JA,
The sky magnitude is an "estimate"
http://www.nightwise.org/magnitudes.htm
http://memebers.ziggo.nl/jhm.vangast...ictionTool.htm
SB0 = 22 - 5Log(10
(1.7-LM/5)-1) as suggested by Jan van Gastel, based on the initial formula by Nils Olof
This doesn't cover the calculations for sky noise.....
We need to use a luminance in electrons(photons)/cm^2/s/Angstrom/arcsec
The Planck Black body and Wein temperature formula seem to be used to determine a spectral flux (photons/cm^2/s/A) based on an (agreed?) stellar magnitude and spectral type.
See also:
https://www.researchgate.net/publica..._the_Night_Sky
Ken