Classical-Main-Problem-Orbital-Perturbations

This project investigates the secular and periodic perturbations of Keplerian orbital elements due to Earth's oblateness. The code calculates and analyzes perturbations for the CHAMP satellite, with visualizations to demonstrate their effects.

Key Tasks

A. Secular Perturbations

1. Code Implementation: Write a program (Python or MATLAB recommended) to calculate secular perturbations of Keplerian elements (Ω, ω, M) due to Earth's oblateness coefficient (c20).
2. Comparison with GPS Data: Compare the calculated perturbed elements with those from GPS broadcast ephemerides.
3. Visualization: Plot the variations of ΔΩ (change in Ω) and Δω (change in ω) as functions of:
   • Semi-major axis 'a' (with fixed eccentricity and inclination)
   • Eccentricity 'e' (with fixed semi-major axis and inclination)
   • Inclination 'i' (with fixed semi-major axis and eccentricity)
4. Perturbed Orbit Calculation: Calculate the perturbed CHAMP orbit using the perturbed Keplerian elements. Consider different reference systems (space-fixed, Earth-fixed, topocentric).
5. Orbit Differences: Plot the differences between unperturbed and perturbed orbital quantities over time. Include differences in position, velocity, azimuth, and elevation.

B. Periodic Perturbations

1. Perturbation Calculation: Calculate two periodic perturbations of CHAMP's Keplerian elements (select two during your lecture or based on your interest). Use provided coefficients (c20, c22, s22, c30).
2. Visualization: Plot the calculated periodic perturbations as a function of time. Analyze and report the periods and amplitudes of these perturbations.

Data

• CHAMP Initial Orbital Elements: (a2000, e2000, etc.)
• Earth Oblateness Coefficients: c20, c22, s22, c30
• GPS Broadcast Ephemerides (for comparison)

Tools/Technologies

• Programming Language: Python or MATLAB
• Libraries:
  • NumPy (for calculations)
  • Matplotlib (for plotting)
  • Potentially specialized libraries like Skyfield or PyEphem

Project Structure

• src: Code files (.py or .m)
• data: Input data (CHAMP elements, ephemerides)
• plots: Generated visualizations.

Contributions

[Explain how others can contribute, if desired]

License

[Include a license, like MIT or GPL]