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    Re: Nautical Almanac Method Reduction
    From: Dan Allen
    Date: 2000 Nov 03, 8:00 PM

    I was nicely informed that in fact I answered a different question, not the
    one that was originally asked.  I apologize, but in the meantime I learned
    some new things about the source of the almanac ephemeris!
    
    In answer to the question as to how the sight reduction tables are derived,
    it is the spherical law of cosines (along with the other tables for
    refraction and the other corrections).  The law of cosines is:
    
       cos(a)*cos(b) + sin(a)*sin(b)*cos(ab) = cos(c)
    
    where
    
       a = 90 - estLat
       b = 90 - decl
       ab = LHA = GHA - estLong
       90-c = altitude
    
    once the altitude is solved for, then change the variables:
    
       b = c, c = b
    
    and recalc to get a formula for azimuth
    
       ab = azimuth (360-az if LHA < 180)
    
    This all assumes that you are using degrees rather than radians...
    
    Dan
    
    -----Original Message-----
    From  Navigation Mailing List
    [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of Dan Allen
    Sent: Friday, November 03, 2000 2:58 PM
    To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    Subject: Re: Nautical Almanac Method Reduction
    
    
    Chapter 14 of the astro.zip collection referred to below does give some
    basic formulas accurate to about a half a minute of arc, but those formulas
    are NOT the formulas used to come up with the Nautical Almanac.
    
    The formulas for the Astronomical and Nautical almanacs come from the Jet
    Propulsion Lab's "DE200" ephemeris.  Here is a description from a friend of
    mine who works at JPL, Dr. Paul A. Finlayson:
    
      "The real data source for the almanacs are the JPL ephemeris positions of
    the Earth, Sun, Moon, and any other bodies listed in the Almanac. This data
    is not obtained from formulas, but rather from a full-fidelity dynamic model
    of the solar system (including relativistic effects) expressed in terms of
    coupled differential equations which are numerically integrated. The final
    result of this numerical integration is a massive database (which is
    available on CD). Body positions (expressed in some convenient frame, such
    as J2000) as a function of time are directly obtained from that data. The
    values in the almanac can then be easily obtained from standard geometric
    transformation formulas."
    
    Some basic info about DE200 is here:
    
       http://ssd.jpl.nasa.gov/eph_info.html
    
    A detailed readme is at:
    
       http://ssd.jpl.nasa.gov/iau-comm4/README
    
    and the actual files (very large!) are here:
    
       ftp://navigator.jpl.nasa.gov/ephem/export/
    
    The results are extremely accurate, to less than a second of arc.  The
    dataset  is HUNDREDS OF MEGABYTES in size.  Hence, DE200 and its relatives
    (DE405, etc.) are sold on a CD for $24.95 here:
    
       http://www.willbell.com/software/jpl.htm
    
    The datafiles must be processed by programs before they are useful.  The
    source code to these programs are on the CD.  However, the programs provided
    are written in FORTRAN.  You must have a FORTRAN compiler on your machine in
    order to use DE200.  There are some versions that have been translated into
    C as well, but they are not definitive.  If you are not a programmer fluent
    in these languages, then use of DE200 or DE405 directly is IMPOSSIBLE!
    
    Dan Allen
    
    -----Original Message-----
    From  Navigation Mailing List
    [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of Robert Block
    Sent: Friday, November 03, 2000 9:37 AM
    To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    Subject: Re: Nautical Almanac Method Reduction
    
    download astro.zip at
    
    http://home.t-online.de/home/h.umland/page2.htm
    
    Let us know how it goes.
    
    regards
    
    robert
    S/Y Connemara
    Santa Barbara
    
    ---
    
    Can anyone tell me the formulas used to generate the numbers in both of the
    Nautical Almanac Method sight reduction tables?
    
    Thanks in advance.
    Gord
    gord{at}smartt.com
    

       
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