# The Solar Constant & Inverse Square Law in Weather

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• 0:00 Constant Energy
• 1:58 Inverse Square Law
• 2:54 Inside the Atmosphere
• 4:01 Lesson Summary

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Lesson Transcript
Instructor: Meredith Mikell
In this lesson, we will explore the solar constant and the inverse square law as they pertain to how much energy is absorbed by Earth's atmosphere and how it affects weather and climate. You can test yourself at the end with a brief quiz.

## Constant Energy

The Sun is constantly radiating energy. It has some cycles involving sunspots, flares, and other disturbances, which cause some minor fluctuations in radiation, but in general, the output of energy stays about the same. If it changed significantly, life on Earth would not be possible!

We live on a fairly comfortable planet. The Sun provides all of the energy that powers life on Earth's surface, and life, as we know it, is only possible because of Earth's distance from the Sun. If Earth was any closer, it would be way too hot for life to thrive. If it were farther from the Sun, it would be way too cold. Like in Goldilocks and the Three Bears, Earth's distance from the Sun is 'just right.' Our distance from the Sun isn't the only factor; the amount of energy Earth is receiving from the Sun also influences our weather and climate.

So, how exactly do we measure the amount of energy Earth receives from the Sun? Let's say you want to get a deep, brown tan and go to a tanning booth to do so. How tan you can get depends upon how close you are to the UV bulbs in the bed, the number of bulbs (or area) over you, and how much time you spend under them. Intuitively, this makes sense: the closer you are to the source of energy, the larger its area, and the longer you spend there, the more radiation you will absorb.

Distance, area, and time are important variables in understanding how much energy Earth receives from the Sun. All three variables are factored into the solar constant, a value that describes how much solar energy hits Earth's atmosphere. More specifically, this energy is defined as irradiance, the total amount of solar energy from the Sun per unit time per unit area at Earth's distance from the Sun measured outside of Earth's atmosphere. This number turns out to be about 1.366 kilowatts per square meter.

## Inverse Square Law

The solar constant makes sense when we want to know how much radiation the Earth receives. But what if you were on the Moon? Or Mars? A different distance away from the Sun? The solar constant formula would change since the distance has changed. Calculating how much of the Sun's radiation you would feel at different distances depends upon the inverse square law, which shows us that solar irradiance is inversely proportional to the square of the distance away from the Sun.

Think of a flashlight turned on in a dark room and the cone shape that the light makes. The farther away from the light source, the more the light spreads outward and decreases intensity, illustrating that inverse relationship between radiation intensity and distance. Because the Sun is spherical, the irradiance spreads out evenly in all directions. The farther away you are from the Sun, the less radiation you receive.

## Inside the Atmosphere

We now know how solar energy can be a constant when measured outside of Earth's atmosphere, but what happens to that energy inside the atmosphere? Weather and climate patterns are greatly influenced by the amount of radiation that makes it through the atmosphere and down to the surface. Because of the speed of the Earth's rotation, the thickness of the atmosphere is slightly greater at the Equator than at the poles, trapping more incoming radiation.

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