The Sun's radiation (sunlight) is closely approximated as blackbody radiation. Accordingly, the intensity or flux of solar radiation, , which is a measure of how much power is being radiated from the Sun's surface per unit area, can be expressed in terms of the temperature, , of the sun using the Stefan-Boltzmann law:
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where is the Stefan-Boltzmann constant.
The luminosity of the Sun is a measure of how much energy the Sun produces per unit time. It is obtained by multiplying the solar intensity by the Sun's surface area:
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where represents the radius of the Sun. To determine the flux passing through any other point in space where the Sun is visible, is replaced by , which is the distance from the center of the Sun to the point in question. So, the formula now becomes:
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In this formula, the flux is proportional to the inverse square of the distance. This means that if an object's distance from the Sun doubles, the amount of sunlight hitting a given area will drop by a factor of four. This property is an example of the inverse-square law, which affects conserved quantities propagating evenly in all directions through three-dimensional space. Consecutive wavefronts of decreasing intensity can be visualized in the following interactive diagram:
As you can imagine, as the radiation moves farther from the Sun, the same amount of energy is spread out over a larger area (which is proportional to the square of the distance from the source), which makes the flux (power per unit area) correspondingly smaller.
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Example
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What is the radiant flux emitted into space by a light source with temperature of ? What is the luminosity of the solar radiation given by this surface if its radius is ?
Adjust the sliders to change the radius and temperature of the surface providing solar radiation. Click the checkboxes to see the flux and luminosity calculations.
Radius:
Temperature:
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Solution
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Using the formulas introduced in the previous section, you can determine both the flux and the luminosity produced by the specified surface.
To begin, calculate the flux:
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You can now use this result to determine the luminosity:
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Therefore, a surface with a radius of and a temperature of has a radiant intensity of and a luminosity of .
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