(meteorobs) Setting Sun Magnitude?

[Malcolm J. Currie]

You need to compute the airmass (number of atmospheres) passed through
where the zenith is one and know the extinction coefficient.  I would
guess the last of these is about 0.2-0.25 mags per airmass.  Higher up
(for photometry the airmass is approximated by the secant of the zenith
distance.  So at 30 degrees altitude the airmass is sec 60 or 2.  Since
the atmosphere is curved this overestimates for high zenith distances.
Also refraction comes into the estimate of the true zenith distance.

The two equations for this I know are Hardie (1962) in "Astronomical
Techniques", Chapter 8 of "Stars and Stellar Systems vol II (U. of
Chicago Press) gives a formula

   airmass = sec z - 0.0018167 * Y - 0.002875 * Y**2 - 8.8033dex-4 * Y**3
             where Y = ( sec z - 1 )

However substituting for z = 89 degrees, for example Y ~ 57.3 and the
result is negative!

Young and Irvine (1967) proposed
   airmass = sec z * ( 1 - 0.0012( (sec z)**2 - 1 )

again negative.  Sensible people don't do photometry at high
zenith distances.

Does anyone know some more modern formulae or empirical measurements to
low altitudes to get a handle on the dimming?

Malcolm