SELENOGRAPH · Lattice OS

Mission Analysis

Lunar logistics depot + relay swarm · Distant Retrograde Orbit.
Earth–Moon CR3BP · μ = 0.01215 DRO depot deterministic · reproducible
SAMPLE — a worked mission analysis computed on the canonical Earth–Moon CR3BP, as described in the published preprint (Matos 2026, DOI 10.5281/zenodo.20721194). Illustrative; not a live operational feed.
THE PROBLEM   You are planning a lunar logistics depot and a relay communications swarm. Four decisions set the cost, the risk, and the fuel budget of the whole program: where to park it (fuel to stay), how to reach it (fuel to arrive), how many craft can safely share the region, and how to fly the swarm without collisions. Today these are four separate studies — weeks of work — and the answers arrive after the orbit is chosen and the capital is largely committed.
THE ANSWER   SELENOGRAPH returned all four from one engine, in seconds, every number computed and auditable — before any fuel, or capital, is committed:

Q1 — Regime & station-keeping

The depot's distant retrograde orbit is classified marginal — the lunar-economy regime: not chaotic (it does not eject) and not perfectly stable (nothing near the Moon is), but nearly self-holding. Its local divergence rate sets the station-keeping clock: a correction about every 150 days. For contrast, an L₂ gateway saddle diverges roughly five times faster — a correction every month. SELENOGRAPH returns this distinction before an orbit is committed.

QuantityValue
Depot DRO — divergence rate0.029
Depot — correction interval~148 d
L₂ gateway saddle — divergence rate0.141
Gateway — correction interval~31 d
Relative station-keeping cost (gateway / depot)~5×

Q2 — Transfer & window

Cislunar transfers do not run in straight lines — they ride low-energy corridors that thread the L₁ and L₂ gateways (the cheap passes on the fuel landscape). A corridor is open only when the spacecraft's energy crosses a precise threshold; below it, the gate is shut and the regions are dynamically separated. For this depot, the inbound (L₁) and outbound (L₂) corridors open below Jacobi energy C = 3.172 — so fuel is committed to the lowest-cost route, in the window when it is open.

Q3 — Carrying capacity

Cislunar space has a hard carrying capacity — a ceiling on how many independent orbits can coexist before collisions become structurally unavoidable. Below the ceiling almost any arrangement is clear; at the ceiling, the collision-free fraction does not fade — it falls to exactly zero. Because that ceiling is exact and combinatorial, not a probabilistic Monte-Carlo estimate, it is a usable input for traffic and capacity planning. This is the question Space Domain Awareness asks for Earth orbit, answered for cislunar space before the region fills.

Spacecraft (orbital families) placedCollision-free arrangements
1–2~100%
347%
417%
52%
6 or more0% — structurally unavoidable

Structural fractions for the canonical configuration; the calibrated absolute count for a specific region and keep-out radius is a per-mission deliverable.

Q4 — Formation & the beat

A relay constellation must hold formation without its members drifting into one another. Two craft on slightly different orbits drift — but the drift is a predictable beat, the slow oscillation of their closest approach, not a runaway. Because the beat is predictable, the intervals of closest approach — the contact and maneuver windows — recur on a fixed schedule. You plan handoffs and phasing burns for the green, instead of fighting the drift.

SELENOGRAPH formation beat — relay close-approach separation vs. time 0 1000 2000 separation between relays (km) 0 150 300 450 600 time (days) contact / maneuver window opens (close approach) |←—— one beat ——→|
Illustrative of the beat structure: the closest approach between two relays oscillates on a slow, deterministic beat — fully parameterized in advance, not an unmodeled drift (blue). Each time it dips, a contact / maneuver window opens (green), so the windows recur on a fixed schedule and are planned, not chased. The validated demonstration held the formation collision-free for 29 m/s over 260 days with zero keep-out breaches.

determinism: the same (mission, configuration) input reproduces this analysis. The relative geometry is characterized exactly in advance — commensurate pairs close into bound relative orbits; incommensurate pairs beat on the schedule above.