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Solar Flux Density

Fusion reactions at the core of the sun power a circulating flow of incredible energies that culminate in the emission of tremendous amounts of electromagnetic radiation. The spectrum of the sun generally follows what̵7;s known as a blackbody spectrum, which contains a certain amount of power across a spectral region stretching from ultraviolet to infrared. The form of the blackbody radiation makes it a relatively straightforward process to calculate the solar flux density that strikes Earth.

Blackbody Radiation
- Every object emits radiation with a spectral structure that depends on its temperature and other properties. For a surprising range of objects, the ̶0;other properties̶1; don̵7;t change their emission spectrum much. Those objects are called blackbodies, and the energy they put into different wavelengths changes as they heat up. You̵7;ve seen this already: the burner on an electric stove is black when it̵7;s cold and not emitting any measurable visible light. But as the burner warms up its color changes̵2;not because the surface changes colors or changes chemically or anything like that̵2;simply because it is at a higher temperature. The sun is just that sort of blackbody, but̵2;luckily for all life on Earth̵2;it only changes its temperature significantly every few billion years.
Power from a Blackbody
- There̵7;s a simple equation that describes the total power emitted by a blackbody. The equation is called the Stefan-Boltzmann law, and it is expressed mathematically as
  Total Power = Stefan-Boltzmann constant x area x temperature^4. The Stefan-Boltzmann constant is 5.67 x 10-8 W/(m^2 K^4), area is measured in square meters, and T is measured in Kelvin. The sun̵7;s surface is at about 5800 K, so the radiant flux density at the surface of the sun (the power in watts emitted from each square meter of the sun) is
  5.67 x 10^-8 x 5800^2 = 64 million watts/m^2, and the total power emitted from the sun is 3.9 x 10^26 watts ̵2; about 400 million million million million watts.
Irradiance at Earth
- Again, luckily for all life on Earth, the planet isn̵7;t too close to the sun. It̵7;s about 150 million kilometers away. The energy output from the sun spreads out in an ever-expanding sphere. At Earth̵7;s orbit, that energy is spread over the surface of a sphere with a radius of 150 million kilometers. The irradiance, also called the flux density, at the top of Earth̵7;s atmosphere, is equal to
  flux density = total power / area of sphere containing the Earth̵7;s orbit
  flux density = 3.9 x 10^26 watts / 2.8 x 10^23 m^2 = 1377 W / m^2.
On the Earth̵7;s Surface
- One more way life on Earth got lucky: The atmosphere filters out a lot of the solar radiation that makes its way out to Earth̵7;s orbit. There̵7;s no easy way to mathematically describe the way the atmosphere absorbs sunlight. Specific atoms and molecules absorb specific wavelengths, there are general absorption regions, there are certain wavelengths that are barely attenuated at all. And all that depends upon how much atmosphere the sunlight happens to be going through at a given moment, which depends on the angle between the sun and the surface of Earth at a particular time and place. An ̶0;average̶1; atmosphere is called an ̶0;air mass 1.5,̶1; or AM1.5, and it reduces the solar flux density to 1000 watts / m^2.

Astronomy