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    Re: Basics of computing sunrise/sunset
    From: Frank Reed
    Date: 2009 Jun 18, 20:48 -0700

    You wrote:
    "which is what telescopes or binocs do: they gather more light radiation and 
    concentrate it into the fovea. "
    That's not really what telescopes do. If you look at the Moon in the night sky 
    for example, without optical aid, a small image of the Moon is formed on your 
    retina, and naturally if you're looking right at it, that image is on the 
    fovea. When you look through a telescope at the Moon, that image on your 
    retina has the SAME brightness per square millimeter, but the image is larger 
    in proportion to the magnification, and only a portion of it falls on the 
    fovea --you have to "scan around" to see the different parts of the Moon. But 
    the key principle here is that there is no more energy per square millimeter 
    than when you look at it without optical aid. The brightness of an 
    astronomical object per unit solid angle is not increased by purely optical 
    systems. The image is enlarged. This increases the TOTAL energy striking the 
    retina since the area is larger, but the brightness per unit area of the 
    retina is the same. 
    So there's no mistaking, I don't wish to imply by any of the above that 
    looking through a telescope at the Sun won't hurt your eyes. It will! The 
    point is merely that the mechanism cannot be by concentrating more light on 
    the fovea simply because telescopes don't do that (and can't do that). I 
    can't recall the mechanism right now but clearly if the whole retina is 
    getting intense light instead of just one tiny patch receiving light of that 
    same intensity, there would be a much more rapid rise in temperature. 
    By the way, it's also true that the brightness per unit solid angle cannot be 
    increased by getting closer to an object. If you're standing on the planet 
    Mercury, the Sun's light is just as intense as if you're standing on one of 
    the moons of Neptune. The difference, of course is that the total angular 
    size is smaller out by Neptune in proportion to the distance squared. If you 
    hold up a sheet or metal foil with a tiny pinhole in it and look at the Sun 
    from either vantage point, it would look just the same. The apparent "surface 
    brightness" doesn't change although the total energy naturally does increase.
    Similarly, if you've ever looked at the Orion Nebula through a telescope and 
    wondered what it would look like from "close up", you needn't wonder; you've  
    already seen it. It would be larger in apparent size in the sky if you were 
    closer to it, but that faint gossamer light would have the same apparent 
    surface brightness (brightness per unit solid angle) at any distance from the 
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