To estimate the temperature of a planet based on its reflectivity (albedo) and distance from the Sun, we can use the following formula derived from the blackbody equilibrium temperature model:

$T = \left( \frac{(1 - A) \cdot L_{\odot}}{16 \pi \sigma d^2} \right)^{\frac{1}{4}}$

Where:

• $T$ is the equilibrium temperature of the planet.
• $A$ is the albedo (reflectivity).
• $L_{\odot}$ is the luminosity of the Sun, approximately $3.846 \times 10^{26} \, \text{W}$.
• $\sigma$ is the Stefan-Boltzmann constant, $5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4$.
• $d$ is the distance from the Sun (1 AU = $1.496 \times 10^{11} \, \text{m}$).

Given:

• Reflectivity $A = 93.9\% = 0.939$
• Distance $d = 1 \, \text{AU} = 1.496 \times 10^{11} \, \text{m}$

We can substitute the values into the formula and calculate the equilibrium temperature $T$.

First, let's break down the problem and perform the calculation.

$T = \left( \frac{(1 - 0.939) \cdot 3.846 \times 10^{26}}{16 \pi \cdot 5.67 \times 10^{-8} \cdot (1.496 \times 10^{11})^2} \right)^{\frac{1}{4}}$

I will calculate the final temperature now.The equilibrium temperature of a planet with a reflectivity of 93.9% at a distance of 1 AU from the Sun is approximately 138.49 K (Kelvin).

Would you like further details on the calculation or have any additional questions?

Here are 5 related questions to deepen your understanding:

1. How does a planet's distance from the Sun affect its temperature?
2. What is the significance of a planet's albedo in determining its temperature?
3. How does the Stefan-Boltzmann law relate to planetary temperatures?
4. How would the temperature change if the albedo were lower (e.g., 50%)?
5. How do atmospheric effects like greenhouse gases alter a planet's equilibrium temperature?

Tip: A high albedo (reflectivity) means a planet reflects more sunlight, leading to a lower equilibrium temperature!