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Satellite Constellation Propagator

Module: 2 (Orbital Mechanics)
Concepts: J2 Perturbations, Nodal Regression, Orbital Elements

🎓 What You'll Learn

Concept Application
J2 Perturbation Why satellite orbits drift over time
Nodal Regression RAAN drift from Earth's equatorial bulge
Orbital Elements The 6 parameters that define any orbit
Ground Tracks How satellites trace paths over Earth
Walker Constellations How to design global coverage systems

Project Overview

This propagator simulates satellite constellation dynamics, accounting for J2 perturbations from Earth's oblate shape. Unlike ideal Keplerian orbits, real satellites experience:

  • Nodal Regression: RAAN drifts westward (for most orbits)
  • Apsidal Rotation: Argument of periapsis rotates
  • Secular Drift: Accumulates over days/weeks

Global Constellation Systems

System Agency/Company Satellites Altitude Inclination
GPS US Space Force 31 20,200 km 55°
GLONASS Roscosmos 24 19,100 km 64.8°
Galileo ESA 30 23,222 km 56°
BeiDou CNSA 35 21,528 km 55°
Starlink SpaceX 6,000+ 550 km 53°
OneWeb OneWeb 648 1,200 km 87.9°
Iridium Iridium 66 780 km 86.4°

Installation & Usage

pip install -r requirements.txt
python propagator.py

Interactive Dashboard

  • 3D VIEW: Animated constellation with Earth
  • GROUND TRACK: Satellite paths over world map
  • COVERAGE: Ground coverage analysis
  • GLOBAL SATS: Statistics and system comparison

The Physics

J2 Perturbation

Earth bulges at the equator by ~21 km. This extra mass creates a torque on inclined orbits:

$$\dot{\Omega} = -\frac{3}{2} n J_2 \left(\frac{R_E}{p}\right)^2 \cos i$$

Where:

  • n = mean motion (rad/s)
  • J₂ = 1.0826 × 10⁻³ (Earth's oblateness)
  • Rₑ = Earth radius (6,378 km)
  • p = semi-latus rectum
  • i = inclination

Sun-Synchronous Orbits

By choosing the right inclination (~98°), RAAN can drift exactly 360°/year, keeping the orbital plane fixed relative to the Sun. Used by:

  • Landsat (NASA)
  • Sentinel (ESA)
  • WorldView (Maxar)

Classical Orbital Elements (COEs)

Element Symbol Meaning
Semi-major axis a Orbit size
Eccentricity e Orbit shape
Inclination i Orbit tilt
RAAN Ω Node location
Arg. of Periapsis ω Periapsis location
True Anomaly ν Current position

See EXPLANATION.md for complete derivations.