SELENOGRAPH — Deterministic Cislunar Mission Analysis

An integrated instrument for cislunar (Earth–Moon) mission analysis. From a single engine, SELENOGRAPH answers the four core questions of cislunar mission design — will an orbit hold and what does it cost to keep; what is the cheapest transfer and when is its window; how many spacecraft can a region hold collision-free; how is a formation coordinated without collision. The same input returns the same assessment, reproducible and auditable, in seconds where conventional case-by-case analysis takes hours to weeks.

The method is published and placed in the public domain (DOI 10.5281/zenodo.20721194). The operational engine is not distributed.

The cislunar fuel landscape in the Earth-Moon orbital plane: filled contour map of the rotating-frame effective potential, with the five Lagrange points and the gravitational wells of Earth and the Moon. — The cislunar fuel landscape (Earth–Moon plane). Altitude is fuel — contour spacing is the cost to move. The collinear points L₁/L₂/L₃ are the cheap passes between regions; the equilateral points and the gravitational wells are the basins. A depot's distant retrograde orbit rides a stable basin near the Moon. This is the terrain every cislunar maneuver must cross.

What it answers

One mission specification — candidate orbits in the Earth–Moon system — in; four deterministic answers out.

Question	SELENOGRAPH returns
REGIME & FUEL	the orbit's stability class and its station-keeping correction interval
TRANSFER & WINDOW	the low-energy corridor between two orbits and the exact energy gate it opens below
CAPACITY	the structural ceiling on collision-free orbits a region can hold
FORMATION	a bounded, scheduled relative-motion plan and its station-keeping budget

All four are deterministic: the same input returns the same assessment, reproducible from the classical definitions in the preprint — no random sampling, no fitted model, no per-case tuning.

Demonstrated — canonical Earth–Moon CR3BP

A cislunar region has a hard carrying capacity. As it fills, the fraction of collision-free arrangements does not fade gently — it falls to exactly zero beyond a structural limit. That ceiling is a combinatorial property of the orbital mechanics, computed directly, not a probabilistic risk estimate.

Result	Value
Depot DRO regime	marginal — the lunar-economy band
Station-keeping: depot vs. gateway pass	~150 d vs ~30 d (≈5× cheaper)
Transfer-corridor energy gate (Jacobi C)	3.172
Carrying capacity: collision-free fraction	~100% → 0% (hard ceiling)
Relay formation held collision-free	29 m/s / 260 d (0 breaches)

Demonstrated on the canonical Earth–Moon restricted three-body problem (mass ratio μ = 0.01215): a logistics depot with a relay formation in a Distant Retrograde Orbit. Every figure computed, not estimated. Full method, configuration, and results: 10.5281/zenodo.20721194.

View a sample mission analysis — the lunar depot & relay swarm →

Scope — stated plainly

The observables are classical; the method is what is new. SELENOGRAPH proposes no new celestial mechanics — the regime, the Jacobi-energy gates, the resonance-overlap ceiling, and the relative-motion beat are all standard. The contribution is the exact, deterministic, integrated delivery of all four, in seconds rather than weeks.
Carrying capacity is structural, not yet an absolute count. The ceiling and the collapse rate are computed; the calibrated spacecraft count for a specific region, energy, and keep-out radius is a per-mission deliverable.
The model is the planar CR3BP. Real operations add the spatial problem, solar gravity, lunar gravity harmonics, and radiation pressure; the framework extends, and the results shown here are for the canonical planar Earth–Moon system.
A canonical demonstration, not a population study. Each answer is shown on one representative mission; a broad mission-catalog validation is the next step.
The engine is proprietary and undisclosed. The observables reproduce from the classical definitions on public dynamics; the speed and exactness come from a sealed engine that is not published.

[ bespoke engagement — direct ] Engage by email →

Mission designers and operators, lunar-economy ventures (relay, navigation, logistics, depots), cislunar traffic-and-capacity services, and underwriters of cislunar risk: email with your mission and operating context, and a scoped evaluation follows.

[email protected]

— Tony Matos