To calculate the equilibrium temperature of a planet, we assume that the planet is a perfect blackbody (absorbing and re-radiating energy) with some reflectivity, also known as albedo.

Given:

• Reflectivity (albedo) = $A = 0.984$ (98.4%)
• Distance from the Sun = $d = 1 \, AU$
• Solar constant at 1 AU = $S = 1361 \, \text{W/m}^2$

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Step-by-Step Calculation:

The formula for the equilibrium temperature $T$ of a planet is:
$T = \left( \frac{(1 - A) \cdot S}{4 \cdot \sigma} \right)^{1/4}$ where:

• $A$ is the albedo (reflectivity)
• $S$ is the solar constant (energy flux from the Sun at the planet's orbit)
• $\sigma = 5.67 \times 10^{-8} \, \text{W/m}^2 \cdot \text{K}^4$ is the Stefan-Boltzmann constant

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Substituting Values:

1. $(1 - A) = 1 - 0.984 = 0.016$
2. Solar energy absorbed = $0.016 \times 1361 = 21.78 \, \text{W/m}^2$
3. Now, divide by 4:
   $\frac{21.78}{4} = 5.445 \, \text{W/m}^2$
4. Applying the Stefan-Boltzmann constant:
   $T = \left( \frac{5.445}{5.67 \times 10^{-8}} \right)^{1/4}$ $T = \left( 9.6 \times 10^7 \right)^{1/4}$
5. Taking the fourth root:
   $T \approx 253.2 \, \text{K}$

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Final Answer:

The equilibrium temperature of the planet is approximately 253 K (or -20°C).

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Do you need more details or have any questions?

Here are five related questions:

1. How does albedo affect the temperature of a planet?
2. What is the significance of the Stefan-Boltzmann constant?
3. How does distance from the Sun influence planetary temperature?
4. How would greenhouse gases change the result of this calculation?
5. What would the temperature be if the planet’s albedo were 0%?

Tip: A planet with a high albedo reflects most incoming radiation, which can significantly reduce its surface temperature!