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Subject: Re: Rocky Mountain Lunar Distance
From: Arthur Pearson (arthurpearson@XXX.XXX)
Date: Tue Dec 17 2002 - 22:40:00 EST
I am in agreement with George's comments. In constructing spreadsheets
where these types of manipulations are required, it requires some
unpleasant nested IF functions to correctly calculate all the
possibilities for adding and/or subtracting GHA, SHA or LHA.
With respect to my interpolations, I reexamined my spreadsheet and
should correct myself. I interpolated only sun declination within a 12
hour period. Sun GHA, moon GHA and moon declination are all interpolated
within a 1 hour range. I got the idea for the 12 hour interpolation from
George's annotations to the "Astronomical Notebook" that Lewis received
from Patterson which state that Lewis' almanac only gave right ascension
and declination sun and moon at 12 hour intervals. I started out to
recreate this methodology but lost my nerve for all but sun declination.
-----Original Message-----
From: Navigation Mailing List
[mailto:NAVIGATION-L@XXX.XXX] On Behalf Of George
Huxtable
Sent: Tuesday, December 17, 2002 9:13 AM
To: NAVIGATION-L@XXX.XXX
Subject: Re: Rocky Mountain Lunar Distance
Arthur Pearson has responded to my questions and quibbles and I think we
have ended up in full agreement.
However, I think there's a bit of profit to be got from looking at my
quibble No 5 in a bit more detail.
I said-
5. Arthur quotes the expression for LHA Moon as-
(LHA Sun +/- difference between GHA Sun and GHA Moon)
but the ambiguities in this could cause trouble and it should be
expressed
more exactly as-
LHA Moon =LHA Sun + GHA Moon - GHA Sun (adding or taking off 360° where
necessary).
and Arthur replied-
>5) George's expression for LHA moon is more exact (LHA Moon =LHA Sun +
>GHA Moon - GHA Sun adding or taking off 360° where necessary). It is
>worth noting that while this was the easiest way for me to understand
>the calculation of LHA moon, the examples provided by Patterson to
Lewis
>in his "Astronomical Notebook" take a different path to the same
result.
>I found it easier to construct calculations by Patterson's method.
>Recall that by assuming longitude we have established a correction
>between local time (LT) and Greenwich Time (GT), and by our time sight,
>we find a correction from watch time (WT) to LT. With WT of the lunar,
>we correct to estimated GT and take GHA and Dec of moon and sun from
the
>almanac (in my case, I interpolated within the hour for GHA, and within
>the 12 hour period for Dec). LHA of either body is simply (GHA ~
>Longitude). I puzzled quite a while before accepting that this arrives
>at the same value as George's expression.
==================
The trouble with using the expression that Arthur quoted-
LHA Moon = LHA Sun +/- difference between GHA Sun and GHA Moon
is this. Obtaining the difference between those GHAs involves (by the
usual
convention) subtracting the lesser from the greater, to obtain a
positive
answer for the angle (in hour angle) between Sun and Moon.
That positive difference would sometimes represent the Moon being to the
Westward of the Sun, and sometimes to the Eastward, depending on their
relative positions in the sky, and whether or not the Greenwich meridian
intervened between them.
Next, according to Arthur, we have to add-or-subtract that result from
LHA
Sun. But which? When should one add it, when subtract it? We are given
no
clue. The LHA of the Sun might be East of the observer in the morning,
or
West in the afternoon. Perhaps if the navigator draws a careful diagram
showing all three angles, he can work out whether to add or subtract by
commonsense. What I deprecate most is the sort of rule that says "Add or
subtract, whichever gets the nearest answer to the expected result".
This whole business of lunars is complicated enough, without the
intrusion
of such awkward decisions.
When I offered an alternative expression that gave the result "more
exactly", perhaps "more exactly" was the wrong phrase to use, because I
wasn't thinking of small differences, but of gross errors caused by
choosing wrongly between + and -. Perhaps it would have been better to
say
"with less chance of gross error".
As for the expression I provided instead,
LHA Moon = LHA Sun + GHA Moon - GHA Sun (adding or taking off 360° where
necessary)
there are no such difficult judgments to be made. You just have to do
what
it says. If it turns out to be more than 360° or less than 0°, just add
or
subtract 360°, until it isn't.
It's hard to go wrong, here.
I'm a bit puzzled when Arthur says-
(in my case, I interpolated within the hour for GHA, and within
>the 12 hour period for Dec)
That is almost certainly adequate for Dec of the Sun, which varies
slowly
and smoothly, but almost certainly inadequate for the Dec of the Moon,
which changes MUCH faster! As the nautical almanac provides Dec at
1-hour
intervals, why didn't Arthur interpolate between those? Or was he using
a
different almanac with more condensed data? If so, I suggest they were
inadequate for his purpose.
===============================
May I wish clear skies and fair winds (and sharp horizons) for Arthur's
cruise in the Grenadines. I think he may come to appreciate the
additional
difficulties faced by an observer of lunars at sea. But it will depend
greatly on the size of his vessel.
Although it's a bit heretical to say so on this list, it might be useful
for Arthur to pack a handheld GPS receiver, to check his observations.
Or
perhaps I should say, on this list, to check the performance of the GPS
system from his celestial observations. I look forward to reading his
results.
George Huxtable.
------------------------------
george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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