e2m2e — Earth to Moon, Moon to Earth
e2m2e (Earth to Moon, Moon to Earth) is a Python library based on the Circular Restricted Three-Body Problem (CR3BP) and ephemeris-based N-body dynamics (SPICE), focused on designing and analyzing cislunar space transfer trajectories. It supports a complete orbit design workflow from theoretical CR3BP models to high-fidelity ephemeris models.
Core Features
- CR3BP System Modeling: Supports Earth-Moon, Sun-Earth, Sun-Jupiter systems
- Ephemeris Dynamics: N-body high-fidelity dynamics based on SPICE kernels
- Solar Radiation Pressure: SRP modeling in the CR3BP framework
- Multiple Orbit Types: DRO, ARO, RO, Halo, Lyapunov, Lissajous, Butterfly, Dragonfly
- Orbit Design Algorithms: Strategy-pattern differential correction, natural/pseudo-arclength continuation, multiple shooting, stability analysis
- Transfer Trajectory Search: DRO/RO transfer search, NLP optimization, impulsive transfer design
- MBSE Architecture: Protocol-based systems engineering, requirements management, architecture components
Supported Orbit Types
| Orbit Type | Description |
|---|---|
| DRO | Distant Retrograde Orbit |
| RO | Resonant Orbit (3:2, 4:3, etc.) |
| ARO | Axial Resonant Orbit |
| Halo | Halo orbit (periodic orbit) |
| Lyapunov | Lyapunov orbit (planar periodic) |
| Lissajous | Lissajous orbit (quasi-periodic) |
| Butterfly | Butterfly orbit (symmetric about xy-plane) |
| Dragonfly | Dragonfly orbit (multiple symmetries) |
New Modules
Ephemeris Dynamics & SPICE
High-fidelity N-body dynamics based on NASA SPICE kernels, supporting multi-body gravitational perturbations. Configure multi-body systems with EphemerisSystem and propagate high-fidelity orbits with EphemerisDynamics. Suitable for mission design requiring real ephemeris accuracy.
from e2m2e.core import EphemerisSystem, EphemerisDynamics
system = EphemerisSystem(bodies=["earth", "moon", "sun"])
dynamics = EphemerisDynamics(system=system)
Solar Radiation Pressure
Introduces solar radiation pressure perturbation in the CR3BP framework, applicable to orbit analysis of spacecraft with high area-to-mass ratios (e.g., solar sails).
from e2m2e.core import CR3BP_SRP_Dynamics
srp_dynamics = CR3BP_SRP_Dynamics(system=system, area=10.0, mass=100.0, Cr=1.5)
MBSE Architecture
A systems engineering framework based on Python Protocol interfaces, including architecture components, requirements management, and data models. Supports the full systems engineering workflow for orbit design.
mbse/architecture/— System architecture component definitionsmbse/requirements/— Requirements management and traceabilitymbse/data/— Pydantic data models and enumerationsmbse/diagrams/— Architecture diagram generation
Multiple Shooting
Multi-segment shooting method for high-fidelity solving of complex transfer trajectories, with multiprocessing support.
from e2m2e.algorithms import MultipleShooting, sample_patch_points
patch_points = sample_patch_points(orbit, n_segments=10)
ms = MultipleShooting(dynamics=dynamics)
result = ms.solve(patch_points)
Installation
pip install e2m2e
Development dependencies:
pip install e2m2e[dev]
Example Usage
import e2m2e
from e2m2e.core import CR3BP_System, Orbit
from e2m2e.algorithms import DifferentialCorrection, Continuation
from e2m2e.visualization import FamilyPlotter
# 1. Create Earth-Moon system and compute libration points
system = CR3BP_System(mu=0.01215, primary="earth", secondary="moon")
system.compute_libration_points()
# 2. Create dynamics object
dynamics = e2m2e.core.dynamics.CR3BP_Dynamics(system=system)
# 3. Differential correction to generate DRO orbit
corrector = DifferentialCorrection(dynamic=dynamics)
corrector.setup_2D_symmetric_x_fixed_x0(x0=0.79188556619742)
seed_orbit = Orbit(states=[[0.79188556619742, 0, 0, 0, 0.53682, 0]], times=[0])
seed_orbit.period = 3.472526005624708
seed_dro = corrector.iterate_correction(initial_guess=seed_orbit)
# 4. Natural continuation to generate orbit family
continuation = Continuation(corrector=corrector)
family = continuation.natural_continuation(
seed_orbit=seed_dro,
param_range=(0.14, 0.9),
step_size=0.005,
)
# 5. Visualize orbit family with Jacobi constant coloring
plotter = FamilyPlotter(system)
plotter.plot_family_2d(family, jacobi_values=family.get_jacobi_constants())
Project Structure
e2m2e/
├── core/ # Core modules
│ ├── system.py # CR3BP system definition
│ ├── dynamics.py # CR3BP dynamics model
│ ├── srp_dynamics.py # Solar radiation pressure
│ ├── ephemeris_system.py # Ephemeris multi-body system
│ ├── ephemeris_dynamics.py # N-body ephemeris dynamics
│ ├── spice.py # SPICE kernel management
│ ├── orbit.py # Orbit data structure
│ └── coordinate.py # Coordinate transformation
├── algorithms/ # Algorithm modules
│ ├── differential_correction.py # Differential correction
│ ├── continuation.py # Orbit continuation
│ ├── stability.py # Stability analysis
│ ├── multiple_shooting.py # Multiple shooting
│ └── strategies/ # Strategy-pattern correction configs
│ ├── halo.py # Halo orbit strategies
│ ├── symmetric_2d.py # 2D symmetric orbit strategies
│ └── symmetric_3d.py # 3D symmetric orbit strategies
├── transfer/ # Transfer trajectory design
│ ├── transfer.py # Transfer orbit class
│ ├── transfer_search.py # DRO/RO transfer search
│ ├── transfer_optimization.py # NLP optimization
│ └── search_config.py # Search configuration
├── mbse/ # Systems engineering modeling
│ ├── architecture/ # System architecture components
│ ├── requirements/ # Requirements management
│ ├── data/ # Pydantic data models
│ └── diagrams/ # Architecture diagram generation
└── visualization/ # Visualization
├── plotting.py # Base plotting
├── family.py # Orbit family plotting
├── transfer.py # Transfer orbit plotting
├── stability.py # Stability analysis plots
└── config.py # Plot configuration