6. Given the Earth's albedo of A = 0.3, what surface temperature do you predict at...

6. Given the Earth's albedo of A = 0.3, what surface temperature do you predict at equilibrium? Is this consistent with the Earth's actual average temperature of 14C? How do you explain the discrepancy?

Solutions

Expert Solution

The formula relates the temperature of a planet to albedo and luminosity of the star.

where = Stefan Boltzmann constant

T = Temmperature of the planet

a = albedo

d = diameter of star

= Luminosity of the star

We can further simplify the formula to

You should input the luminosity in watts, the distance to the star in meters and the Stefan-Boltzmann constant as

σ=5.670373×10−8Wm−2K−4.

The albedo is dimensionless. The resulting temperature will be in Kelvins. Let me make an example for Earth:

d=149,000,000,000m

L=3.846×10^26W

Albedo of Earth is 0.3. You will get

$T ^ {4} = \frac{ 3.846�10^{26}(1 - 0.3)}{16 \pi * (149,000,000,000) ^ {2} * (5.670373*10^{-8})}=4,315,325,985 K^{4}.$

After powering this number to 1/4, we obtain temperature 256 K, which is -17° C. This looks reasonable. The real average temperature on Earth is closer to 15° C, but the greenhouse effect is responsible for the difference.

genius_generous answered 1 year ago

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