The intensity of solar radiation reaching the top of the Earth’s atmosphere is 1 340 W/m2. The temperature of the Earth is affected by the so-called greenhouse effect of the atmosphere. That effect makes our planet’s emissivity for visible light higher than its emissivity for infrared light, for comparison, consider a spherical object with no atmosphere, at the same distance from the Sun as the Earth. Assume that its emissivity is the same for all kinds of electromagnetic waves and that its temperature is uniform over its surface. Identify the projected area over which it absorbs sunlight and the surface area over which it radiates. Compute its equilibrium temperature. Chilly, isn’t it? Your calculation applies to
(a) The average temperature of the Moon,
(b) Astronauts in mortal danger aboard the crippled Apollo 13 spacecraft, and
(c) Global catastrophe on the Earth if widespread fires should cause a layer of soot to accumulate throughout the upper atmosphere, so that most of the radiation from the Sun were absorbed there rather than at the surface below the atmosphere.
Solution:
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