comp123

This repo contains the simulation framework, analysis code, and results for a study investigating the characteristics, mainly the topological stability, of Low Earth Orbit (LEO) mega-constellations. Specifically, this project compares the Walker-Delta (Starlink) and Walker-Star (OneWeb) architectures to determine their rich-club status over time.

Walker-Star (OneWeb)

Walker-Delta (Starlink)

Summary

• gen-temporal-graph.py: The main simulation engine. Fetches TLE data, propagates orbits using skyfield (SGP4), builds temporal graphs, and calculates network metrics.
• plot_results.py: Visualisation library. Generates static plots, the stability dashboard, and the interactive 3D globe.
• interactive.html: A fully interactive 3D visualisation of the satellite network plotted on an orthographic globe projection.
• *.png: Generated figures including degree distributions, stability comparisons, and topological metrics.
• *.gexf: Graph export files for further visualisation in Gephi.

Getting Started

Prerequisites

The simulation requires Python 3.8+:

pip install -r requirements.txt 

Usage

To run the full simulation pipeline:

python gen-temporal-graph.py

This will:

1. Fetch the latest TLE data from CelesTrak (filtered for operational shells)
2. Simulate 95 minutes of orbital dynamics (one orbital period)
3. Generate topological metrics (Degree, Path Length, Clustering, Rich-Club, etc.)
4. Produce all output figures and the interactive HTML map

Methodology

Data Source

• Starlink: Filtered for the primary shell ($530-550$km altitude). Note: A strict latitude filter ($|\text{lat}|<54^{\circ}$) is applied to exclude secondary polar shells and ensure analysis focuses on the main Walker-Delta configuration.
• OneWeb: Filtered for operational altitude ($1150-1250$km).

Parameter	Starlink (Walker-Delta)	OneWeb (Walker-Star)
Altitude Shell	530 - 580 km	1150 - 1250 km
ISL Range (Max)	1,200 km	2,500 km
Latitude Filter	$|\text{lat}| < 54^{\circ}$ (excl. polar shells)	None
Link Logic	Geometric Line-of-Sight distance	Geometric Line-of-Sight distance

Network Construction

• Links (ISLs): Established based on geometric proximity (Starlink: $1,200$km; OneWeb: $2,500$km) to approximate Line-of-Sight and laser link capabilities.
• Rich-Club Definition: Nodes are considered 'rich' if their degree exceeds the 90th percentile threshold ($k>k_{\text{thresh}}$) established at $T=0$.

Network Metrics

• Rich-Club Coefficient ($\phi$): Determines if high-degree nodes connect preferentially to each other.
• Topological Stability: Uses Jaccard Index and Kendall’s Tau to measure how much the core network changes over time.
• Small-World Properties: Compares Clustering Coefficients and Path Lengths against random null models.
• Null Model Benchmarking: Generates random configuration models for every timestamp to normalise results (calculating $\rho = \phi_{\text{real}} / \phi_{\text{rand}}$).