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    Re: Rocky Mountain Lunar Distance
    From: Arthur Pearson
    Date: 2002 Dec 17, 22:40 -0500

    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{at}LISTSERV.WEBKAHUNA.COM] On Behalf Of George
    Huxtable
    Sent: Tuesday, December 17, 2002 9:13 AM
    To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    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---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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