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Why Can We Feel The Heat Energy From The Sun?

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Well first of all, it is a good thing that Earth is where it is.  If it was any closer to the Sun, we would burn up.  And if we were any farther away, we would freeze.

Earth systems have both internal and external sources of energy, both of which create heat. The sun is the major external source of energy.

The sun emits energy as electromagnetic radiation. Unlike sound, such radiation requires no medium, therefore this energy is able to travel through the near vacuum of space from the sun to the earth.

Most radiant energy from the sun is concentrated in the visible and near-visible parts of the EM spectrum

Since the sun has a surface temperature 20 times greater than that of Earth, the reradiated energy has a spectrum that peaks at a wavelength 20 times longer than the 500 nm for the sun, or at about 10,000 nm, well into the infrared. Since the atmosphere is more absorptive to such long-wavelength terrestrial radiation, the atmosphere is heated from the ground up instead of vice versa
so in short:Via radiation. The energy travels through the vacuum of space and excites the molecules here on Earth.

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