The sun's radiant energy is of shorter wavelengths than the earth's is because the sun has higher temperature than the earth.
As the temperature of a blackbody radiator increases, the total energy emitted increases and the peak of the radiation curve shifts to shorter wavelengths. Calculating the maximum from the Planck radiation formula shows that the product of peak wavelength and temperature is constant.
Because the Sun is hotter than the Earth, it emits radiation at shorter wavelengths, and the hot Planck curve peaks at shorter wavelengths. For this reason, the Earth's radiation is called long-wave, and the Sun's is called short-wave.
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