The Four Topologies

Four views, one record

Four Questions, Asked of Every Destination the Same Way

The twelve destinations carry one record each. A topology is that record read through a single question, so the twelve line up on one axis.

A destination is not one thing. Earth Orbit is close in velocity and crowded with hazards; Callisto is far in velocity and, below the Jovian belts, comparatively safe. Describing each place in its own terms makes them impossible to rank against one another. Four topologies fix that by asking the same four questions everywhere — what it costs to arrive, where it sits in the flow, what bounds the work, and what degrades the hardware — and plotting all twelve on each.

Energy, Industrial and Constraint are static views: they describe a place as it stands, and the numbers do not move with time on station. Hazard is the one view with time built into the axis — every entry is a rate or a probability, a dose per year or an event with a return period. That split is deliberate. A constraint bounds what can be done and does not change with exposure — comms latency to Mars is 4 to 24 minutes whether a crew stays a day or a decade. A hazard accumulates, and the longer the exposure the larger the integrated harm, so it is defended against on a clock the constraint never runs. Folding the two together — radiation dose next to light-time — hides exactly the distinction that decides how long anyone can stay. Building

View 01

Energy Topology — What It Costs in Velocity to Be Somewhere

Gravity wells, transfer costs, aerobraking windows, Oberth regions, depot placement. The only distance that matters is Δv.

The solar system does not sort by kilometers. It sorts by Δv — the velocity change a vehicle must spend to move between two states — because propellant, not distance, is what a mission pays. The Moon is a quarter of a million kilometers away and costs about 5.9 km/s from low Earth orbit to the surface; geostationary orbit is far closer yet costs 3.9 km/s to reach. Mars is tens of millions of kilometers out and, through the atmosphere, arrives for less Δv than a propulsive lunar landing. Energy Topology is the map drawn on that axis, and reading it is the first thing the Corridors dataset does.

Two features bend the map. Aerobraking turns a planet’s atmosphere into free Δv, which is why Mars and Earth return are cheaper than their bare numbers suggest and why the airless Moon is dearer than its proximity implies. The Oberth effect makes a burn deep in a gravity well worth more than the same burn higher up, which sets where depots and departure stages belong. The flown corridors are Observed; the outer-system legs that depend on high-power propulsion are Projected.

View 02

Industrial Topology — The Circulatory System as a Graph

Production nodes, logistics hubs, and the corridors between them, weighted by mass and propellant flow.

Where Energy Topology prices a single trip, Industrial Topology draws the whole network: which nodes make things, which store and transfer them, and how much mass moves along each edge. The weight on an edge is the gear ratio — the launched mass needed to deliver one tonne to a point. Delivering a tonne to the near libration point, EML-1, costs roughly 17 tonnes lifted from Earth, so anything produced locally is worth about seventeen times its mass in launched equivalent. That one number decides whether a supply chain closes or stays on a resupply clock.

The first real edge is lunar: water mined at Shackleton, lifted 2.5 km/s to an EML-1 depot, and sold as propellant into cislunar traffic — the Moon exports water up the well, and the depot, not the Moon, owns the refuelling. Past that, the graph thins fast. Mars produces nothing anyone off-Mars buys, so its industrial question is what the surface must make for people to leave, not what it ships. The belt and outer system appear on the graph only as modelled edges until high-power propulsion makes the transit times bearable. Building

View 03

Constraint Topology — The Operating Envelope

Insolation and its seasonal floor, gravity, comms latency and bandwidth, thermal sink temperature, local resource inventory. What bounds capability, and none of it moves with time on station.

Constraint Topology records the fixed walls of a place. Available sunlight sets how much power an array returns — the Shackleton rim holds a capacity factor near 90% at roughly 10% of Earth’s nominal insolation, while past the frost line solar collapses and fission becomes the enabling condition. Light-time sets how much of the control loop Earth can hold: 1.3 seconds to the Moon keeps a human in the loop, 4 to 24 minutes to Mars does not, and hours to the outer system means autonomy is the mission. Gravity sets what excavation and anchoring cost and what the body endures — the Moon at 0.16 g, Mars at 0.38 g. A permanently shadowed crater floor at 40 K sets the thermal sink. These are bounds, not threats: they cap what the site can do and are the same on day one and day ten thousand.

The per-destination version of this view is the Constraint Fingerprint — the twelve plotted on the same envelope axes so the walls can be read side by side. Observed for the physical quantities; Building for the composite scoring.

View 04

Hazard Topology — What Damages, at What Rate

Chronic dose and acute events, thermal cycling, abrasive and charged surfaces, vacuum, impact flux, and the cost of partial gravity. The only view with time on the axis.

Hazard Topology is the roaring wilderness, measured. Galactic cosmic radiation is a chronic dose that climbs the moment a crew leaves the magnetosphere; solar particle events are acute and arrive on a return period, which is a probability rather than a level. Thermal cycling has an amplitude and a transition rate that fatigue structure and electronics. Lunar regolith is abrasive, electrostatically charged, and clings to everything it touches. Jupiter’s radiation belts impose a dose gradient so steep that Callisto, outside the worst of them, is habitable where Europa is not. Partial gravity is itself a slow hazard to the human body, distinct from the engineering ones.

Every entry here is a rate or a probability, so the same place reads differently for a week-long sortie and a permanent base — the integrated dose is what closes a destination to crews long after the instantaneous numbers look survivable. The per-destination version is the Hazard Fingerprint. Observed for measured environments; Projected for event return periods at sites never occupied. Projected

Same number, opposite sign

One Parameter Can Mean the Reverse Thing in Each View

The record stores a number once. Which topology reads it — and whether it helps or hurts — depends on what the site is trying to do.

A permanently shadowed crater floor at 40 K is three different things at once. To cryogenic compute it is a resource — a free cold sink that cuts the energy cost of cooling a dense rack, which is why cold compute is kept native to the lunar poles. To habitat thermal design it is a constraint — a bound on the heat budget, a wall the system has to work inside. To every exposed mechanism, lubricant and seal it is a hazard — cold that embrittles and seizes, degrading on a clock. The fingerprint records 40 K a single time; Constraint Topology reads it as a limit, Hazard Topology reads it as a threat, and the Energy and Industrial views may not read it at all.

This is why the four are kept as separate views over one shared record rather than merged into a single score. A merged ranking would have to decide in advance whether 40 K is good or bad, and the answer depends entirely on intent. Keeping the record single and the readings plural is what lets the same twelve destinations be compared fairly for mining, for compute, for crews, and for transit — four questions, four answers, one set of facts underneath.

Record

Provenance and Data Sources