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    Re: Refraction
    From: Marcel Tschudin
    Date: 2005 Aug 4, 19:55 +0300

    The self-made program contains also a goographical database with the
    coordinates of about half million locations and mountains and from the
    mountains also their altitude. In addition I incorporated recently a
    atmospheric model for approximate temperature and pressure values for a
    given location at a given day and time... Ask my wife how many years I
    already spent in this private project ;-)
    ----- Original Message -----
    From: "Fred Hebard" 
    Sent: Thursday, August 04, 2005 7:35 PM
    Subject: Re: Refraction
    > Marcel,
    > I am still wondering under what conditions you would get a negative
    > elevation.
    > If it's for locating yourself on land, it seems hopeless: If you're at
    > an unknown location in a valley, and trying to use surrounding
    > mountains as an indication of horizon, you wouldn't know your height
    > above sea level to begin with, so wouldn't know how much higher the
    > mountains were than you, not to mention not knowing how far away they
    > were.  Also, the height of mountains varies, so you would have to know
    > the precise spot on the mountain below the celestial object, to
    > determine its height above sea level at that point.  It seems hopeless
    > to me.  Better to use an artificial horizon or a plumb bob.
    > Fred
    > On Aug 4, 2005, at 12:20 PM, Marcel E. Tschudin wrote:
    >> Fred,
    >> Yes, how do I get in this? Just trying to cover in a self-made program
    >> the
    >> situation from an object at the horizon (over sea level) as seen from a
    >> mountain or air craft.
    >> The "real" calculation is done via integration. But since this is not
    >> very
    >> practical one uses approximative formulae like e.g. the one from
    >> Bennett
    >> which Meeus mentions in his book Astronomical Algorithms. All tables on
    >> refraction I found so far do end at 0? elevation and for none of the
    >> approximative formulae I could find an indication that they also would
    >> be
    >> valid for negative elevations.
    >> I also was wandering whether the approximate formulae could be used by
    >> calculating the Refraction R for e.g. -2? the follwing way:
    >> R(-2?)  =  R(0?)  +  (  R(0?) - R(+2?)  )
    >> If this would be correct then one would not need separate formula for
    >> negative elevations.
    >> Greetings from Marcel

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