Page 95 - Intro to Space Sciences Spacecraft Applications

Introduction to Space Sciences and Spacecraft Applications
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E, x 4zR: = E, x 4m-Z (4-4)
where E, represents the solar-generated energy per unit area in the vicin-
ity of the earth. Of course, due to the increased surface area of the larger
sphere, the energy in the vicinity of the earth is less than that at the sur-
face of the sun. Using the value obtained for a 6,000 OK sun, we get a
value of E, = 1,631 W/m2. This is the amount of energy that would
impinge on a square meter area at a distance of 1 A.U. due to the energy
output of the sun and is an important value when considering energy pro-
duction via solar cells or for determining thermal inputs for a spacecraft.
This value (E,) is known as the solar constant. Even though recent
studies have shown that solar power output may fluctuate slightly (which
may have affected the climate on earth severely at times in the past, per-
haps contributing to the ice ages), for our purposes we shall consider it a
constant value.

Wien’s Displacement Law. In 1895, German physicist Wilhelm Wien,
discovered that the wavelength corresponding to the maximum energy
output for a blackbody at a particular temperature could be found from a
simple relationship:

For a temperature of 6,000 OK, equation 4-5 yields a maximum-energy
radiated wavelength of 0.483 pm which corresponds to the yellow-green
light frequencies close to the middle of the visible spectrum. The fact that
human vision has adapted to take advantage of the maximum portion of
the solar energy output seems like a good argument in support of the the-
ory of evolution.

Planck’s Law. In 1899, another German physicist, Max Planck, derived a
relationship that combined the findings of his predecessors and described
the distribution of blackbody radiation as a function of temperature and
wavelength: