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Calculating Temperature Of A Planet

Planetary Temperature Equation:

\[ T = \left( \frac{L (1 - A)}{16 \pi \sigma D^2} \right)^{1/4} \]

W
(0-1)
W/m²K⁴
m

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1. What is the Planetary Temperature Equation?

The planetary temperature equation estimates the equilibrium temperature of a planet based on its distance from a star, the star's luminosity, the planet's albedo (reflectivity), and fundamental physical constants. This calculation assumes the planet is in radiative equilibrium with its star.

2. How Does the Calculator Work?

The calculator uses the planetary temperature equation:

\[ T = \left( \frac{L (1 - A)}{16 \pi \sigma D^2} \right)^{1/4} \]

Where:

Explanation: The equation balances the incoming stellar radiation (adjusted for albedo) with the outgoing thermal radiation from the planet.

3. Importance of Planetary Temperature Calculation

Details: Calculating a planet's equilibrium temperature helps astronomers determine potential habitability, atmospheric composition, and energy balance. It's a fundamental calculation in exoplanet studies.

4. Using the Calculator

Tips: Enter star's luminosity in watts, albedo as a value between 0 (perfect absorber) and 1 (perfect reflector), Stefan-Boltzmann constant (default value provided), and distance in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is this an equilibrium temperature?
A: This calculation assumes the planet has reached a steady state where incoming and outgoing radiation are balanced, ignoring atmospheric effects.

Q2: How does albedo affect temperature?
A: Higher albedo means more radiation is reflected, leading to lower temperatures. An albedo of 1 would mean all radiation is reflected.

Q3: What's a typical value for solar luminosity?
A: Our Sun's luminosity is approximately 3.828×10²⁶ W. For other stars, values vary widely.

Q4: Why is distance squared in the equation?
A: Radiation follows an inverse-square law, spreading out over a sphere's surface area (4πD²).

Q5: How accurate is this for real planets?
A: This gives a basic estimate. Real temperatures are affected by atmosphere, rotation, internal heat, and other factors.

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