithms for various orbital analysis scenarios, making it an essential tool for aerospace engineering projects and astronomical research.