What is the temperature of a planet with a reflectivity of 93.9 % at a distance of 1 AU?

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!

Find the equilibrium temperature of a planet with a reflectivity (albedo) of 93.9% located 1 AU from the Sun. This calculation uses the blackbody equilibrium temperature model and the Stefan-Boltzmann law to demonstrate how planetary albedo and solar distance influence temperature. Ideal for undergraduate physics and astronomy students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation