Effect of Earth-Sun Distance Variance on Effective Temperature

[il27]

Homework Statement

The distance between the Sun and the Earth varies during the year: it is a minimum in January, and about 3.3% larger at its maximum in July. What is the corresponding change in the Earth's effective temperature?

Homework Equations

Energy absorbed: $$ E_{abs} = \pi R^2 (1- \alpha) F_0 $$
energy emitted: $$ E_{emit} = 4 \pi R^2 \sigma (T_E)^4 $$

The Attempt at a Solution

I tried finding the effective temperature equation:

The effective temperature equation:

$$ T_E^4 = \frac{(1 - \alpha) F_0}{4 \sigma} $$

but I am stuck on how to account for the changing distances between the sun and the earth.
Please help, thank you!

 

[phyzguy]

F0, the flux of solar radiation at the Earth, is dependent on the distance between the Earth and the Sun. Do you know how much F0 changes if the Earth-Sun distance doubles, for example?

 

[il27]

F0, the flux of solar radiation at the Earth, is dependent on the distance between the Earth and the Sun. Do you know how much F0 changes if the Earth-Sun distance doubles, for example?

Oh okay. the solar constant would decrease right?
what is the equation to find the solar contsant where it relies on the distance between the sun and the earth?

 

[il27]

help

 

[il27]

i think i understand the equation. i use the effective temperature equation but find two different solar constant values.
however, what does it mean when it is a minimum in January, and about 3.3% larger at its maximum in July?
is the minimum the distance between the sun and the earth? while 3.3% larger than that is 3.3% added to the distance?

 

[phyzguy]

i think i understand the equation. i use the effective temperature equation but find two different solar constant values.
however, what does it mean when it is a minimum in January, and about 3.3% larger at its maximum in July?
is the minimum the distance between the sun and the earth? while 3.3% larger than that is 3.3% added to the distance?

Yes. Whatever the distance is in January, it is 3.3% larger in July. When the distance increases by 3.3%, how much does the solar flux decrease?