## Problem Set 9 ASTR 502 Fall 2015

Due: November 23 (in class). Points: 8

1. (2 pts) Solar Energy The most recent measured value for the solar constant at the top of the atmosphere is now 1361 W/m2. Given that 1 AU = 1.496 E8 km, what is the total energy output of the Sun, in Watts, to four decimal places? (watch units!)

2. (2 pts) Energy balance

The energy absorbed by the Earth is given by Ein = (1-a) * (1361 W/m2 ) * (π) * (RE )2
Where a is the albedo of the Earth, the fraction reflected back into space by clouds and snow, and 1 RE = radius of the Earth = 6378 km.

The energy which is emitted by Earth, assuming it is a black body with no Greenhouse effect, is

Eout = σ * 4π (RE )2 * T4

Where T is the temperature in deg Kelvin and σ = 5.67 E-8 W/(m**2 x K**4)
(Because of the ocean and atmosphere, it reradiates over the entire surface area 4π r2 ).
OK, so given a = 0.3, what would be the equilibrium temperature of the Earth, in K? __________
(Set the energy in = energy out and solve for T)

What does that turn out to be in °F? __________

3. (2 pts) Greenhouse!

The energy which is emitted by Earth, assuming it is a black body but with a Greenhouse effect, can be expressed as

Eout = σ * (1-g) * 4π (RE )2 * T4

Where g is the fraction of the infrared light from Earth that is absorbed by clouds, water, and other greenhouse gasses and radiated back to Earth, allowing less to escape.
If we put in g = 0.45, what would be the equilibrium temperature of the Earth, in K? __________

What does that turn out to be in °F? __________

4. (2 pts) Ice Ages!

Now, use in the input function, a much higher Earth albedo, such as we might have in an ice age. Use a = .8 in the equation Ein = (1-a) * (1361 W/m2 ) * (π) * (RE )2

and keep g = 0.45, what would be the equilibrium temperature of the Earth, in K? __________

What does that turn out to be in °F? __________

last update 11/15/2015