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    Re: Precomputed lunar distance tables 2004
    From: Steven Wepster
    Date: 2003 Oct 20, 12:30 +0200

    Dan, Jared, Jan, and Arthur,
    Thanks very much for the kind comments. We have here Acrobat 5 and the
    pages come out right, I have no idea how they look on a Acrobat 4. Arthur,
    thanks for putting them on the LD homepage; I hope that the homepage, the
    tables, and anyone interested in lunar distances may benefit from it. I
    admit that I have used these tables only 4 or 5 times.
    The tables are generated by a bunch of cooperating scripts and programs.
    Basically I use Moshier's aa program to generate the positions; I did not
    change the code of it. I thought of doing so but when I looked into the
    code, I realised that it would be all too easy to get some of the
    corrections wrong. So I just use the aa program as it is, and I feed it
    automatically with dates and bodies. Selected bodies that have interesting
    LD's fulfill several criteria: They should be bright, near the ecliptic,
    and neither too close to the sun nor to the moon. There should be an
    easterly as well as a westerly object included, some spread in distances,
    and preferably fast changing distances. The sun is always included if its
    distance is less than about 120 degrees. For each day a script picks out
    the bodies that it thinks are interesting. LD's are computed for them, the
    results put in a LaTeX input file together with all the other data of the
    month, and then the pdf files are generated from the LaTeX. LaTeX is superb
    for formatting; I have the impression that the printed Nautical Almanac is
    also generated with it.
    By the way, the '+' and '-' along the body names in the tables indicate
    increasing (ie, easterly) or decreasing (ie, westerly) lunar distances.
    It was (and is) recommended to take an easterly and a westerly observation,
    and average the results after reduction.
    The 'P.L.' column has the Prop.Log. or Proportional Logarithms
    invented by Nevil Maskelyne, Royal Astronomer and the initiator of the
    Nautical Almanac, to make computation of LD's a little bit easier.
    The Prop. Log of a number, say x, is
       log 10800 - log x
    where the logs are common logs to the base 10. The number 10800 is the
    number of seconds in 3 hours. You will notice that my LD tables, just like
    the original tables of Nevil Maskelyne, have a tabular interval of 3 hours.
    Therefore, the Prop.Logs come in handy when interpolating LDs.
    Let d0 and d1 be two tabulated lunar distances, d0 for time t0, and d1 for
    time t0 + 3 hours. Let d be the (measured and reduced) distance at the time
    t, which is to be determined. Then we have
      Prop.Log t = Prop.Log (d-d0) - Prop.Log (d1 - d0).
    Besides, the Prop.Logs are helpful because a smaller Prop.Log in the table
    corresponds to a farter changing lunar distance to the body. Thus they help
    to select those bodies which have a potential for the most accurate
    determination of time and/or longitude.

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