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Detailed Description

-orbital-manipulations
LEO Orbital Manipulations Visualization Script

@file
@ingroup leo

This script demonstrates how different orbital parameters affect the shape and orientation
of Low Earth Orbit (LEO) satellite trajectories. It generates 3D visualizations showing
the effects of various parameters on orbital planes and satellite positions over time.

The script mirrors the orbital mechanics implemented in the ns-3 LeoCircularOrbitMobilityModel,
providing a visual understanding of how each parameter influences satellite motion.

USAGE:
    python leo-orbital-manipulations.py

    The script will display a 3D matplotlib plot showing:
    - Satellite positions sampled over one orbital period (blue dots)
    - Starting position (green dot)
    - Ending position (red dot)
    - Earth reference circle (black dashed line)

PARAMETER EFFECTS:

1. orbit_alt_km (Orbit Altitude):
   - Controls the distance from Earth's center
   - Higher altitude = larger orbit radius = slower orbital speed
   - Affects orbital period (T ∝ r^(3/2))

2. time_step_sec (Time Resolution):
   - Controls sampling frequency of orbital positions
   - Smaller values = more position samples = smoother orbit visualization
   - Larger values = fewer samples = coarser orbit representation

3. inclination_deg (Orbital Inclination):
   - Angle between orbital plane and Earth's equatorial plane
   - 0° = equatorial orbit (over equator)
   - 90° = polar orbit (over poles)
   - >90° = retrograde orbit (opposite direction)

4. raan_deg (Right Ascension of Ascending Node):
   - Longitude where the satellite crosses the equator going north
   - Rotates the entire orbital plane around Earth's Z-axis
   - 0° = orbital plane aligned with prime meridian
   - 90° = orbital plane rotated 90° east

5. plane_rotation_deg (Plane Rotation):
   - Additional rotation of the orbital plane about its normal vector
   - Affects the starting position within the orbital plane
   - Equivalent to rotating the satellite's position along its orbit

GENERATED FIGURES:
This script was used to generate the figures in src/mobility/doc/figures/:
- leo-orbit-res-*.png: Various parameter combinations showing orbital effects

DEPENDENCIES:
- numpy
- matplotlib
- mpl_toolkits.mplot3d

EXAMPLE OUTPUT:
The script produces a 3D plot with:
- Blue dots: Satellite positions over one orbit
- Green dot: Starting position
- Red dot: Ending position
- Black dashed circle: Earth's equatorial radius reference