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    Re: Latitude by Lunar Distance
    From: Frank Reed CT
    Date: 2006 Oct 05, 03:10 -0700

    Here's an example of fixing your position using angles measured from
    the Moon to stars only, no altitudes whatsoever. This approach assumes
    that GMT is a known quantity so its resemblance to historical lunar
    distance observations is only superificial.
    I am somewhere southeast of New England, rough DR = 38N, 70W, early in
    the morning of October 11, 2006. It's the middle of the night and a bit
    hazy, too. The sea horizon is invisible. But I can see the Moon and
    some bright stars... At 06:36:00 GMT I look up high in the South at the
    Moon with Aldebaran below it. With my sextant, I carefully measure the
    angular distance (Far limb) between the Moon and Aldebaran and find
    that it is 11d 39.9'. Then I turn to Pollux and measure the distance
    from that star to the Moon (Near limb this time). I find that the
    Pollux-Moon lunar distance is 38d 13.1'. The GMT for this sight is
    06:39:00 exactly. I believe that my sextant is perfectly adjusted, and
    I'm skilled at using it, so I trust these angles to the nearest tenth
    of a minute of arc.
    With the two "lunar distance" observations above, I can get a fix on my
    position, both latitude and longitude, accurate to about five nautical
    miles. I can generate two lines of position for these sights something
    like the early calculation of Sumner lines by finding the latitude for
    two given longitudes that yields the exact value for the observed
    distance at the exact GMT of those observations. For the Aldebaran
    sight, at longitude 69W, a latitude of 38d 41'N would yield that
    observed distance. At longitude 70W, a latitude of 38d 46'N would yield
    the same observed distance. I can draw a line through those two points,
    and my position must lie along it. For the Pollux sight, in the same
    way, at longitude 69W, a latitude of 38d 05' produces the correct
    observed lunar distance, and at longitude 70W, the latitude would have
    to be 39d 41'. Now I have a second line of position. I can cross them
    on a chart. My position must be very close to latitude 38d 46',
    longitude 69d 25'W. This postion is accurate to about five nautical
    miles if my observations are accurate to the nearest tenth of a minute
    of arc (and the GMT has no error). I have determined latitude and
    longitude by measuring angles between the Moon and bright stars.
    How can this be?? Position-fixing without a horizon?! In fact, there is
    a horizon involved -- the limb of the Moon. These altitudes are
    measured from the lunar horizon instead of the ordinary sea horizon.
    Each "altitude" above the lunar horizon, really a "lunar distance",
    generates a "cone of position" with its apex at the Moon's center
    instead of the Earth's center. When those "cones of position" intersect
    the Earth, they locally create crossing lines of position. And where
    they cross is where we are...
    Cool, huh?
    PS: I should emphasize that this viewpoint on "lunar distances" is
    radically different from the historical "lunar distance observations"
    which treated GMT as an unknown.
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