Stefan-Boltzmann law question (astronomy)

[lk31]

Homework Statement

in about 6X10^7 y from now, the sun will be a red giant star with a temperature 1/2 its present value and a radius 100 times larger.
a) what will be the luminosity of the red giant sun be compared to its current value?
b) assume that the new luminosity gives you the change in energy absorbed by the earth, and that the Earth is a black body. how much hotter or cooler will the Earth be?
c) if the temperature of the Earth is 300K now, what will be its termperature when the sun is a red giant star?

Homework Equations

E= (5.67x10^-8)(T^4)= Luminosity/(4*pi*r^2)

The Attempt at a Solution

i figured out part a, but then for question b, i don't really understand what they mean by the new luminosity is the change in energy? how can it be the CHANGE? do they mean the delta of the luminosities?
anyhow, any help/explanation would be greatly appreciated!

 

[zhermes]

Some of the sun's light is absorbed by the earth. The luminosity of the sun (in addition to other factors) determines how much light. They are just asking how much the temperature of Earth will change from the given change in luminosity---you'll have to make a few assumptions.

Does that help?

 

[lk31]

thank you for your reply, much appreciated.

The only way I can see how this question would work is if I assume that the energy absorbed by the Earth is equal to the energy emitted by the sun.
Then I can use the sun's initial luminosity and the red giant luminosity, plug the values into the equation E= Luminosity/(4*pi*r^2) to get two separate energy values. Then I can plug the two energy values into the equation E= (5.67x10^-8)(T^4) to obtain two temperature values for the Earth (again making an assumption that the amount of energy absorbed by Earth = amount of energy emitted by earth). but then it means that the amount of energy emitted by the sun is equal to the amount of energy emitted by the earth, which does not make sense to me, so is my initial assumption incorrect? i.e. that the energy emitted by the sun = energy absorbed by the earth?

any help is appreciated, thank you.

 

[zhermes]

You're on the right track Ik31. Just keep in mind that the luminosity of the sun is emitted in all directions, while the Earth only occupies a small portion of the sky (from the Sun's perspective).

 

[lk31]

okay thank you, i really appreciate all of your help!