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    Re: N.A. Moon phases
    From: George Huxtable
    Date: 2004 Oct 30, 13:46 +0100

    Bill asked, about the Moon data in the daily pages of the almanac-
    >"I am not certain how the moon diagrams in the lower hand corner of the
    >daily pages are correlated to time. My best guess is that the
    >percentage-lighted figure is for 12:00 UT."
    >I should have said "percentage lighted figures" instead of "moon diagrams."
    >As the lighted portion of the moon changes from day to day, I *assume* as
    >the Sun/Moon/Earth changes while to moon is visible, the percentage lighted
    >will also change to some degree.  If the daily page states "52%" it might
    >range from 50% to 54% during the viewing period.
    >My corrected question is:  Is the percentage figure given on the daily page
    >tied to a specific GMT/UC?  If so, what?
    >I understand I have failed to take observer position into account as of yet.
    My guess is that the percentage lighted figures are at the time of
    Greenwich Noon, but for a mythical observer who is at the centre of the
    Earth. Usually, the almanac is careful to define such matters, but I can
    find no mention in the back pages.
    Bill should be able to check this for himself, though. When the Moon is lit
    just 50%, then it seems to me that the Moon-Sun lunar distance must be just
    about 90 degrees. (Actually, something like 89.85 degrees, which is as near
    as dammit.)
    Bill has access to a number of sources of lunar distance. For example, from
    Frank Reed's or Steven Wepster's web pages. All he has to do, then is to
    check the timing of a 90deg lunar distance against an almanac page which
    gives 50% illumination.
    There's an interesting historical connection here. Once the distance of the
    Moon had become known (by measuring its parallax), the next question was
    "how far is the Sun, and what's the size of the Solar system?". Attempts
    were made to measure the angle between Sun and Moon, when the Moon was just
    50% illuminated. At that moment, the angle between Earth and Sun, measured
    at the Moon, must have been 90 degrees, so by drawing similar triangles it
    should have been possible to find the ratio between the distances of the
    Sun and Moon. Unfortunately, the Sun is so much further, that the measured
    angle was also 90 degrees, an near as anyone could tell. So the result was
    that a lower limit could be set, that the Sun must be at least so many
    times the distance of the Moon, but as for measuring its actual distance,
    the only answer was "very large".
    As for the observer's position on the Earth's surface, depending on where
    he is, the direction of the Earth's viewpoint of the Moon can change by
    about a degree either way (which is the parallax of the Moon). For an
    observer in the tropics, then near moonrise and moonset this could shift
    the apparent shadow edge by about 1 degree either way (measured round the
    Moon's equator) with respect to the Moon's profile. I leave it to Bill to
    estimate what effect that would have on the percentage illuminated.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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