Selected Questions-Answers From All Experts Astronomy Forum (Solar Constant Calculation)

Question: Hello. I am interested in learning how one can obtain the solar constant without a lot of advanced (e.g. calculus)  math. Can you help?

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