Question about intensity and area

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SUMMARY

The discussion centers on the relationship between intensity, power, and area in the context of solar energy received by Earth. It clarifies that while the hemisphere facing the Sun receives energy, the area considered for calculations is the circular projection of that hemisphere, represented by the formula πR², where R is the radius. The equation "intensity = Power/Area" holds true only when the area is perpendicular to the radiation direction, which is crucial for accurate energy calculations.

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  • Understanding of basic physics concepts such as intensity and power.
  • Familiarity with geometric principles, specifically the area of circles and spheres.
  • Knowledge of solar radiation and its interaction with planetary bodies.
  • Basic mathematical skills for applying formulas involving π and radius.
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  • Study the concept of solar intensity and its calculation methods.
  • Explore the geometry of spheres and their projections in physics.
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Hi everyone. Firstly, I know that intensity= Power/Area. But this question made me my mind confused.


The question shows the sun shining upon the Earth and the soln is:

Only the hemisphere facing the Sun receives energy at any moment.
power received by Earth
= intensity × area of Earth facing the Sun

And it shows the area of the Earth facing the sun is projected to a circle (pi R square, where R is the radius of the circle)! But shouldn't the area be the half the area of a Earth (sphere)?

Anyone can help me? I am really confused. Thanks.
 
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Yes, the area is a hemisphere but, when viewed from the Sun's perspective, it looks like a circle with the poles at the top and bottom, and the Equator across the middle.
 
Another way to think of it is that, strictly speaking, your equation "intensity= Power/Area" is ONLY correct if the area is perpendicular to the direction of the radiation.
 

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