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    Re: Lunars Tables
    From: Frank Reed
    Date: 2007 Dec 03, 01:22 -0500

    Scott, you wrote:
    "Bought a copy of Bruce Starks, Tables for Clearing the Lunar Distance a few
    weeks ago.  From the archives it looks as though Bruce was a regular
    contributor but I did not see anything of late."
    
    Something I've been meaning to say about Bruce's tables: while the
    development of another clearing method holds some technical interest (how
    much depends on your tastes for such things), Bruce Stark's book had a
    really significant impact on modern navigation education that I don't think
    is widely enough recognized. He brought back lunars almost single-handedly.
    By publishing his book and spending cash to advertise it and making it
    available to distributors, he helped make people aware of this once arcane
    historical method and sparked a lot of curiosity among practical navigators.
    Bruce Stark's book, combined with the generally too negative, albeit very
    prominent, account of lunars in Sobel's "Longitude," generated most of the
    modern interest in lunars among navigation enthusiasts. Of course, once the
    Navigation list started generating significant traffic, everything changed,
    and this is now "lunarian central." But Bruce Stark's tables started it all.
    
    
    You asked:
    "1)  Are these the tables most members use for reducing Lunar observations
    or is there some other preferred method/tables?  [I know there are many
    methods to do this, I'm just trying to get a feel for what method list
    members are using and what may be considered the most accurate method.]"
    
    Most? Probably not. There are as many answers to this as there are lunarian
    enthusiasts. When you first start thinking about lunars, you have to ask a
    number of questions (and everyone answers them differently).
    1) Why shoot them?
    Is it for historical interest (either serious historical analysis, perhaps
    of old logbooks, or even just antiquarian re-enactment), or is it for modern
    entertainment (just something new and challenging to do with your sextant),
    or for modern practical use (as a method for testing your sextant), or for
    modern disaster thinking (hard to imagine losing GMT but lunars will get it
    back if you do)?
    2) How will you observe them?
    With an antique or traditional sextant (related to the question of
    historical interest above), or a modern sextant (probably, but how much are
    you willing to "cheat" with modern technology)? And after you've observed
    them or acquired observations from a historical document,
    3) how will you clear them? With a "historical" computer method (in other
    words, use software but base the algorithms on traditional methods in order
    to see how well they work), with a historical pen-and-paper method (this is
    much more practical today than even five years ago since you can download
    19th century editions of Bowditch, Norie, etc. and use the old tables
    directly), or wih a modern computer method (the tools on my web site, for
    example, which include the almanac data thus making very short work of the
    whole process), or FINALLY will you use a modern pen-and-paper method (for
    which the best, maybe only, option is Bruce Stark's tables)?
    
    With so many options and possible ways of answering all these questions,
    it's not hard to see that relatively few people end up using Stark's tables
    exclusively. There have been a couple of list members, though, who really
    enjoy them (Mike B, where are you?).
    
    You asked:
    "2)  Is anyone familiar with the trig/math that Bruce used to derive his
    lunar tables?  If so, does anyone know if Bruce is amenable to posting
    it on the list or has it been posted in the past and I just missed it in
    the archives?"
    
    You probably know this bit already, but at the basic level, it's really
    simple. You set up the Sun-Zenith-Moon spherical triangle with the observed
    altitudes (zenith distances actually) of the bodies and the observed
    Sun-Moon distance. You use that to calculate, very exactly, the difference
    in azimuth between the Sun and the Moon. Next you correct the altitudes for
    refraction and parallax (just as you would clear normal altitudes --but use
    the bubble sextant rules in the Nautical Almanac altitude correction tables)
    and then since the difference in azimuth is NOT changed by the altitude
    corrections, you reverse the triangle and calculate the cleared distance.
    Compare that with known values of the distance at Greenwich for known values
    of GMT and a simple interpolation gives GMT at your location. This is a
    "direct" solution to the problem. Historically, and sometimes on this list,
    this was erroneously called a "rigorous" solution ("series" solutions which
    were morepopular historically were sometimes dismissed as "approximate").
    Bruce Stark's tables are a clever, modern re-working of this "direct"
    solution. There's an easy way to find posts describing his tables in the
    archive. Go here: http://www.fer3.com/arc and in the search box, type
    "Stark's tables" (quotes not needed in this case). Click search and you
    should find about 87 matching pages. You can find all the details you want
    regarding the underlying calculational method by browsing through those
    messages. Somewhere along the way, you should find one from Bruce Stark
    himself describing the mathematical tricks he used.
    
    Follow the link after my initials for the online clearing tool on my web
    site. If there's sufficient demand, I am prepared to make a stand-alone tool
    with all the bells and whistles people ask for (historical clearing methods,
    graphing tools, automatically generating arc error from long series of
    observations, star-star distances, etc.), but I find that many lunarian
    enthusiasts are graduates of the "roll-your-own" school. They would rather
    build their own calculating tools carefully suited to their own personal
    answers to all those questions I described above...
    
     -FER
    http://www.HistoricalAtlas.com/lunars
    
    
    
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