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    Re: NA daily pages, moon
    From: Frank Reed
    Date: 2008 Nov 02, 22:58 -0500

    Bill, you wrote:
    "Slipping into astronomy, at what time/longitude is the exact percentage
    quoted? When I see it at 86d W can it be the same percentage as the
    time/longitude used for the percentage? (I've never quite figured out all
    the moods of the moon.)"
    
    The P.I. (percent illumination --my abbreviation) is calculated for 0h GMT.
    It's geocentric. There is a slight difference for different longitudes. If
    the Moon's geocentric P.I. is 50% at some instant of time, then if you're on
    the Earth's surface at the same instant and the Moon is at the zenith, the
    observed P.I. is also 50%. But if the Moon is on the horizon and the Sun is
    near the zenith, the observed P.I. is closer to 51%. Or if the Moon is on
    the horizon and the Sun is near the nadir, the P.I. is closer to 49%. You
    can see why by drawing a little diagram. The observer "under the Sun" with
    the Moon near the horizon sees a little more of the sunlit side.
    Incidentally, the P.I. is equal to the "haversine" of the Moon's elongation
    from the Sun, or in other words, [1-cos(LD)]/2 where LD is the Sun-Moon
    lunar distance. So...  that little table of the Moon's illumination is
    actually equivalent to a low accuracy table of geocentric lunar distances.
    Ha!
    
    And you added:
    "On the warm-fuzzy side it changes so much day-to-day it is just comforting
    to know vs. the diagram."
    
    Sure. No harm in it. :-)
    
    And:
    "Percentage coupled with rise/set/or meridian passage is also a nice way to
    determine the day in a lifeboat situation if I recall."
    
    For emergency navigation, if you need the date and you are fortunate enough
    to have a Nautical Almanac or equivalent, just read out the Moon's
    Declination, calculate the Moon's SHA, and plot on the little star chart in
    the back of the almanac for your best guess of the date and time (or two
    bracketing times). You can observe the position among the stars to within a
    degree or so without a sextant. That will give you the date and also the GMT
    to within a couple of hours. If you don't have a star chart handy, but you
    do have a list of the navigational stars, you could also measure very rough
    lunar distances using a homemade "kamal", e.g. an index card held at arm's
    length.
    
    
    And you concluded:
    "A sliver may be theoretically visible during daylight, but below a certain
    percentage I am totally unable to see it with the naked eye, as well with
    the sextant scope."
    
    Oddly enough, this particular game has been a popular challenge for
    millennia. Many lunar calendars use (or formerly used) actual visual
    sightings of the "new" Moon (distinct from the "New Moon" in the
    astronomical sense) to time holidays. You will probably find, like those
    observers historically, that your ability to detect a thin crescent Moon in
    the sky depends critically on sky transparency and also on observational
    experience and simple patience. The limiting value of the percent
    illumination varies from one month to the next. The historical lunar
    calendar case, by the way, deals with observations of the crescent just
    after sunset. In daylight, the limits are different because of the bright
    sky glow around the Sun, but like the post-sunset observations, a lot
    depends on sky transparency. Try hunting for the crescent Moon (or Venus
    when its near maximum brightness) when the sky seems unusually blue. Those
    are the days with the best transparency.
    
    There's an interesting thing about percent illumination, by the way. It's
    VERY difficult to guess by looking at the Moon, even to the nearest 15%,
    unless you have trained yourself with many observations.
    
     -FER
    
    
    
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