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    Re: Basics of computing sunrise/sunset
    From: Frank Reed
    Date: 2009 Jun 30, 19:51 -0700

    Bill B, you wrote:
    "My questions. If I recall the GP would be approximately 5400 nautical miles 
    (nm) away when I see Sun set (using appropriate eye protection of course). In 
    my mental picture, I am not wrapping my vision along the surface of the 
    Earth. I have a line of sight from my eye position to the Sun, which will run 
    out of atmosphere *long* before 5400 nm "
    Aha. A good little technical point there, Bill! As Christian noted in a later 
    message, I wasn't taking his wording too literally. I was merely agreeing 
    that if we had detailed observational information on the state of the 
    atmosphere between us and the object we're viewing, then the problem is 
    straight-forward physics: a numerical integration of the differential 
    equations for the law of refraction in a continuous medium. It's solvable 
    with enough data.
    But you're right in pointing out that the points we would require for this 
    integration do not extend to the GP of the Sun but rather they extend along a 
    line inclining up through the atmosphere. The details in the high atmosphere 
    don't much affect the refraction so let's suppose we stop when we reach an 
    altitude of 40,000 feet. So if I am standing on the roof of a building 100 
    feet above sea level, and I look out and see the lower limb of the Sun just 
    on the horizon (sea horizon), how many "weather balloons" (observation 
    points) would I need? Just for fun, let's suppose I place a detector every 
    500 feet between me and the top of the troposphere (around 40,000 feet) all 
    the way out towards the lower limb of the Sun. From my location to the 
    horizon is a distance of about 10n.m. (sqrt(ht in feet)). From that spot, 
    continuing on a straight ray to an altitude of 40,000 feet is about 200 n.m. 
    (sqrt again). So that's 210 miles or, doing the math, around 2500 detectors 
    or "weather balloons". We're very lucky that all of that detail is irrelevant 
    to most refraction. For altitudes above 3 or at worst 5 degrees, nothing 
    matters except the temperature and pressure right at the observer's location 
    at the bottom of the atmosphere. It's worth remembering that this fortunate 
    circumstance is what made celestial navigation possible. If we were dependent 
    on the observation of altitudes very close to the horizon, the accuracy of 
    celestial navigation would be ten times worse and sometimes considerably 
    worse than that.
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