The Sun: Advanced math isn't needed to find the solar constant, i.e. the mean intensity of solar radiation received on Earth per unit area per unit time).
Answer:
For many stars, the
solar constant S can be computed if its angular diameter is known. If the
angular radius of a star is: a =R/r ( a is measured in radians) with r the distance to Earth and R
the star’s linear radius then:
p F = S (r/R)2
If
the Sun’s angular radius is 959.63 arcsec then the solar constant S can be obtained and without the use of calculus. The method which follows shows how this is done.
We re-arrange the earlier equation to
find:
S = π F/
(r/R)2
Where we already
know the solar flux (e.g. from an astrophysical data source, e.g. Astrophysical Concepts by Harwit) is:
π F = 6.3 x
10 7 Jm-2 s-1.
Now, let a = 959.63 "
but this must be in
radians before one can use the equation.
One radian = 57.3
degrees
Change to seconds ("):
= 57.3
deg/rad x (3600"/ deg)= 206 280 "
Then:
a = (R/r) = 959.63"/ 206
280"/rad = 0.00465 rad
So: (r/R) =
1/0.00465 rad = 215 rad-1
Therefore:
S = [6.3 x
10 7 Jm-2 s-1 ]/ [215 rad-1]2
= 1360 W/m2
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