From: zellner@stsci.edu
Subject: Re: Why is the sky blue?
Organization: Space Telescope Science Institute
Distribution: na
Date: Mon, 14 Dec 1992 22:19:27 GMT

It's an excellent question, not stupid at all.  I believe the answer eluded 
such as Newton, Gauss, and Maxwell and wasn't known until Lord Rayleigh in
the late 19th century.

  >  Actually, I know *why*, ie. scattering... but why specifically blue?
  >  Does it matter what molecules are in the atmosphere, or just that
  >  there happens to be an atmosphere?

The discussion by Steve Vejcik was lucid and accurate.  It doesn't matter 
what the molecules are so long as they are much smaller than the wavelength 
of light and only scatter, not absorb, which is true of our oxygen-nitrogen 
atmosphere in visible light.  In that case the classical Rayleigh theory 
says that the scattered light is proportional to the fourth power of the 
frequency.  More generally the scattering efficiency Q is usually expressed 
in terms of a dimensionless size parameter

     x = 2 pi a / lambda

where a is the particle radius and lambda the wavelength.  For non-absorbing
particles with very small x (like molecules) the efficiency Q(x) is also 
very small but increases as x^4.  It then passes through a rather linear 
domain (e.g, interstellar dust), and peaks at Q = 2 for some x near unity.  
For large particles (e.g., fog or ice in our atmosphere) Q tends to be 
independent of size or wavelength and the scattering is neutral unless you
have prism effects like rainbows or unless the particles actually absorb at 
some wavelengths. 

The blue color of our sky is a result of the spectrum of the sun convolved 
with a fourth-power law, plus the limited sensitivity of our eyes to short-
wavelength light.  Also the color is diluted somewhat by ground reflection
(you get the deepest blues in twilight, when the ground is dark), by dust in 
the atmosphere, and by multiple scattering.  When the optical depth is very 
large, as near the horizon, the sky always looks whitish.  As a ground-
reflection effect, one can often see red-bottomed clouds over the painted
desert in Arizona. 

  >  If you look directly at the sun you see it as white because the absolute 
  >  probability of scattering is still small.

Actually the sun is somewhat yellowed compared to what it would look like
outside the atmosphere.  When the sun is high the effect is small, and we
don't have anything to compare it to, so ordinarily we don't notice the
reddening until the sun is quite low.

  >  With regards to other planets, I think this principle should still hold
  >  except possibly that the regime of frequency (energy) of photons for
  >  which Rayleigh scattering is valid might depend on the scatterer (type
  >  of molecules in the atmosphere).  

Rayleigh scattering is Rayleigh scattering.  Differences would come only
with aerosols (dust, ice crystals, etc.) in the atmosphere or with molecular
species like methane that actually _absorb_ and not just scatter specific
wavelengths of visible light.

  >  Would all planets with air breathable by earth creatures have to have 
  >  blue skies?  (Referring to green/brown/orange skies so prevalent on Star 
  >  Trek).  I've seen pictures of Mars where the sky and ground were orange, 
  >  and others with brown rocks and a blue sky.  What color is the sky on 
  >  Mars? 

Rayleigh scattering alone gives exactly the same color on Mars as on earth;
the same sun illuminates both, and the molecules don't matter.  However the
Martian atmosphere is very much less dense than that of the earth, which 
means the blue would be much darker; not a different _shade_ of blue, just
less light associated with it.  

BUT:  Thin as it is, the Martian atmosphere can support lots of dust; the 
surface is dusty, and Mars is a windy place.  The dust is reddish in color
due to absorption (not scattering) by iron oxides, and it doesn't have much 
blue Rayleigh-scattered light to compete with.  So largely as a matter of 
contrast the Martian sky often looks reddish from the surface. 

The atmosphere of Venus is mostly carbon dioxide, and that of Titan mostly
nitrogen, but both are very thick with aerosols.  I suppose the sky could look
green or yellow on some planet with a clear molecular atmosphere of about the
same thickness as ours, if the illuminating sun were a red star, but I haven't
actually done the computation. 

Ben

PS: It is paradoxical but true that large particles scatter out of a beam an 
amount of light equal to TWICE their geometrical crossection.  Think about 
that, the next time that you see a flower-pot in the window and its shadow
on the floor.