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Population N against the capacity set by habitat volume, power and supply, over the years
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How to use
Pick a site and a preset, or move the sliders; everything is live. The map (left) shows Earth, the target and the Hohmann ellipse; the yellow marker is where the target must be when you launch. When the banner turns green the window is open: Launch ship now (or leave auto-launch on). Skip to next window runs the clock forward. The cards (right) show colony size and what limits it, stocks in days of supply, power over one solar day, radiation and the mission Δv. Things to try: (1) Mars with dust optical depth 4: the arrays collapse, fission and batteries carry life support; (2) Moon with Equatorial site and no fission: the 14-day night starves the base, now move to the Polar ridge; (3) drop water recycling to 0.6 and see supply limit growth; (4) raise Isp to 900 s and watch the mass in LEO fall; (5) set shielding to 0 and read the years to the 600 mSv limit; (6) compare the three sites in the table below the graphs. Drag to orbit, wheel to zoom. Space pauses, R resets.
The planets (baked albedo and normal maps), the transit ship with its spinning habitat ring, solar wings, tanks and lander, and the surface kit (cratered terrain and horizon ridge, habitat modules, inflatable dome, greenhouse, solar trackers, fission units, ISRU plant with drill, lander, rover, antenna, rocks and a suited astronaut) were modelled in Blender 5.2 with Cycles-baked PBR textures and exported as two Draco GLB files. Three.js r160 instances them as the colony grows: modules follow the pressurised volume, solar trackers follow the array area, fission units the reactor count, and the regolith berm height follows the shielding thickness.
The science
A colony is a set of coupled budgets: how much it costs to get there, how much power and consumables it needs to stay alive, how much radiation the crew absorbs, and how many people the scarcest of these budgets can support. The page keeps all of them live and lets you see which one limits growth.
1. Transfer window and delta-v. The cheapest path between two circular, coplanar heliocentric orbits is the Hohmann ellipse. For radii r1 (Earth, 1 AU) and r2 (target):
Th = π √( ((r1+r2)/2)3 / μ☉ ), v∞,dep = |v1(√(2r2/(r1+r2)) − 1)|
ΔvLEO = √(v∞2 + 2μE/rp) − √(μE/rp), Δvcapture = √(v∞2 + 2μ/rl) − √(μ/rl)
The target must be ahead of Earth by the lead angle φ = π − nT Th when the ship leaves (44 degrees for Mars, 79 for Ceres). The angle changes at the rate |nE − nT|, so windows repeat every synodic period 2π/|nE − nT| (26 months for Mars). For the Moon the same Hohmann formula is applied in the Earth frame (Th about 5 days, lead angle 114 degrees) and the window is treated as daily because the parking-orbit plane can be rotated. The landing Δv is 1.12 vcirc for airless bodies (gravity and steering losses) and a fixed 0.8 km/s of propulsive descent for Mars after the entry heat shield; this is an engineering assumption, not a computed trajectory.
2. Mass. Each burn is a stage obeying the Tsiolkovsky equation with structure fraction ε = ms/(ms+mp):
x = Δv/(Isp g0), mp = (ex−1) mpl / (1 − (ex−1) ε/(1−ε)), m0 = mpl + mp/(1−ε)
The landing, capture and departure stages are chained, so the mass in low Earth orbit is the product of three stage factors. When (ex−1) ε/(1−ε) reaches 1 no amount of propellant works and the page reports the plan as not feasible. Aerocapture removes the capture burn but adds 12 % to the landed payload for the heat shield (illustrative).
3. Power. Sunlight falls as S = 1361 W/m2 / a2 (a in AU): 586 W/m2 at Mars, 178 at Ceres. A fixed horizontal array on an airless equator sees S sin(elevation) with sin(el) = cos(lat) cos(h); its day-average is S/π, which the page checks numerically. A tracking array sees the full beam while the sun is above about 2 degrees. On Mars the dust attenuates the beam as exp(−0.35 τ / sin(el)) (a fudge that keeps a diffuse part; the 0.35 is tuned, not measured). Panels deliver S · A · η · 0.85 (wiring, dust, degradation); fission units give a flat 10 kWe each (Kilopower-class). A battery with 92 % one-way efficiency fills the night. Loads are served in priority order: life support, oxygen electrolysis, other base loads, ISRU, plant lighting. The day is simulated in 96 steps for three cycles so the battery reaches a periodic state; the Moon day is 29.5 Earth days long, which is why the lunar night kills solar-only bases.
4. Life support (mass balance). Per person per day: 0.84 kg O2, 12 kg of water (drinking, food preparation, hygiene), 0.62 kg dry food (typical Baseline Values and Assumptions-style numbers; recycling rates ISS-like 0.93). The unrecovered fraction has to be made or shipped: oxygen is split from water at 6.3 kWh/kg using the factor 18.015/15.999 = 1.126 kg of water per kg of O2; ISRU water comes from power divided by a site-specific specific energy (illustrative 3 to 12 kWh/kg); greenhouse food = area × productivity × lighting served. When the power for life support is short, recycling efficiency is multiplied by the fraction served. If a stock runs out the crew declines (evacuation or attrition).
5. Radiation. Galactic cosmic rays make a floor of dose that shielding reduces only slowly: D(σ) = D0 [0.5 + 0.5 e−σ/30 g/cm²]. D0 = 2.33 mSv/day in deep space (Curiosity RAD measured 1.84 mSv/day inside a 16 g/cm2 cruise stage), 0.64 mSv/day on Mars (measured), 1.37 on the Moon (Chang'e-4), and an illustrative 1.0 on Ceres. Solar particle events are Poisson (0.4 per year) and are stopped far better: 150 mSv × e−σ/10. The career limit shown is 600 mSv (NASA 2022 effective-dose standard).
6. Population. Growth is logistic dN/dt = r N (1 − N/K) with K = min(Khabitat, Kpower, Ksupply) (Liebig's law of the minimum). Khabitat = pressurised volume / volume per person; Kpower is the largest crew whose life-support, base and plant loads are all served over a solar day (found by bisection on the power profile); Ksupply is the larger of what food shipments and what ISRU water can sustain. Ships add crew only when the colony has room; otherwise they carry cargo only.
Numerical checks run in the page. (1) The Hohmann apoapsis radius and (2) the transfer time from an independent RK4 two-body integration; (3) the rocket equation integrated step by step against the mission Δv; (4) the solar constant from the Sun's luminosity L/(4πd2); (5) electrolysis stoichiometry from atomic masses; (6) the synodic period from scanning the simulated planet angles; (7) logistic growth against its analytic solution; (8) the S/π day-average of an equatorial flat array; (9) the run's mass-balance residual.
Honest simplifications. Circular coplanar orbits (Mars e = 0.093 and its 1.85 degree inclination change real windows and Δv by tens of percent); no gravity assist, no low-thrust, no free-return abort; one stage per burn; fixed landing Δv; crew health, psychology, construction labour and economics are not modelled; the radiation and growth parameters are illustrative; ISRU yields and the dust law are rough. This is a teaching model of how the budgets interact, not a mission design.