Apogee

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A two-stage rocket ascent simulator with shooting-method optimization for circular Low Earth Orbit (LEO) insertion.

Falcon 9 Launch

Overview

Apogee is a comprehensive space mission simulator designed to model the complete lifecycle of a satellite deployment mission. It combines rigorous mathematical modeling with modern numerical methods to achieve highly accurate circular orbit insertions.

Key Capabilities

  • Target altitudes: 160–400 km LEO
  • Payload capacity: 0–10,000 kg
  • Orbital accuracy: Eccentricity < 0.001
  • Velocity error: < 2 m/s

Mission Phases

Phase Status Description
1. Rocket Launch & Ascent ✅ Complete Two-stage Falcon 9 simulation with gravity turn
2. Orbital Insertion ✅ Complete Shooting method optimization for circular orbits
3. Orbital Propagation ✅ Complete Yaw steering for solar panel optimization
4. 3D Visualization 🚧 In Progress Real-time trajectory rendering

Mathematical Foundation

The simulator is built on first-principles physics:

\[ \mathbf{y}(t) = \begin{bmatrix} r(t) \\ \lambda(t) \\ v(t) \\ \gamma(t) \\ m(t) \end{bmatrix} \]

Where:

  • \(r(t)\): Geocentric radius [m]
  • \(\lambda(t)\): Downrange central angle [rad]
  • \(v(t)\): Speed magnitude [m/s]
  • \(\gamma(t)\): Flight-path angle [rad]
  • \(m(t)\): Vehicle mass [kg]

See Theory → State Vector for complete derivation.

Design Principles

The implementation follows these core principles:

  • Mathematically rigorous: Every equation explicitly derived and mapped to code
  • Numerically robust: Adaptive RK integration, event root-finding, bounded optimization
  • Physically accurate: USSA76 atmosphere, variable mass dynamics, non-constant gravity
  • Production-ready: JSON-serializable output, FastAPI backend, modular architecture

Quick Start

# Install
git clone https://github.com/daxrpm/apogee.git
cd apogee && uv sync

# Run simulation
uv run apogee-launch --h-target-km 200 --payload-kg 5000
from apogee_launch import solve_to_circular_orbit

result = solve_to_circular_orbit(
    h_target_km=200,
    payload_kg=5000,
)

print(f"Eccentricity: {result.summary['ecc']:.6f}")
print(f"Altitude error: {result.summary['h_err_m']:.1f} m")
# Start server
uv run uvicorn apogee_api.main:app --reload

# Simulate launch
curl -X POST "http://localhost:8000/launch/simulate" \
  -H "Content-Type: application/json" \
  -d '{"h_target_km": 200, "payload_kg": 5000}'

Package Architecture

apogee/
├── packages/
│   ├── apogee-physics/     # Core numerical engine (JAX/Diffrax)
│   ├── apogee-launch/      # Launch simulator + CLI
│   ├── apogee-orbit/       # Orbital mechanics & yaw steering
│   └── apogee-api/         # FastAPI REST backend
└── frontend/               # React Three Fiber 3D visualization

Documentation Sections

Academic References

This documentation includes proper citations to foundational texts:

  • Battin, R.H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics
  • Curtis, H.D. (2013). Orbital Mechanics for Engineering Students
  • Stoer & Bulirsch (2002). Introduction to Numerical Analysis

See Reference → Bibliography for complete citations.

Getting Started