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    HO 211 and Calculator Almanacs
    From: Gordon Talge
    Date: 1999 Sep 07, 11:12 PM

    First HO 211:
    I have seen several HO 211s for sale at used book stores. They usually
    sell for around $3.00 to $6.00. I have also seen Ageton's later methods
    that contain HO 211 plus combine it with a later method of his.
    Second Calculator Almanacs:
    There seems to be several ideas for Calculator Almanacs.
    1) Have polynomial approximations for the Sun, Moon, Planets etc.
       a la the USNO's now out of print, "Almanac for Computers".
       HMNAO in Britain publishes almost the same thing with their
       polynomials. Matter of fact, you can take the USNO's polynomials
       and turn them into HMNAO's.
       A couple of years back I wrote a program to make these polynomials
       from DE200/LE200 the JPL ephemeris that the Nautical Almanac is
       based on.
    2) Another method is to use the French "VSOP87". An abreviated version
       is in the book, "Astronomical Alogrithms", by Jean Meeus. The full
    versions    you can get off the net from the BDL in Paris.
       The HP48 Navigation Card by Sparcom uses this. The series for
       the Moon is lifted verbatum from Meeus' book.
       For the Planets, it uses a truncated VSOP87C which is the "Heliocentric
       Dynamical Eclipitc and Equinox of the Date in rectangular coordinates
       (X,Y,Z) then converted to GHA and Dec.
       The series are "Poisson Series" which means the terms of the series
       are themselves series. A real bear to evaluate without a computer
       or high powered calculator.
       For example, a reasonable series for the Earth ( Sun ) might take
       43 terms for the 1st term of X, 3 terms for the 2nd term for X,
       and 1 term for the 3rd term for X. Duplicate this for Y.
       Things are a little better for Z. Maybe only 2 terms for only
       1 term for Z. The precision of the retained terms can be
       calculated from a little formula given nu sq(n)A where nu =2
       and n is the number of retained terms and A is the smallest
       amplitude retained.
       You can get all the info from "Planetary theories in rectangular
       and spherical variables. VSOP87 solutions" by P. Bretagnon and
       G. Francou. Astron. Astrophys. 202, 309-315 (1988).
       3) Another method which I am thinking about working on is to
          use the BDL's "Connaissance des Temps". These are chebyshev
          series that are much faster and easier to evaluate and give
          the full accuracy of the VSOP87 which has thousands of terms.
          The down side is that the polynomials have to replaced every
          year. Upside, you can get them free off the net and down load
          them into your calculator.
     -- Gordon
                                        (. .)
             |  Gordon Talge WB6YKK            e-mail: gtalge@pe.net  |
             |  Department of Mathematics      QTH: Loma Linda, CA    |
             |  Aquinas High School            Lat.  N  34� 03.1'     |
             |  San Bernardino, CA 92404       Long. W 117� 15.2'     |
             |  http://www.AquinasHS.net                              |

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