Planetary Energy Balance: Albedo & Equilibrium Temperature Calculator

simulator beginner ~8 min
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T_surf = 288 K (15°C) — Earth's actual mean temperature

Earth at 1 AU with albedo 0.3 has equilibrium temperature 255 K (-18°C). Adding 33 K of greenhouse warming gives the observed mean surface temperature of 288 K (15°C) — the greenhouse effect makes Earth habitable.

Formula

T_eq = [L_star × (1 - A) / (16 × π × σ × d²)]^(1/4)
S = L_star / (4 × π × d²)
T_surface = T_eq + ΔT_greenhouse

Energy In, Energy Out

A planet's temperature is set by a simple energy balance — it absorbs a fraction (1-A) of incoming stellar radiation and re-emits thermal infrared radiation to space. When absorption equals emission, the planet reaches equilibrium temperature T_eq = [L(1-A)/(16 pi sigma d²)]^(1/4). This elegant equation contains all the essential physics: stellar luminosity L, orbital distance d, albedo A, and the Stefan-Boltzmann constant sigma.

The Role of Albedo

Albedo determines what fraction of sunlight a planet reflects back to space unused. Fresh snow reflects 80-90% of sunlight; ocean water absorbs 94%. A planet covered in ice would reflect so much light that it cools further, making more ice — a positive feedback loop called the ice-albedo feedback that may have caused Snowball Earth episodes 700 million years ago. Cloud albedo is Earth's largest uncertainty in climate modeling.

Greenhouse Warming

Earth's atmosphere is transparent to visible sunlight but partially opaque to outgoing infrared radiation. Greenhouse gases (CO₂, H₂O, CH₄) absorb and re-emit thermal photons, effectively insulating the surface. This natural greenhouse effect adds 33 K to Earth's temperature, making it habitable. Venus demonstrates the extreme: its 90-atmosphere CO₂ blanket adds over 500 K, creating surface temperatures hot enough to melt lead.

Habitable Zone Science

The habitable zone is defined as the orbital distance range where a planet with reasonable atmospheric conditions could support liquid surface water. Too close, and water vapor triggers a runaway greenhouse. Too far, and CO₂ condenses, collapsing the greenhouse. This concept guides the search for Earth-like exoplanets with missions like Kepler, TESS, and the James Webb Space Telescope.

FAQ

What is planetary equilibrium temperature?

Equilibrium temperature is the surface temperature a planet would have if it absorbed solar radiation and re-emitted it as a perfect blackbody with no atmosphere. For Earth, T_eq = 255 K (-18°C). The actual surface temperature of 288 K is 33 K warmer due to the greenhouse effect of CO₂, H₂O, and other gases.

What is Bond albedo?

Bond albedo is the fraction of total incoming solar radiation reflected by a planet in all directions. Earth's Bond albedo is ~0.30 (30% reflected by clouds, ice, and surfaces). Venus has the highest albedo (0.75) due to thick sulfuric acid clouds, while the Moon has one of the lowest (0.12).

Why is Venus hotter than Mercury?

Despite being farther from the Sun, Venus has a massive CO₂ atmosphere producing ~510 K of greenhouse warming. Mercury has virtually no atmosphere, so its dayside temperature (700 K) comes solely from proximity to the Sun, while its nightside drops to 100 K. Venus's uniform 735 K surface exceeds Mercury's average.

What defines the habitable zone?

The habitable zone is the range of orbital distances where a planet with an Earth-like atmosphere could maintain liquid surface water (273-373 K). For the Sun, this extends roughly from 0.95 to 1.67 AU. The exact boundaries depend on atmospheric composition, with strong greenhouse gases extending the outer edge.

Sources

Embed

<iframe src="https://homo-deus.com/lab/planetary-science/albedo-temperature/embed" width="100%" height="400" frameborder="0"></iframe>
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