Mapping Unstable Invariant Manifolds in the Earth-Moon System

This repository implements a thesis-grade numerical pipeline for CR3BP halo orbits, invariant manifolds, and re-entry mapping.

Quick Start

1. Create a virtual environment and install dependencies:

   • python3 -m venv .venv
   • source .venv/bin/activate
   • pip install numpy matplotlib plotly

2. Run validation (Phase 1):

   • PYTHONPATH=. python3 scripts/phase1_validate.py

3. Solve a 3D halo orbit (Phase 2):

   • PYTHONPATH=. python3 scripts/phase2_halo_orbit.py

4. Generate manifolds (Phase 3):

   • PYTHONPATH=. python3 scripts/phase3_manifolds.py

5. Compute Poincaré section (Phase 4):

   • UTC_EPOCH="2026-02-07T00:00:00Z" PYTHONPATH=. python3 scripts/phase4_poincare.py

6. Plot 3D orbits + manifolds:

   • PYTHONPATH=. python3 scripts/plot_3d_orbits.py

7. Plot re-entry globe:

   • PYTHONPATH=. python3 scripts/plot_reentry_globe.py

8. Plot halo family:

   • PYTHONPATH=. python3 scripts/plot_halo_family.py

Reproducible Pipeline

Run these in order:

1. PYTHONPATH=. python3 scripts/phase1_validate.py
2. PYTHONPATH=. python3 scripts/phase2_halo_orbit.py
3. PYTHONPATH=. python3 scripts/phase3_manifolds.py
4. UTC_EPOCH="2026-02-07T00:00:00Z" PYTHONPATH=. python3 scripts/phase4_poincare.py
5. PYTHONPATH=. python3 scripts/plot_3d_orbits.py
6. PYTHONPATH=. python3 scripts/plot_reentry_globe.py
7. PYTHONPATH=. python3 scripts/plot_halo_family.py

Outputs are written to outputs/.

Structure

• cr3bp/: core library (EOMs, integrator, shooting, manifolds, continuation)
• scripts/: reproducible runs for each phase
• notebooks/: exploratory and results notebooks
• phase_*.md: phase summaries
• report/: LaTeX thesis scaffold
• notebooks/results.ipynb: polished results notebook

Report

• report/main.tex is a LaTeX scaffold including the Error Budget section.
  • Build with pdflatex main.tex from report/ if LaTeX is installed.