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What Frank Reed has written below is all very well, but has little to do
with the question being asked, which was about deficiencies in a particular
full formal clearing procedure, not some shortcut.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message ----- 
From: 
To: 
Sent: Monday, March 02, 2009 8:49 PM
Subject: [NavList 7518] Re: Possible limitaion for lunar distance
measurement



George wrote:
"It's certainly the case, as Frank has frequently pointed out, that when the
lunar distance is near 90�, it's very insensitive to the details of the
correction."

To elaborate on this, there are several things at work:
First, there's the simple practical point which I mentioned a few days ago.
Navigators seem to have preferred shooting Sun-Moon lunars, and that's most
convenient from an observational perspective when the Moon is close to 90
degrees elongation.

Second, there are shortcuts in some clearing methods that can be applied
when the distance is close to 90. When using one of the series methods, the
quadratic correction is proportional to cot(LD) so it can be ignored near 90
degrees (except in some methods, like Bowditch's principal method, where the
quadratic correction is rendered always positive by adding a constant at an
earlier step). This is not a significant savings in work since the quadratic
correction was usually just a simple table lookup.

Third, as I discovered a few years ago and have mentioned many times since,
the clearing of lunar distances has a remarkable, and as I have said
"seemingly miraculous", freedom from errors in the Moon's altitude when the
distance is close to 90 degrees. If the observed lunar distance is between
85 and 95 degrees (and the objects aren't too low in the sky), the observed
altitude of the Moon can be wrong by a degree or more and it won't make any
difference. This makes the whole observation and calculation much more
convenient since it means a quick observed altitude for the Moon is
sufficient.

Fourth, and almost certainly not relevant historically, it's possible to
clear lunars when the distance is close to 90 degrees (and over a rather
broad range around that) without solving any spherical triangles at all. Any
observation can be reduced to the geometrically "degenerate" case of
vertically aligned bodies when the measured lunar distance is around 90
degrees. That makes clearing lunars in many common practical cases a
relatively trivial project. Too bad they didn't know this two hundred years
ago!

-FER








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