Planetary Equilibrium Temperature Calculator

Planetary Equilibrium Temperature Equation:

\[ T = \left( \frac{(1 - A) F}{4 \sigma \epsilon} \right)^{1/4} \]

Equilibrium Temperature (T):

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1. What is the Planetary Equilibrium Temperature?

The planetary equilibrium temperature is the theoretical temperature of a planet's surface assuming it is a black body being heated only by its parent star. This simplified model provides a first-order estimate of a planet's temperature without considering atmospheric effects.

2. How Does the Calculator Work?

The calculator uses the planetary equilibrium temperature equation:

\[ T = \left( \frac{(1 - A) F}{4 \sigma \epsilon} \right)^{1/4} \]

Where:

\( T \) — Equilibrium temperature (K)
\( A \) — Albedo (reflectivity, 0-1)
\( F \) — Incident solar flux (W/m²)
\( \sigma \) — Stefan-Boltzmann constant (5.670374419×10⁻⁸ W/m²K⁴)
\( \epsilon \) — Emissivity (0-1, 1 for black body)

Explanation: The equation balances incoming stellar radiation (modified by albedo) with outgoing thermal radiation (modified by emissivity).

3. Importance of Equilibrium Temperature

Details: The equilibrium temperature provides a baseline for understanding planetary climates and is used in exoplanet studies to estimate potential habitability.

4. Using the Calculator

Tips: Enter albedo as a decimal between 0 (perfect absorber) and 1 (perfect reflector). Solar flux is the stellar energy received per unit area. Emissivity is typically near 1 for most planetary surfaces.

5. Frequently Asked Questions (FAQ)

Q1: How does this differ from actual surface temperature?
A: Actual temperatures may differ due to atmospheric greenhouse effects, internal heat, and other factors not accounted for in this simple model.

Q2: What are typical albedo values?
A: Earth's albedo is ~0.3, Venus ~0.75, Moon ~0.12. Ice planets have higher albedos while dark surfaces have lower values.

Q3: How to calculate solar flux for a planet?
A: Solar flux can be calculated as \( L_{\star} / (4 \pi d^2) \), where \( L_{\star} \) is stellar luminosity and \( d \) is orbital distance.

Q4: Why is emissivity usually set to 1?
A: Most planetary surfaces approximate black bodies in the infrared, where thermal radiation occurs.

Q5: Can this be used for moons?
A: Yes, but you must account for both stellar and planetary (primary) radiation sources.