Re: [magnitude6] Earth from above (continuing ``for your amusement'')

[Jan Hollan <jhollan@amper....muni.cz>]

>   But you say a "1 kW source with a 5 degree beam would produce 1e-4 lm/m2
> (-4 mag)."  I'd expect the Lincolnshire beams to be floodlights, not
> spotlights - and even then, spotlights tend to have 15 degree openings.
>
>
>   What would you have said to the reporter?

Hi Das,

I don't know what I would do, if I'd be in a hurry. As I read the text you
sent to mag6 (its publicly available copy is
  http://amper.ped.muni.cz/jenik/letters/public/msg00146.html
  -- the follow-ups are further items with just one to be skipped),
it seems to me to be based on actual info from the ISS crew. I'd be
inclined to take it seriously.

Looking at the image of the Boston Stump tower, it's really tall.
Having 15 degree cones would be surely a maximum, to have a substantial
part of the light hit the top of the building. Such broad cones would mean
a need for far more than 1 kW. So I'd still expect something similar to
the results I gave earlier.

Now I got an idea how to arrive at more reliable results.

There is another way of estimating the luminous flux densities. The absurd
CIE recommendations for luminances are of the order of tens of cd/m2.
Let's assume the lighting people liked to achieve 50 cd/m2. Assuming the
stone albedo being 20 per cent, and a lambertian diffusion by it, the
needed illuminance would be 5*3.13*50 lux. Producing it by a beam angled
15 degrees from zenith would need a luminoux flux density still four times
larger, or about 3 klm/m2.

That's at 90 m from the ground. Going to 90 km, the value would diminish
to 3 mlm/m2, going three times farther, to 0.3 mlm/m3 or 3e-4 lm/m2,
-5 mag.

If the beam tilt would be more than 15 degrees from zenith, say whole 30
degrees, so that the beamers would be more than 40 m from the tower, and
the achieved tower luminance would be 30 cd/m2, we would get to that 1e-4
lm/m2. Or we could take the albedo as 30 per cent.

Of course, the tower can be illuminated not so strongly. The Big Ben has
just around 1 cd/m2 (I should publish my results I got when I was at the
Childhood Leukaemia conference), it's illuminated much more reasonably
than e.g. the castle in my home town, Brno, which has 20 cd/m2. But if
they write about Boston Stump as being really remarkable, I'd bet it's not
below 10 cd/m2. So my lowest guess is
  (10 cd/m2) * (3 because of albedo) * pi steradians *
  (2 for a 30 degree tilt of the beam) = some 200 lm/m2
 at the tower top. At 270 km, it's 1e-7 less, or 2e-5 lm/m2.

Now I checked the real positions of ISS with respect to Boston,
Lincolnshire. It gets up to 69 degrees over horizon. If this is the moment
when people there try to photograph the UK below, the beam tilt is not 30
degree from zenith, but rather just over 20 degrees, so the flux density
would to be 3/2 of that minimum one. But the ISS is farther than 270 km,
approaching to the minimum distance of some 370 km from Boston Stump. And
there is a minimum extinction of 20 per cent. So the minimum estimate for
ISS closest approach to the Boston Stump is just again those 2e-5 lm/m2.

This is still a lot. The upper estimate with, 20 per cent albedo and 50
cd/m2, is then 1.5e-4 lm/m2, just a bit above my old crude guess.

So my analysis given in the
  http://amper.ped.muni.cz/jenik/letters/public/msg00148.html
 seems to be no far from the reality.

Moreover, a general conclusion follows: any luminance higher than one
candela per square metre, for tall buildings with tops bathed in the
upward stream of light, results inevitably in spoiling the view of the
Earth from the universe, if the viewers come into the beam. The larger the
beam cone, the larger the cone in the space from which the view is
spoiled...

So, that's it. The story deserves to appear in the Times and elsewhere,
feel free to point to my analysis, (with this very text being available as
  http://amper.ped.muni.cz/jenik/letters/public/msg00152.html).

I'm happy to arrive at the general conclusion. This is may be just a minor
adverse aspect of bad lighting, but a catchy one.

> > Illuminating buildings further from below is strongly discouraged but not
>
>   If you consider the effect of light scattering off the atmosphere,
> it is predominantly forward scattered, so any light shining directly
> upwards tends to escape directly into space.
>   It is the low angles where light can be scattered back to Earth.
>
>   My head accepts that point, but my heart doesn't!

Yes, for the majority of us, who are seldom in planes and never in space,
the ordinary bad lights shining approx. horizontally are by far the worst
polluters.

Church illumination is mostly horrible, but is usually just a local
problem. Still, strong beamers can spoil the sky over a settlement even by
the backward scatter in the atmosphere. And vast majority of cheap (=
first choice) flood/spotlights don't obstruct the direct light from their
HID burners, so they often produce tremendous glare even for earthbound
observers, viewing from many places around the church. (This may concern
any illuminated building or monument, unfortunately.)

cheers,
 jenik