Radiative rejection
\[ P = \epsilon \sigma A T^4 \]
Steady-state cooling is governed by the Stefan-Boltzmann relation.
Physics reference
The setting runs on radiators, photons, geometry, and very patient braking.
This page is the technical spine of The Light Between: the equations, scaling rules, and engineering consequences behind throughput-limited civilization. For the broader canon guide, start with Settings.
Typical cruise at 0.03c-0.1c
No FTL, shields, or reactionless drives
Capture begins far before arrival
Thermal reality
Sustained power in space is limited first by how fast you can dump heat.
Canonically, heat is not the explanation for everything, but it is the primary bottleneck for continuous, infrastructure-scale activity.
T4 scaling
Higher radiator temperature cuts area requirements sharply, but raises material stress.
Throughput, not scarcity
Solar power is abundant. The hard part is continuous high-power use without thermal collapse.
Reference scaling at 1500 K
With \(\epsilon = 0.9\) and \(T = 1500\) K, radiative flux is about 258 kW/m², or roughly 3.87 km² of radiator per TW of waste heat.
Terms
- \(P\): radiated power in watts.
- \(\epsilon\): emissivity of the radiator surface.
- \(\sigma\): Stefan-Boltzmann constant.
- \(A\): radiator area in square meters.
- \(T\): temperature in kelvin.
| Installation | Waste Heat | Radiator area |
|---|---|---|
| Mercury Helioforge Cluster | ~40 TW | ~155 km2 |
| Cis-Lunar Power/Pop Hub | ~8 TW | ~31 km2 |
| Main Belt Metallurgy Swarm | ~10 TW | ~39 km2 |
| Sol Beam Accelerator Array | ~300 TW | ~1162 km2 |
Beam mechanics
Corridors work because photons can push, but the math is expensive and unforgiving.
Beam power, sail reflectivity, packet mass, wavelength, and aperture size all show up directly in the transport math. The equations are compact; the infrastructure they imply is not.
Photon pressure
\[ F = \frac{(1+R)P}{c} \qquad a = \frac{(1+R)P}{mc} \]
Terms
- \(F\): force exerted by the beam on the sail.
- \(R\): sail reflectivity, from 0 to 1.
- \(P\): beam power in watts.
- \(c\): speed of light in vacuum.
- \(a\): packet acceleration under beam thrust.
- \(m\): total mass of the packet.
A 100 TW beam pushing a 1,000 tonne packet yields about 667 kN and 0.67 m/s².
Sail heating
\[ P_{\text{absorbed}} = (1-R)\Phi \]
Terms
- \(P_{\text{absorbed}}\): power absorbed by the sail.
- \(R\): sail reflectivity.
- \(\Phi\): incoming beam flux, or power per unit area.
Small reflectivity losses become dangerous quickly at corridor power densities.
Dropping from \(R = 0.999\) to \(R = 0.99\) increases absorbed heat tenfold.
Diffraction
\[ \theta \approx \frac{1.22\lambda}{D} \]
Terms
- \(\theta\): beam divergence angle in radians.
- \(\lambda\): wavelength of the beam.
- \(D\): effective aperture diameter.
Long-range beam coherence demands enormous apertures and enormous sails.
Beam energy budget
\[ E_{\text{beam}} = Pt_{\text{accel}} = \frac{mvc}{2} \] \[ t_{\text{accel}} = \frac{mvc}{2P} \] \[ \eta = \frac{v}{c} \]
Terms
- \(E_{\text{beam}}\): total energy delivered by the beam.
- \(P\): beam power in watts.
- \(t_{\text{accel}}\): total beam-on acceleration time.
- \(m\): packet mass.
- \(v\): final cruise velocity.
- \(c\): speed of light in vacuum.
- \(\eta\): propulsion efficiency.
Photon propulsion stays inefficient: about 3% at 0.03c, 5% at 0.05c, and 10% at 0.1c.
Beam arrays
The diffraction relation is easiest to grasp when attached to actual corridor hardware. These examples are not handheld optics or single mirrors. They are distributed, phased optical systems operating as civilization-scale beam lenses.
| System | Typical role | Effective aperture | What that implies |
|---|---|---|---|
| Sol backbone array | Primary interstellar launch and return corridor work | ~10-20 km class | Extreme coherence, long beam-on campaigns, and the best shot at high-speed backbone traffic |
| Proxima legacy array | First-generation capture and relay infrastructure | ~6-10 km class | Capable but legacy-heavy, with more constraints from older standards and geometry compromises |
| Alpha Centauri outer capture stack | Precision routing, redirection, and independent return growth | ~8-12 km class | Built for cleaner capture authority and tighter alignment control than inherited Proxima systems |
| Tau Ceti designed array | High-performance mature corridor operations | ~10-15 km class | Better thermal culture and cleaner design assumptions make sustained precision easier to maintain |
| Epsilon Eridani field arrays | Environment-compensating launch and capture work | ~5-9 km class | Performance is limited less by raw ambition than by a harder-to-model operating environment |
| Wolf 1061 sovereignty arrays | Symbolic autonomy and late-route corridor capability | ~4-8 km class | Smaller and less efficient, but politically important because they create independent external interface |
As a rule of thumb, larger apertures buy tighter beams and smaller distant spot sizes, but only if the array can also maintain phase coherence, thermal stability, and pointing precision across the whole structure.
Cooling stack
Thermal control is layered: radiate what you can, buffer what you must, dump what you dare.
- Radiative cooling: primary steady-state mechanism.
- Thermal storage: sensible and latent heat buffers for burst operations.
- Expendable rejection: dumped coolant or hot disposable mass for emergencies.
- Operational cycling: charge, operate, cool, maintain.
Why expendable cooling gets absurd fast
If \(Q = mc_p\Delta T\), then a plausible refractory sink stores only about \(10^6\) J/kg.
\[ \dot{m} = \frac{\dot{Q}}{c_p \Delta T} \]
Terms
- \(\dot{m}\): mass-flow rate of dumped coolant or hot mass.
- \(\dot{Q}\): thermal power that must be rejected.
- \(c_p\): specific heat capacity of the sink material.
- \(\Delta T\): allowed temperature rise before dumping.
Rejecting 1 GW through expendable mass costs about 1,000 kg/s, or 86,400 tonnes per day.
Corridor energetics
Corridors are discrete campaigns because beam time is too valuable to waste.
These campaign figures follow directly from \(E = mvc/2\) and \(t = mvc/(2P)\): beam energy and beam time scale linearly with both payload mass and target cruise velocity.
| Payload | Cruise speed | Beam-on time | Beam energy |
|---|---|---|---|
| 1,000 t | 0.05c | ~65 days | ~1.1 × 1021 J |
| 1,000 t | 0.10c | ~130 days | ~2.2 × 1021 J |
| 100 t | 0.05c | ~6.5 days | ~1.1 × 1020 J |
Interstellar transport is low-volume and high-value. Bulk commodities do not justify the beam-time.
Capture geometry
Arrival is a long braking campaign, not a last-minute burn.
\[ d_{\text{brake}} = \frac{v^2}{2a} \]
Terms
- \(d_{\text{brake}}\): distance required for braking.
- \(v\): incoming cruise velocity.
- \(a\): sustained braking deceleration.
Because distance scales with the square of velocity, even modest speed increases make arrival much harder.
A 1,000 tonne packet under a 10 TW braking beam decelerates at roughly 0.067 m/s². From 0.1c, it needs about 0.71 light years to brake; from 0.05c, about 0.18 light years.
Those campaigns take roughly 14 years and 7 years respectively.
Layered capture sequence
- Far-out acquisition: low-intensity alignment, hundreds of AU out.
- Primary beam braking: the main photon deceleration campaign.
- Intermediate relays: optional coherence and geometry support.
- Inner-system capture: trajectory and velocity refinement.
- Final capture: tugs, transfer arcs, or local beam systems.
Quick reference
The compact ruleset behind the setting.
| Quantity | Expression | Note |
|---|---|---|
| Radiator area | \(A = P / \epsilon \sigma T^4\) | \(A\): area, \(P\): power, \(\epsilon\): emissivity, \(\sigma\): Stefan-Boltzmann constant, \(T\): temperature in kelvin |
| Photon force | \(F = (1+R)P/c\) | \(F\): force, \(R\): reflectivity, \(P\): beam power, \(c\): speed of light |
| Beam energy | \(E = mvc/2\) | \(E\): beam energy, \(m\): mass, \(v\): cruise velocity, \(c\): speed of light |
| Beam-on time | \(t = mvc/(2P)\) | \(t\): beam-on time, \(m\): mass, \(v\): cruise velocity, \(c\): speed of light, \(P\): beam power |
| Braking distance | \(d = v^2/(2a)\) | \(d\): braking distance, \(v\): velocity, \(a\): deceleration |
| Beam divergence | \(\theta = 1.22\lambda / D\) | \(\theta\): divergence angle, \(\lambda\): wavelength, \(D\): aperture diameter |