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    Almanac Calculation Questions
    From: Bill Murdoch
    Date: 1997 Mar 24, 12:43 EST

    From: W. S. Murdoch, Polymers D&C (Kpt. 1027)
    Subject: Almanac Calculation Questions
    When I wrote my navigation program, I did not worry so much about the
    programming language.  These were some of the issues I tackled.
    Why not just buy a $200 GPS and forget the celestial ?
       I have the GPS, but this is all a hobby and celestial is part of that
    Why not just use the Nautical Almanac and Sight Reduction Tables for Marine
    Navigation or just the Nautical Almanac and a simple trig calculator for the
    sight reduction ?
       My experience is that I often make mistakes and that I am lazy.  When half
       sick, tired, and with other things to do, the navigation slips.  A few
       keystrokes is easier for me than a quarter page of figures.
    Why do you want to write your own navigation programs when commercial versions
    are available and cheap ?
       There was no commercial program available for a TI-80 series calculator
       and to me a calculator seems a more "marine" bit of electronics than a
       I wanted to learn how almanac calculations were done.
       I had the time to spare and could not do any real sailing at the time.
       I was in England and the library system was excellent.
    What is the proper balance of speed, program length, and accuracy, usability.
       and bells & whistles ?
       I wanted a 200 year almanac with no need to update any of the constants.
       I shot for a one sigma accuracy of 0.1' and achieved about 2 sigma.
       I kept the program length under 28K because that was the memory constraint.
       I made the input and output displays as logical as possible using about
       10 of the 28K in input and output displays.
       Bells & whistles needed to include reductions to a lat/long fix both
       stationary and running.  The running needed allowances for changes in
       both course and speed.  Sunrise, sunset, phase of the moon, the almanac
       data in both N.A. and A.A. formats, unknown body identification, sight
       planning, Mercator and great circle sailings, Rude starfinder data, time-
       speed-distance, vector addition, current sailing, .....
       This part is fun but uses 10k or more.
    What should be the source of the lunar and planetary almanac data ?
       Because of my accuracy needs, I did not use Duffet-Smith or Van Flandern.
       Because of the need for periodic updating, I did not use Yallop.  That
       left Montenbruck and Meeus.  Both are usable.  Dr Yallop recommended
       Montenbruck and I found it somewhat shorter for the equal accuracy.  I
       removed terms and shortened constants not needed for 0.1' accuracy.  (I
       was aware of Emerson and copied his use of a Poisson rather than Fourier
       series for the perturbation terms to shorten the program length at the
       expense of calculational speed.)
    What should be the source of the stellar almanac data ?  How many stars should
    be included ?
       Dibbons-Smith has J2000 positions in a nice compact format.  It has a few
       mistakes that can be found by comparing his work to Hirchfield.
       The Astronomical Almanac gives a vector method of converting J2000
       positions to epoch of date which is short and quick if some of the
       smaller corrections are ignored.
       92 stars seemed enough.
    How do you make sure you have no mistakes ?
       This is a tough one; test and document and hope.
                      Bill Murdoch

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