How Is the Surface Temperature of the Earth Calculated?

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Homework Help Overview

The discussion revolves around the calculation of the Earth's surface temperature, focusing on the relationship between radiant energy flux density, the solar constant, and the Stefan-Boltzmann law. Participants are exploring the underlying physics and assumptions involved in these calculations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the appropriateness of using the Earth's surface area versus its cross-sectional area for calculations. There is also discussion about the formula involving the Stefan-Boltzmann constant and the implications of multiplying by certain factors, such as the ratio of the Sun's radius to the distance from the Earth to the Sun.

Discussion Status

The discussion is active, with participants raising questions about specific aspects of the formulas and the reasoning behind certain multiplications. Some have provided alternative perspectives on the area to consider in calculations, while others seek clarification on the relationships between variables.

Contextual Notes

There appears to be some ambiguity regarding the definitions of surface area and cross-sectional area in the context of this problem, as well as the assumptions made about energy flux and temperature relationships.

Shackleford
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This looks to be a fairly straightforward problem. I'm not sure why I'm having trouble.

The radiant energy flux density is the energy emission per unit area. Why would I not simply multiply the solar constant of the Earth times the surface area of the Earth? Of course, it would be a plane area approximation. Then, whatever that energy emission value that is, set it equal to the Stefan-Boltzmann constant*(TE)4*4pi*(RE)2?

Is the radiant energy flux density multiplied by the area equal to the power?

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110318_204153.jpg?t=1300499036
 
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The cross section of the Earth you would use is not its surface area. It will be Pi*R^2. It is the area of the shadow that the Earth would cast on a plane perpendicular to the sun's intensity vectors.
 
AlexChandler said:
The cross section of the Earth you would use is not its surface area. It will be Pi*R^2. It is the area of the shadow that the Earth would cast on a plane perpendicular to the sun's intensity vectors.

Sorry, I was ambiguous. I meant plane area approximation, not surface area.

How do you calculate the radiant energy flux density at the Earth in terms of the Sun's temperature?
 
The manual has

JE = sigmaB*(TS)4*[(RS)/(DE)]2

I'm not quite sure why they multiplied it by the tangent squared.
 
Why did they multiply it by [(RS)/(DE)]2?
 

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