How Do You Calculate Mars' Theoretical Equilibrium Temperature?

[coffeem]

[SOLVED] Solar Constant Question?

Define Solar constant and Albedo of a planet. Calculate the solar constant for Mars and hence evaluate the theoretical equilibrium surface temperature. You may ignore the greenhouse effect in your calculations.

The sun has a temperature of 5777 k and a radius of 6.96 *10^5km. The sun-mars distancy is 2.28*10^8 km. The albedo of Mars is 0.16.


MY ANSWER

Ok I know that the solar constant is the mount of energy asorbed my a planet per m^2. And also that the albedo of a planet is the amount of light energy which is absobed (not reflected) by the atmosphere.

I can work out the Solar Constant using:

S = q*(R/Des)^2*^4

S = 588.5 W/m^2

But I have not idea of what is meant by the equilibrium surface temp or how I go about working this out. Any help would be apretiated. Thanks.

 

[mgb_phys]

The solar constant is the sun's power per unit area on a planet, it is quoted as the top of atmosphere value so you don't have to take into account absorption - a planet with no atmosphere still has a solar constant !
Albedo is defined as the relative proprtion of light REFLECTED. albedo=0 is totally balck and albedo=1 is a perfect reflector.

The planet's surface reaches an equibrium temperature between the radiation incoming from the sun and re-radiating into space. So you need an equation telling you the amount of radiation given off by a surface at a certain temperature.
The incoming radiation from the sun must balance the outgoing radation if the planet is to stay at the same temperature - so you just need to work out what temperature this will occur at.

 

[kamerling]

the equilibrium surface temperature is the temperature where the surface radiates as much infrared radiation as is received from the sun. This assumes that Mars has the same temperature everywhere. (so the number is pretty meaningless for mars) You have to take into account the albodo of the planet, and the fact that the surface area of Mars (4 pi r^2) is bigger than the area that collects sunlight (pi r^2)

 

[coffeem]

The solar constant is the sun's power per unit area on a planet, it is quoted as the top of atmosphere value so you don't have to take into account absorption - a planet with no atmosphere still has a solar constant !
Albedo is defined as the relative proprtion of light REFLECTED. albedo=0 is totally balck and albedo=1 is a perfect reflector.

The planet's surface reaches an equibrium temperature between the radiation incoming from the sun and re-radiating into space. So you need an equation telling you the amount of radiation given off by a surface at a certain temperature.
The incoming radiation from the sun must balance the outgoing radation if the planet is to stay at the same temperature - so you just need to work out what temperature this will occur at.

Hi. Thanks for everyone for being so helpful. I now know what I have to calculate but I do not know how to do so. I have seached my notes and cannot find an equation which does what you say... this is probably becasue I am being stupid though. Any chance you could give me a push in the right direction?

Actually I have worked it out. Thanks for the help.

 

[mgb_phys]

for anyone searching the question: see Stefan Bolztman law