The Valen–Homecoming Planet Builder:
Design, Physics, and Calibration of a
Single-Page Exoplanetary Climate Tool

Technical Companion Paper — How the Tool Works and Why
© 2026 James Franklin
May 2026  ·  Version 1.0
This Paper was edited and the formatted using an LLM. Stated for Clarity
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Abstract

The Planet Builder is a single-file, browser-based tool for constructing physically plausible exoplanetary environments for the Valen–Homecoming science-fiction universe. It accepts a small set of measurable inputs — planetary radius, density, rotation period, orbital parameters, atmospheric composition, stellar luminosity and effective temperature — and computes, from first principles where possible and from documented Earth-calibrated parameterisations elsewhere, a self-consistent chain of outputs: surface gravity, pressure, albedo, greenhouse warming, surface temperature, scale height, habitable-zone position, atmospheric circulation regime, latitudinal temperature profile, and habitability zones. Two supplementary panels assess industrial-gas technosignatures and atmospheric biosignatures.

IMPORTANT NOTE:

This tool is designed as an educational and worldbuilding aid for plausible planetary modelling only and is not intended to provide scientifically rigorous predictive climatology. The model is primarily calibrated against Earth and selected Solar System planets because they are the only worlds for which we possess detailed observational data and ground-truth measurements.

The exact atmospheric, geological, magnetic, and climatic conditions of exoplanets remain largely unknown. Consequently, all outputs produced by this tool should be interpreted as physically plausible approximations rather than exact predictive models.

Please do not use this modeller to make authoritative claims regarding the climate of Earth or real exoplanets. Planetary climates are extraordinarily complex systems involving coupled atmospheric, oceanic, geological, orbital, magnetic, and stellar processes that extend well beyond the scope of this simplified model, despite the sophistication of the underlying mathematics and parameterisations.

The design standard is: as scientifically accurate as is logical and practicable for worldbuilding. The tool does not break physics, chemistry, or common sense; all approximations are documented in the tool itself; and it is anchored to the only planetary climate we have measured in situ — Earth's. This paper describes the physics of each computational block, explains why the solar-system planets serve as essential calibration anchors, justifies every significant approximation, and provides the full reference chain from peer-reviewed literature.

1. Introduction and Design Philosophy

Science-fiction worldbuilding has always faced a tension between dramatic freedom and physical plausibility. A planet can look like anything on a page, but a reader with a physics education — or access to a search engine — will notice when surface gravity is wrong for the stated mass, when a tidally locked world somehow has Earth-like seasons, or when an atmosphere full of methane coexists happily with free oxygen for geological time. The Planet Builder exists to resolve that tension: give the author a physically honest scaffolding, and let the story happen inside it.

The tool runs entirely in the browser as a single HTML file with no server dependencies. It is not a general circulation model (GCM); it does not resolve weather, seasons, or ocean currents. It is, deliberately, a one-dimensional, steady-state, globally averaged climate calculator — the same level of abstraction as early habitable-zone models (Kasting et al., 1993; Kopparapu et al., 2013) — with an Earth-calibrated latitudinal overlay added for habitability mapping. This is the right level of fidelity for its purpose: detailed enough to catch nonsensical configurations, fast enough to iterate interactively, and transparent enough that every number can be traced back to an equation.

The central anchor is Earth. We know Earth's surface temperature (287.8 K, or 14.7 °C), its albedo (~0.30), its atmospheric composition, its scale height, its equator-to-pole temperature gradient (~45 K), and we have ground-truth measurements of all of these. No other planet offers this calibration quality. Venus, Mars, Jupiter, and Titan serve as secondary anchors for specific subsystems (superrotation, banding, band saturation), but Earth is the load-bearing calibration for the climate engine, and the tool is honest about this dependency.

2. Computational Structure

The Planet Builder computes its outputs in a strictly sequential chain of eight numbered blocks, followed by two diagnostic panels. Each block depends only on the blocks before it (and on the user's inputs), so the calculation is deterministic and reproducible. The chain is:

BlockNameKey Outputs
1Physical PropertiesSurface gravity, escape velocity, volume, mass, core mass fractions
2OrbitalYear length, perihelion/aphelion distances, rotation period
3InsolationStellar flux at planet (mean, perihelion, aphelion), relative to Earth
4Atmospheric ChemistryMean molecular weight, atmospheric mass, surface pressure, scale height
5AlbedoBond albedo from Rayleigh scattering, cloud, and surface/ice terms
6Iterative ClimateEquilibrium temperature, greenhouse ΔT, water vapour, surface temperature
7Atmospheric StructureSurface pressure (repeated for context), scale height, habitable-zone position
8Circulation & Habitability ZonesSuperrotation factor, banding index, heat transport, equator/pole temps, zone map
Additive Greenhouse / TechnosignatureCommitted warming from industrial trace gases; technosignature flags
BiosignaturesDisequilibrium and combination biosignature assessment

Blocks 1–8 constitute the "engine spine." The two supplementary panels are bolted on after the engine and do not feed back into it — a deliberate safety discipline to ensure that optional trace-gas inputs cannot corrupt the core climate calculation.

3. Block-by-Block Physics

3.1 Block 1 — Physical Properties

Given the planetary radius R (km) and mean density ρ (g/cm³), the tool computes volume, mass, surface gravity, and escape velocity from first principles. These are exact closed-form equations with no approximation:

g = (4/3) · π · G · ρ · R (1)
v_esc = √(2 · g · R) (2)

The gravitational constant G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² and the Stefan–Boltzmann constant σ = 5.670374419 × 10⁻⁸ W m⁻² K⁻⁴ are used throughout at their CODATA 2018 values. The user also specifies core mass fractions (total core, liquid core, core density), which feed interior-structure outputs but do not affect the climate chain. Density and radius together constrain what kind of planet is physically plausible: a world of 1 Earth-radius at 8 g/cm³ is an iron ball; one at 1.5 g/cm³ is an ice-rock mix. The tool does not enforce these constraints automatically — the user is responsible for choosing sensible values — but the outputs (gravity, mass, escape velocity) immediately reveal when a configuration is unphysical.

3.2 Block 2 — Orbital

Orbital period follows Kepler's third law exactly, given the semi-major axis a (AU) and stellar mass (derived from luminosity). Perihelion and aphelion distances are computed from a and eccentricity e. The rotation period is entered as hours, minutes, and seconds; this drives the sidereal day length, which feeds the circulation model in Block 8. Axial tilt is recorded but does not yet feed a seasonal channel — this is an acknowledged limitation deferred to the Exoworld phase.

3.3 Block 3 — Insolation

The stellar flux at the planet's orbital distance is computed from the star's luminosity (in solar units) and the distance:

F = L☉ · L_star / (4π · a²) (3)

where L☉ = 3.828 × 10²⁶ W is the solar luminosity. The tool reports flux at mean distance, perihelion, and aphelion, plus the flux relative to Earth's 1361 W/m². The stellar effective temperature (T_eff) is a separate input used for the albedo calculation (spectral dependence of Rayleigh scattering) and as a display parameter. In the current build, the star is specified manually; a future build will offer a live dropdown from the Grattat Galaxy Star Catalogue (GGSC).

3.4 Block 4 — Atmospheric Chemistry

The user enters the atmospheric composition as a percentage breakdown across fifteen gases (N₂, O₂, CO₂, H₂O, Ar, He, CH₄, H₂, NH₃, CO, SO₂, H₂S, O₃, ethane, benzene). The gas sum must equal 100% — the tool refuses to calculate otherwise, which prevents garbage-in/garbage-out configurations. From the mole fractions, the tool computes the mean molecular weight of the atmosphere. Combined with the atmospheric mass fraction (entered as a percentage of planetary mass, a single input that controls surface pressure and scale height), this yields:

P_surf = (M_atmo · g) / (4π · R²) (4)
H = (k_B · T) / (μ · g) (5)

where M_atmo is the atmospheric mass, μ is the mean molecular mass, and H is the scale height. Earth's atmosphere is approximately 0.000088% of its planetary mass — about one millionth. Venus is approximately 0.0092% (~100×). This single input, often overlooked, drives surface pressure, scale height, and consequently the entire climate calculation. The tool flags this to the user.

Water vapour note: The entered H₂O percentage is an initial condition only. Water vapour is governed by temperature through the Clausius–Clapeyron relation and is recalculated iteratively in Block 6. The entered value seeds the first iteration; the converged value may differ substantially.

3.5 Block 5 — Albedo

The Bond albedo is the fraction of incoming stellar energy reflected back to space before it can warm the planet. It is the single most important determinant of surface temperature after insolation itself, and getting it wrong by even 0.05 can shift the surface temperature by several kelvins. The tool computes albedo from three physically distinct contributions:

Rayleigh scattering depends on surface pressure, atmospheric composition (specifically the molecular polarisability), and the stellar spectral type (bluer stars produce more scattering). This is computed from a pressure-scaled scattering optical depth.

Cloud albedo is the dominant term for most habitable worlds. The user sets cloud coverage fraction; the tool computes cloud type from atmospheric chemistry (water/ice clouds for water-bearing atmospheres, H₂SO₄ clouds for sulphur-dioxide-rich ones). The two-sided cloud model accounts for both shortwave reflection (cooling) and longwave trapping (warming), with the balance determined by cloud altitude and optical thickness — a parameterisation anchored to Earth's observed net cloud radiative effect.

Surface/ice albedo depends on ocean coverage, ice coverage (computed from temperature in the iterative loop), and surface type. Ice-albedo feedback is included: as the planet cools, ice extent grows, albedo rises, and the planet cools further — a positive feedback that can trigger glaciation cascades below approximately −12 °C global mean temperature, as the tool warns the user.

The total Bond albedo for Earth converges to approximately 0.29–0.30, consistent with satellite measurements (CERES). For Venus, the sulphuric-acid cloud pathway produces albedos above 0.70.

3.6 Block 6 — Iterative Climate (the core engine)

This is the heart of the tool and where the most significant physics decisions live. The equilibrium temperature is computed from the Stefan–Boltzmann law:

T_eq = [ F · (1 − A) / (4 · σ) ]^(1/4) (6)

For Earth, this gives approximately 255 K (−18 °C). The observed surface temperature is 288 K (15 °C). The difference — approximately 33 K — is the greenhouse effect. The tool must reproduce this difference from the atmospheric composition, without smuggling in an ad hoc constant.

The greenhouse warming is computed iteratively. At each cycle, the tool:

(a) Computes the non-H₂O optical depth from the partial pressures and known absorption properties of CO₂, CH₄, NH₃, and other greenhouse gases in the composition. Each gas contributes according to its mass-absorption coefficient and its column abundance (partial pressure × atmospheric column).

(b) Computes water vapour from the Clausius–Clapeyron equation, which gives the saturation vapour pressure as a strong function of temperature. This is the leading greenhouse term on any world warm enough to hold liquid water. The Clausius–Clapeyron relation means that water vapour is a feedback, not a forcing: warmer temperatures → more water vapour → more greenhouse warming → warmer still. This positive feedback approximately doubles the warming from CO₂ alone on Earth, and the tool captures it through the iterative loop.

(c) Accounts for longwave cloud warming (clouds trap outgoing infrared as well as reflecting incoming shortwave), which partially offsets the albedo cooling from Block 5.

(d) Computes latent heat export (the "brake"): evaporation removes energy from the surface and deposits it aloft, moderating surface warming. This term is negative (cooling) and is essential for preventing runaway greenhouse behaviour in wet atmospheres.

(e) Ice coverage is updated based on the new temperature, feeding back to albedo (Block 5) for the next iteration.

The iteration continues until convergence (surface temperature changes by less than a threshold between cycles) or until a maximum cycle count is reached. For Earth, convergence typically occurs within 25–30 cycles. The converged surface temperature for an Earth-composition, Earth-albedo, Earth-mass world at 1 AU from a solar-luminosity star is 287.8 K (14.7 °C), within one degree of the observed value.

The 14.7 °C anchor. This is the single most important validation of the engine. Earth's observed global mean surface temperature is approximately 14.0–15.0 °C depending on the dataset and averaging period (HadCRUT5, ERA5, Berkeley Earth). The tool's 14.7 °C sits comfortably within this range. If any code change shifted this anchor by more than ~1 K without physical justification, it would indicate a regression and the change would be reverted. This anchor was tested after every modification made during development.

3.7 Block 7 — Atmospheric Structure

Block 7 reports the converged surface pressure, scale height (recomputed at the converged surface temperature), and the habitable-zone boundaries for this star. The habitable zone is computed using a Kopparapu-style effective-flux criterion:

HZ_inner = √(L_star / S_eff,in) ; HZ_outer = √(L_star / S_eff,out) (7)

where S_eff,in = 1.107 and S_eff,out = 0.356 are the moist-greenhouse and maximum-greenhouse flux limits respectively, approximated for a solar-type star (Kopparapu et al., 2013). Earth at 1.0 AU falls within this range (0.95–1.68 AU for the Sun), and the tool reports the planet's position relative to its own star's habitable zone.

3.8 Block 8 — Circulation and Habitability Zones

Global mean temperature alone hides the thing that matters most for worldbuilding: where on the surface is it warm enough for liquid water, and where is it frozen? Two worlds of identical mean temperature can have utterly different habitable geographies depending on how efficiently the atmosphere transports heat from equator to pole. Block 8 addresses this.

3.8.1 Superrotation

Atmospheric superrotation — where the atmosphere rotates faster than the solid body beneath it — is a real and important phenomenon. Venus's atmosphere completes a circuit in ~4 Earth days despite the planet rotating once every 243 days, a superrotation factor of ~60. This strong circulation transports heat efficiently, producing a remarkably uniform surface temperature despite Venus receiving no sunlight at all on its night side for months at a time. Earth, by contrast, has a superrotation factor near 1.0 — its atmosphere broadly co-rotates with the surface.

The tool derives superrotation from the planet's rotation rate, atmospheric mass, and insolation. Slow rotation with a substantial atmosphere drives a single-hemisphere Hadley cell that carries heat to the poles efficiently (shallow equator-to-pole gradient, as on Venus). Fast rotation produces Coriolis-deflected jets — Rossby-regime banding — that block pole-ward transport (steep gradient, as on Jupiter). The parameterisation is:

S = f(rotation_period, surface_pressure, insolation) (8)

where the functional form captures the transition from tidally locked superrotators (S ≫ 1) through Earth-like co-rotation (S ≈ 1) to fast rotators with strong zonal banding (S ≈ 1 but banding index high). Venus's ~60× superrotation and Jupiter's banding (used as a normalisation reference) serve as the secondary calibration anchors.

3.8.2 Heat-Transport Efficiency and Latitudinal Profile

The heat-transport efficiency E (0 to 1) quantifies how well the atmosphere redistributes heat from equator to pole. E = 1 would mean perfect redistribution (isothermal surface); E = 0 would mean no transport at all (each latitude band radiatively independent). The tool computes E from the superrotation factor, banding index, and atmospheric thickness.

The equator-to-pole temperature gradient is then:

ΔT_eq-pole = ΔT_Earth · f(E) (9)

where ΔT_Earth ≈ 45 K is Earth's observed equator-to-pole difference, and f(E) is a function anchored so that Earth's heat-transport efficiency (E ≈ 0.572 under the co-rotating model) produces the observed 45 K. This is explicitly Earth-calibrated — we have no other planet for which we know both the atmospheric circulation and the surface temperature profile to comparable accuracy. The tool documents this on every output.

From the gradient and the global mean temperature, the tool computes equator temperature, pole temperature, and a three-zone breakdown (Tropical / Temperate / Polar-Ice) with latitudinal boundaries, zone-average temperatures, and surface-area fractions. Permanent ice-cap coverage is estimated from the pole temperature and the latitude at which the zonal temperature crosses 0 °C.

3.8.3 Circulation Regime

The tool classifies the atmospheric circulation into regimes based on the banding index and superrotation factor: Few-cell (Earth-like Hadley/Ferrel/Polar), Moderate banding, Strong zonal banding (Jupiter-type), or Single Hadley cell + superrotation (Venus/Titan-type). This is a qualitative classification, not a GCM output, but it gives the worldbuilder an immediate handle on what kind of weather and climate geography to expect.

4. Supplementary Panels

4.1 Additive Greenhouse / Technosignature Panel

This panel models trace greenhouse gases added on top of the baseline atmosphere — the kind of atmospheric modification a technological civilisation would produce. It is deliberately separate from the equilibrium engine: these are transient flows (timescale ~100 years), not bulk composition, and they do not feed back into the surface temperature computed by Block 6. The panel reports the committed warming — the temperature change that would occur if the atmosphere were allowed to reach radiative equilibrium at the new composition, using a linearised climate sensitivity:

ΔT = λ · ΔF (10)

where λ = 0.8 K per W/m² is the climate-sensitivity parameter (corresponding to an equilibrium climate sensitivity of approximately 3 °C per CO₂ doubling, the IPCC AR6 central estimate; Forster et al., 2021).

4.1.1 Carbon Dioxide

CO₂ radiative forcing follows the logarithmic form established by Myhre et al. (1998) and carried through to AR6 (Meinshausen et al., 2020):

ΔF_CO₂ = 5.35 · ln(C / C₀) [W/m²] (11)

where C is the total CO₂ concentration (baseline + industrial, in ppm) and C₀ is the baseline. Critically, the baseline is not a hard-wired Earth value of 278 ppm. It is derived from the world's own Block 7 composition: CO₂ percentage × 10⁴ = baseline ppm. A world with 1% atmospheric CO₂ has a baseline of 10,000 ppm, and any industrial addition sits high on the logarithmic curve where each additional ppm contributes less forcing (band saturation). This is physically correct and removes a hidden Earth assumption from the tool.

4.1.2 Nitrous Oxide

N₂O forcing follows the square-root form (Myhre et al., 1998; Etminan et al., 2016):

ΔF_N₂O = 0.12 · (√N − √N₀) [W/m²] (12)

where N is the total N₂O in ppb (baseline + industrial) and N₀ is the pre-industrial baseline in ppb. The tool provides two separate input boxes: a pre-industrial baseline in ppb (user-set, defaulting to 270 ppb for Earth), and an industrial increment in ppt. The different units are a deliberate design choice to prevent the unit-conflation errors that arose during development when both were in the same unit. The baseline serves double duty: it is both the reference for the forcing calculation and the threshold for the biosignature panel's N₂O assessment.

4.1.3 Synthetic Halocarbons and SF₆

Eight synthetic greenhouse gases are modelled: CFC-11 (CCl₃F), CFC-12 (CCl₂F₂), HFC-134a (CH₂FCF₃), HFC-23 (CHF₃), CF₄, C₂F₆, NF₃, and SF₆. At present-day concentrations, all sit in the "weak limit" — their absorption is unsaturated and forcing scales linearly with concentration:

ΔF = RE · (ppt / 1000) [W/m²] (13)

where RE is the radiative efficiency in W m⁻² ppb⁻¹ and the input is entered in ppt (to match EEA/IPCC/WMO reporting units). The radiative-efficiency values are drawn from the AR6/Hodnebrog et al. (2020) lineage:

GasFormulaRE (W m⁻² ppb⁻¹)Technosignature threshold (ppt)
CFC-11CCl₃F0.259100
CFC-12CCl₂F₂0.320100
HFC-134aCH₂FCF₃0.1671000
HFC-23CHF₃0.191100
CF₄CF₄0.099100
C₂F₆C₂F₆0.261100
NF₃NF₃0.20100
SF₆SF₆0.56710

These compounds have no known abiotic source, as far as we know they should not occur naturally on any planet. Any detectable quantity in an exoplanetary atmosphere is therefore a candidate technosignature: evidence of industrial chemistry. The tool flags each gas above its threshold as a technosignature detection.

4.1.4 Caveats and Limitations

The committed-warming estimate is calibrated to an Earth-like atmosphere. On very water-rich or very thick atmospheres, the actual effect would be lower because water vapour already absorbs in overlapping infrared bands. Around very cool or red stars, the spectral distribution of outgoing radiation shifts, and the figure becomes approximate. The non-linear forcing forms (logarithmic for CO₂, square-root for N₂O) correctly capture band saturation — a given increment of gas produces less forcing on an already-rich atmosphere — but the linearised ΔT = λ·ΔF response does not capture second-order feedbacks. All of these caveats are displayed on the tool's output alongside the numbers.

4.2 Biosignatures Panel

The biosignatures panel assesses the atmospheric composition for indicators of biological activity. Its central design principle — drawn from the astrobiology literature — is that biosignatures are judged on disequilibrium and combination, not bare presence. A single gas, by itself, is rarely diagnostic; it is the co-existence of gases that should not coexist abiotically that constitutes evidence.

The gold-standard example is O₂ + CH₄. Free oxygen is a powerful oxidant; methane is a reducing agent. In the absence of a continuous replenishment source, they react away within geological timescales. On Earth, both are maintained by biology — photosynthesis produces O₂, methanogenesis and other microbial processes produce CH₄. Their simultaneous presence at detectable levels is therefore strong evidence of a biosphere. This is not a new observation; it was articulated by Lovelock (1965) and has been central to the astrobiology remote-sensing programme since. The tool implements it by flagging O₂ > 1% and CH₄ > ~0.1 ppm simultaneously as a "strong biosignature — redox disequilibrium."

Other indicators assessed, in order of decreasing diagnostic strength:

DMS (dimethyl sulphide, (CH₃)₂S): No identified abiotic source. On Earth, produced almost exclusively by marine phytoplankton. Flagged as a strong biosignature. Note: DMSO (the oxidation product of DMS) is sometimes discussed interchangeably with DMS in the literature, but for remote atmospheric detection, DMS is the volatile species of interest and DMSO the weaker, less-volatile cousin. The tool includes DMS only.

PH₃ (phosphine): Biosignature on rocky worlds (no known abiotic rocky-planet production mechanism). On gas giants, PH₃ is produced abiotically by deep atmospheric chemistry (as on Jupiter), so the flag is conditional on planet type.

O₃ (ozone): Implies O₂ via UV photolysis. More easily detected at a distance (strong UV signature) than O₂ itself. Flagged as a biosignature with appropriate caveats.

N₂O (nitrous oxide) above the natural baseline: Biology is the dominant terrestrial source of N₂O, and UV photolysis destroys it efficiently, so a standing atmospheric level implies continuous production. Flagged as a possible biosignature. Note: N₂O is also a combustion product, so industrial N₂O (entered separately in the additive panel) could be either biological or technological in origin — the tool flags industrial N₂O as a technosignature only above a separate threshold.

H₂S + SO₂ together: Possible chemosynthetic biosignature, but also a volcanic signature. Flagged as ambiguous.

CH₄ alone: Not flagged as a biosignature. Abiotic methane sources are large and well-documented (serpentinisation, cometary delivery, outgassing; Titan is saturated with abiotic methane). Without an accompanying oxidant like O₂, methane carries no diagnostic weight.

Ammonia: Deliberately excluded. While occasionally discussed at astrobiology conferences as a potential biosignature in exotic contexts, the case for ammonia as a solvent at temperatures consistent with life has not been made convincingly. Its inclusion would have weakened the panel's diagnostic credibility.

5. Why Solar-System Planets Are Used as Calibration Anchors

A purely first-principles climate model would, in principle, compute surface temperature from the radiative-transfer equations alone, requiring no reference to observed planetary climates. In practice, such models (GCMs) require hundreds of parameterisations for cloud microphysics, convection, turbulent mixing, ocean heat transport, and land-surface interactions — each of which introduces tuneable parameters that are themselves calibrated to observations. The Planet Builder, as a one-dimensional tool running in a browser, cannot carry a GCM's parameterisation apparatus. Instead, it uses a smaller set of documented Earth-calibrated parameterisations that are transparent and auditable.

Earth serves as the primary calibration anchor because it is the only planet for which we have:

(a) Precise ground-truth surface temperature from a dense meteorological network (14.0–15.0 °C depending on dataset and period).

(b) Satellite-measured Bond albedo (CERES: ~0.29–0.30).

(c) Detailed atmospheric composition with sub-ppm precision.

(d) Measured equator-to-pole temperature gradient (~45 K).

(e) Understood atmospheric circulation (three-cell: Hadley, Ferrel, Polar).

No other planet offers all five. Venus provides points (b) and (c) and a coarse surface temperature (from Venera landers and Pioneer Venus), plus the dramatic example of superrotation, but its circulation is less precisely characterised. Mars provides surface temperature and composition but has an atmosphere too thin to calibrate the pressure-dependent greenhouse model. Jupiter and Saturn provide circulation-regime examples (banding) but no solid surface temperature.

The specific calibrations drawn from each body are:

AnchorWhat it calibratesWhy it is needed
Earth (14.7 °C)Greenhouse ΔT, water-vapour feedback, albedo, latent heat, ice-albedo, equator-pole gradientOnly planet with ground-truth for all five quantities above
Venus (superrotation ~60×)Superrotation factor for slow rotatorsDemonstrates that slow-rotating thick-atmosphere worlds redistribute heat efficiently
Jupiter (banding)Normalisation of banding indexExtreme fast-rotator: banded jets block meridional transport
Earth (~45 K ΔT_eq-pole)Latitudinal temperature profileOnly body where we know the surface gradient and the circulation to comparable accuracy

The tool is transparent about this dependency: the Block 8 output explicitly states that the latitudinal profile is "Earth-calibrated, not first-principles," and explains in plain language what that means for interpretation. A future Exoworld phase may replace some of these parameterisations with physics-based alternatives (particularly the greenhouse model, where a radiating-level + adiabatic-depth formulation following Taylor, 2018, is planned), but the Earth anchor will remain as the primary validation target.

6. Assumptions, Limitations, and Scope Boundaries

The following are acknowledged simplifications, documented here and in the tool itself:

One-dimensional, steady-state. The tool computes a single global-mean surface temperature and overlays a latitude profile on it. It does not resolve longitude, seasons, diurnal cycles, ocean currents, weather, or transient phenomena. A tidally locked world's permanent day/night asymmetry is not captured beyond its effect on the globally averaged energy budget.

No seasonal channel. Axial tilt is recorded but does not yet modulate the temperature profile. A high-obliquity world experiences extreme seasons that can dominate the habitability picture; the tool does not model these. This is the single largest missing physics feature and is earmarked for the Exoworld phase.

Earth-calibrated greenhouse. The greenhouse model is tuned to reproduce Earth's ~33 K warming from the observed composition. It is most reliable for atmospheres broadly similar to Earth's in pressure and composition; for very thick CO₂ atmospheres (Venus-like) or very thin ones (Mars-like), it is approximate. A structural upgrade to a radiating-level model is planned.

Linearised climate sensitivity for industrial gases. The additive panel uses ΔT = λ·ΔF with fixed λ = 0.8. This is accurate to first order but does not capture state-dependent feedbacks (λ increases at higher temperatures, for instance). For the ~1–5 K warming range of typical industrial perturbations, this is a reasonable approximation.

No ocean heat transport. Ocean currents redistribute significant heat on Earth (Gulf Stream, thermohaline circulation). The tool's heat-transport efficiency captures atmospheric transport only. For ocean-covered worlds, the actual equator-to-pole gradient would be smaller than the tool predicts.

Cloud model is parameterised, not microphysical. The user sets cloud fraction; the tool computes the radiative effect. It does not model cloud formation, convection, or the cloud-feedback response to warming. On Earth, cloud feedback is the largest source of uncertainty in climate sensitivity (Forster et al., 2021); the tool sidesteps this by using a fixed cloud model.

Radiative-efficiency values for synthetic gases. The RE values for CFC-11 (0.259) and CF₄ (0.099) should be verified against the full Table 4 of Hodnebrog et al. (2020) if watertight precision is required. The remaining values (particularly SF₆ at 0.567) are well-established.

7. Validation Against Known Planets

The primary validation target is Earth. With the following inputs — radius 6371 km, density 5.514 g/cm³, rotation 23h 56m 4s, orbital distance 1.0 AU, eccentricity 0.0167, atmospheric mass fraction 0.000088104%, composition 78.08% N₂, 20.95% O₂, 0.04% CO₂, 0.93% Ar, cloud coverage 67%, ocean coverage 71%, stellar luminosity 1.0 L☉, stellar T_eff 5778 K — the tool produces:

OutputToolObserved
Surface gravity9.82 m/s²9.81 m/s²
Surface pressure1.013 bar1.013 bar
Bond albedo~0.290.29–0.30 (CERES)
Equilibrium temperature256 K~255 K
Surface temperature287.8 K (14.7 °C)~288 K (14–15 °C)
Scale height8.4 km~8.5 km
Equator-pole ΔT45 K~45 K (by calibration)
Habitable-zone positionWithin HZYes (by definition)

For the additive panel, hand-calculated validation cases include: CO₂ +50 ppm on a 400 ppm baseline → +0.50 K (hand-calc: 5.35 × ln(450/400) × 0.8 = 0.504 K); N₂O +68 ppb industrial on 270 ppb baseline → +0.19 K (hand-calc: 0.12 × (√338 − √270) × 0.8 = 0.187 K); SF₆ 1000 ppt → +0.45 K (hand-calc: 0.567 × 1.0 × 0.8 = 0.454 K). All within rounding of the analytical values.

8. Future Development (Exoworld Phase)

The following enhancements are catalogued for the Exoworld phase, a planned upgrade intended to bring the tool closer to research-grade accuracy where the physics justifies it:

Greenhouse recalibration using a radiating-level + adiabatic-depth structural model. Seasonal/obliquity channel so axial tilt affects the temperature profile. Ocean heat-transport parameterisation. Verification of all synthetic-gas RE values against Hodnebrog et al. (2020) Table 4. Blocks 9–16 of the specification: ice and volatile chemistry (Krasnopolsky photochemistry), magnetic field and atmospheric escape (Persson et al., 2020), stellar evolution, interior structure detail, spaceflight viability. Live GGSC star catalogue integration. Deployment to the Valen–Homecoming website with server-hosted media assets.

References

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