c (Bill Ferris) wrote in message ...
At best, I suspect such a conversion would get an observer in the ballpark,
perhaps to within 0.5 magnitude. Here's a table I'll throw out for commentary.
I'd be interested in hearing how well this reflects the real life experiences
of other observers:

NELM.(+/- 0.5)..===..Sky Brightness (mag./sq. arc sec.)
.......8.0............22.0
.......7.0............21.0
.......6.0............20.0
.......5.0............19.0
.......4.0............18.0

I believe that I have read somewhere that NELM scales roughly
as the 2/3 power of sky brightness, not directly proportional.
In other words, every extra 3 mag of sky brightness decreases
the NELM roughly 2 mag. Sorry I cannot cite the source.
Certainly, playing around with the program the Schaefer
published in S+T some while back indicates that NELM varies
much more slowly than sky brightness.

That accords with my own intuition, which is that light pollution
hurts the visibility of diffuse sources much more than it hurts
the visibility of stars. Also, I can see mag 4.0 stars fairly
easily in Manhattan, and the sky there sure *seems* more than
16 times as bright as a dark sky where I can see mag 7.0 stars.
But that is pure hunch, of course.

I would also expect NELM to vary more slowly than sky brightness
on theoretical grounds, for two reasons. First, stars to the
naked eye are effectively point sources, with (theoretically)
infinite contrast against the background. In practice, of
course, defects in your eye blur that theoretical point source.

Second, even for diffuse sources, the surface brightness of an
object at the edge of visibility must vary more slowly than
the sky brightness. That is because invisibility has two
components, one due to lack of contrast against the background
and one due to sheer faintness. As you can easily determine
by experiment inside a house at night with shades drawn, there
is some threshold surface brightness below which a light
source becomes completely invisible even against a perfectly
dark background -- a situation in which the contrast is,
again, theoretically infinite. Put another way, there are
some astronomical objects that the human eye simply can't see,
not even if you were in outer space, not even if there were no
zodiacal light.

- Tony Flanders