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    Re: Basics of computing sunrise/sunset
    From: Bill B
    Date: 2009 Jun 18, 08:53 -0400

    > "I recall .... using..... binoculars to spot the moment of sunrise/sunset"
    
    >> Readers be warned never to do this if you value your eyesight.
    
    As I see it the sun is an orange (elongated horizontally, actually squashed
    vertically) ball as it is rising or setting, and does not have the magnitude
    it does higher in the sky thanks to the added atmosphere.  Of course lenses
    may magnify its "brightness."  At any rate, what we want to look at is when
    the upper limb is just kissing the horizon (rising or setting) and I do not
    perceive this as a great danger because of atmosphere, refraction, and the
    sliver we can see when the body is physically below the horizon. I am open
    to correction, which is one of the uses of a group like this.
    >
    > I like your idea of finding the GHA of the sun from its LHA and then using
    > the published values for the GHA of the sun at different times to avoid the
    > EoT.
    
    It is also a convenient and precise way to find local noon when longitude is
    known.
    >
    > If you want to work it out right down to the second of arc of where you are
    > and second of time then you must consult refraction tables and work your dip
    > out carefully. For this there is a formula making using of the square root,
    > but the one I'm thinking of is a rough approximation.
    
    Yes, dip is a factor, but take it as is (from a table or from calculating).
    Unless you are on a beach or large ship, exact dip is as much art as science
    IMHO.
    >
    > "Back on track, if you have a longitude, elevation (given as -0d 49!6 to -0d
    > 49!8 for the center of the Sun) "
    >
    > May I ask do you mean zenith distance by elevation?
    >
    > "0d 49!6 to -0d
    > 49!8"
    >
    > What units are these in? I'm thinking you are referring to to semi-diameter,
    > but not sure.
    
    I am not certain I understand your question(s). In simple terms, the
    Nautical Almanac has tables in the front for baseline refraction values.  It
    is my understanding that in celestial navigation all elevations/altitudes
    are in degrees and and their parts (minutes and seconds or tenths of
    minutes) measured from the horizon to the *center* of the body.
    
    Table A3 in the NA, "Altitude Corrections Tables 0d-10d--Sun Starts Planets"
    lists refraction for standard conditions with the center of the body from 0
    degrees (tangent to the horizon) to 10 degrees above the horizon.
    
    If you note the refraction for a star on the horizon or a planet split by
    the horizon (planets can be larger than a point source) is - 33.8 minutes of
    an arc.  The correction for the upper limb of the Sun as it kisses the
    horizon rages from 49.8 to 49.6 minutes of an arc based on season.  This is
    because the the Earth's orbit is not a perfect circle, so the diameter or
    semi diameter (SD) changes throughout the year.  An average semidiameter for
    the Sun in the refraction table would be 15.9 minutes (plus a star
    refraction of 33.8) or 49.7 minutes to the center of the Sun.
    
    Put another way, if we could see a star kiss the horizon it would already be
    33.8 arc minutes below the horizon in a vaccum but is lifted by that amount
    by air refraction. As a side note, list members have pointed out in the past
    that almost any point source would be "extinguished" by the atmosphere at
    that elevation (amount of air between the observer and the body) and could
    not normally be observed.
    
    The Sun does not approximate a point source. The point being the upper limb
    of a Sun with a nominal SD of 15.9 arc minutes (31.8 arc minutes diameter)
    is already 33.8' minutes below the the horizon and the center 49.7' below
    the horizon (33.8 + 15.8).
    
    Two other observations.
    
    As the list Gurus  have discussed, refraction near or on the horizon can get
    very strange.  Terms like thermal inversions and lapse rates come into play.
    What you see may not be what you get, so your mileage (times of rise or set)
    my vary up to four minutes from theoretical if memory serves.
    
    The other twist brought up had to do with 6, 12, or 18 degrees below the
    horizon if I recall.  These standards have little to do with actual rising
    or setting time, other than serving as a mark for the time lapse between
    rise or set and civil, nautical, or astronomical twilight.
    
    Bill B.
    
    
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