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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?

-FER
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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