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    Clearing the Lunar Distance via Trig Tables
    From: Brian Johnson
    Date: 2016 Mar 22, 07:55 -0700

    Hello NavList!  This is my first post and I’m a little nervous mixing in with the celestial navigation greats.  I have been teaching myself celestial navigation over the last 5 year by way of developing software to do it.

    Hold on - don’t throw me out yet - I know software is a bad word here!  My focus, however, is to generate the tables necessary to perform celestial navigation exactly as it has been done for centuries.  The tables can be easily printed or saved to a PDF file to use manually.

    My latest project involves the tables necessary to do Lunars.  Standing on the shoulders of past list members George Huxtable and Steven Wepster, I have been able to generate tables of pre-computed lunar distances, and the proportional logarithm tables.  I also generate a table to compute the Moon’s semidiameter, and “Table I” from the 1905 Nautical Almanac which corrects for second differences when finding UT from a corrected lunar distance.

    With the Moon SD table and a current Nautical Almanac I can determine all of the parameters to compute the corrected lunar distance using Young’s method as described by Mr. Huxtable.  I can then compute universal time from the corrected distance exactly as it was done in 1905 using the other tables I generate.

    The piece I am still missing is the trig tables for clearing the distance.  I am currently using Young’s method and just computing the value:

    D = acos ((cos d + cos (m+s))*(cos M*cos S)/(cos m*cos s) - cos (M+S))

    Are there special trig tables designed for celestial navigation?

    Sorry if this is a dumb question … pocket calculators came out when I was in grade school and I don’t remember using trig tables.  Did the education system fail me?

    I do have the “Stark Tables” but haven’t really broken them down to see if there is a subset that could be used just for this purpose.

    George Huxtable shows an example of Borda’s Method in “About Lunars” that clears the distance with calculations using “log cos” and “log sin”, etc. but doesn’t specifically reference the tables to use for these functions.

    I found a 2007 post from Dave Walden on the NavList referencing the following book :

    Logarithms of Sines and Tangents for Every Second By Robert Shortrede,

    John Caulfield Hannyngton, 1873.  (and I was able to locate the Google scan)

    Would this be the tables to use with Borda’s Method?  Are there other posts on the NavList I could be directed to for clearing the distance via tables? 

    So much great information!  Thanks in advance for any suggestions!

       
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