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Re: Lunars
From: Peter Smith
Date: 1998 Jul 01, 2:07 PM

```On Wed, 1 Jul 1998 12:15:27 GMT, Rick Emerson  asked:
>
> With the anniversary of Capt. Slocum's trip at hand and my mention of
> older editions of Bowditch, the question of how "lunars" are done has
> come around.  Aside from a vague notion that the system has something
> to do with tables predicting the moon's position relative to key
> source explaining this system or, pushing my luck, a source for
> tables, trusty alarm clocks[g], etc.?

Since the Moon moves with respect to the Sun and stars, by measuring
the distance between it and a body near its path, one can interpolate
the time at which that distance was current from a table of lunar
distances -- although such tables haven't been published since the
beginning of this century (US Nautical Almanac dropped them in 1912).

Bowditch editions printed before before 1914 give several methods of
solving this.  Each is based on three simultaneous observations:
lunar altitude, a second body's altitude, and the angular distance
from the moon to the second body.  While the key to the solution is
the moon-body distance, the altitudes are required to compute the
refraction and parallax corrections necessary to correct the observed
distance from the moon's limb to the second body's limb to an actual
distance from the moon's center to the second body's center.

When only a single observer or instrument is available, the navigator
must approximate the altitudes at the time of the distance sight by
taking timed altitudes of both bodies before and after the distance
sight.  The altitudes at the time of the distance sight are then
interpolated by proportional logs.  Clearly, this will only be accuate
when both the moon and the second body are well off the meridian and
their altitudes are changing fairly linearly.  However, since the
corrections for refraction and parrallax do not change too rapidly at
moderate altitudes, the errors introduced by imprecition here shouldn't
be large.

Once the true lunar distance is calculated, the navigator enters the
almanac.  In Bowditch's day, the Nautical Almanac tabulated the true
distance from the moon to the sun, four major planets, and nine stars
for every three hours.  One would use the actual distance observed
to interpolate between tabulations and approximate the Greenwich time
of the observation.  Given the non-linearities in the motions of the
two bodies, this was not precise. Ol' Nat has this to say for the
expected accuracy:

As the moon moves in her orbit about 1' in 2m of
time, it follows that if her angular distance can be
ascertained from the sun or star within 1', the time
at Greenwich will be known within 2 minutes, and the
longitude within 30 miles.

As for the details of the calculation behind the now-extinct tables,
I can send you (back-channel) a posting by once (and perhaps, still)
listmember Jeff Gottfred, who's grasp of theory and wealth of
experience far exceeds mine.
--
Peter Smith -- psmith@wellspring.us.dg.com
Data General Corp., Westboro, Massachusetts  (for whom I do not speak)
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