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    Pocket Calculator Almanac
    From: Gordon Talge
    Date: 2005 Feb 12, 00:58 -0800

    I noticed a discussion about Navigation with a pocket calculator.
    
    A few years ago I wrote a program to compute the polynomial
    coefficients of the GHA, Dec, and SD of the Sun, Moon, and Planets
    from JPL's DE200/LE200.
    
    I did a printout of the Sun for 2005. Maybe someone might
    be interested. I do not have a current almanac, so I am
    not able to check the output. The figures should
    (I hope) be within 0.1' of the Air Almanac. These calculations
    are my own and unofficial. The authority is the NAO/AA not
    me. I just did it for fun.
    
    -- Gordon
    
    --
                                  ,,,
                                 (. .)
    +-------------------------ooO-(_)-Ooo------------------------+
    | Gordon Talge WB6YKK         mail: gtalge AT silcon DOT com |
    | (o-    Debian / GNU / Linux                                |
    | //\    The Choice of the GNU Generation                    |
    | v_/_                  .oooO                                |
    |    - E Aho Laula -     (  )   Oooo. - Wider is Better -    |
    +-------------------------\ (---(  )-------------------------+
                               \_)  ) /
                                   (_/
    How to use the Sun Polynomials by Gordon Talge.
    
    The Sun Polynomials follow the now defunct "Almanac for Computers" that
    used to be published by the NAO USNO in Washington D.C. for use with
    pocket calculators.
    
    I have also done the same for the Navigational Planets and the Moon,
    but not the stars.
    
    
    Here is how they are used by example.
    
    Suppose we want to know the GHA, Dec, and SD of the Sun for July 5, 2005
    at 00h 00m 00s UT (GMT).
    
    -------------------------------------------------------------------------------
    
                             Dates:  Jul.  1 - Jul. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           6054.9169    5938.4742      21.2173       0.2626
      1           5775.7705    5759.6584      -2.7037       0.0003
      2              0.0003       0.2879      -0.7651       0.0001
      3              0.0000       0.0258       0.0427       0.0000
      4             -0.0003      -0.0133       0.0030       0.0000
      5              0.0001       0.0022      -0.0008       0.0000
    
    Sums         11830.6875   11698.4352      17.7934       0.2630
    
    -------------------------------------------------------------------------------
    
    First, we compute  t, where t = d + UT/24,  UT is expressed in hours, and d
    is the day of the month.
    
    So in our case UT=0.0 and d=5, thus t=5.0
    
    Second, we compute x, where x = ((t-W)/A)-1. If done right x will be
    in the range -1 <= x <= +1.
    
    Now for July A=16.0 and W=1.0 so, x = ((5-1)/16)-1 so,
    x = -0.75.
    
    The terms in the above table are the terms of a polynomial in the
    form
        f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4 + a5x^5.
    
        (The sums are just for a check to see if they were entered right
         in your program. They are not part of any calculations.)
    
        It is (usually) better to evaluate this like
    
        f(x) = a0 +x(a1+x(a2+x(a3+x(a4+xa5)))).
    
        For the GHA of the Sun we have
    
        f(x) = 5938.4742+x(5769.6584+x(0.2879+x(0.0258+x(-0.0133+x0.0022)))).
    
        so for f(-0.75) we get 1618.8767 for the GHA
    
    Next we remove multiples of 360 degrees so
        the GHA is now 178.8767 in decimal form.
    
        We convert it to dms form by multipling .8767 by 60 to get
    
        52.6037. Thus the GHA is 178 degs 52.6' rounded to the nearest minute.
    
    Declination is next with Dec being 22.7978 or 22 degs 47.8693 rounded
    we get N 22 degs 47.9' ( positive number is N, negative is S ).
    
    Last the SD is done the same way. We get 0.2624 and multiplying it by 60
    the result is 15.7459' or 15.7'
    
    So, for July 5, 2005 at 00h 00m 00s for the Sun we get
    
               GHA 178 degs 52.6'
               Dec N 22 degs 47.9'
               SD 15.7'
    
    ------------------------------------------------------------------------------
    
                     Power Series for Sun and Aries,  2005
    
    
                             Dates:  Jan.  1 - Jan. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5876.5142    5937.4963     -20.7645       0.2713
      1           5775.7706    5758.6728       3.1445      -0.0003
      2              0.0000       0.3843       0.8406      -0.0002
      3             -0.0001       0.0472      -0.0637       0.0000
      4             -0.0001      -0.0184      -0.0055       0.0000
      5             -0.0001      -0.0006       0.0019       0.0000
    
    Sums         11652.2845   11696.5816     -16.8467       0.2708
    
                             Dates:  Feb.  1 - Feb. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5907.0694    5936.4898     -12.0233       0.2701
      1           5775.7702    5760.2832       5.5956      -0.0009
      2              0.0000       0.3817       0.4044      -0.0001
      3              0.0002      -0.0390      -0.0793       0.0000
      4             -0.0001      -0.0115       0.0029       0.0000
      5              0.0000       0.0019       0.0007       0.0000
    
    Sums         11682.8397   11697.1061      -6.0990       0.2691
    
                             Dates:  Mar.  1 - Mar. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5934.6674    5937.8824      -1.3928       0.2682
      1           5775.7701    5761.1484       6.3265      -0.0012
      2              0.0000       0.1117       0.0133       0.0000
      3              0.0002      -0.0565      -0.0714       0.0000
      4             -0.0001      -0.0049       0.0037       0.0000
      5              0.0000       0.0000       0.0006       0.0000
    
    Sums         11710.4376   11699.0811       4.8799       0.2670
    
                             Dates:  Apr.  1 - Apr. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5965.2223    5940.0877      10.4352       0.2659
      1           5775.7702    5760.9267       5.6353      -0.0012
      2             -0.0001      -0.1950      -0.3715       0.0000
      3              0.0001      -0.0417      -0.0627       0.0000
      4              0.0002      -0.0001       0.0033       0.0000
      5              0.0000       0.0007      -0.0002       0.0000
    
    Sums         11740.9927   11700.7783      15.6394       0.2647
    
                             Dates:  May   1 - May  32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5994.7918    5940.9106      19.3029       0.2639
      1           5775.7705    5759.8907       3.6146      -0.0008
      2              0.0000      -0.2895      -0.7012       0.0001
      3              0.0001       0.0120      -0.0489       0.0000
      4              0.0001       0.0036       0.0051       0.0000
      5             -0.0001       0.0004      -0.0004       0.0000
    
    Sums         11770.5624   11700.5278      22.1721       0.2632
    
                             Dates:  Jun.  1 - Jun. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           6025.3472    5939.7992      23.3777       0.2627
      1           5775.7707    5759.1384       0.4712      -0.0003
      2              0.0002      -0.0287      -0.8802       0.0001
      3             -0.0001       0.0614      -0.0042       0.0000
      4             -0.0002      -0.0037       0.0073       0.0000
      5              0.0000       0.0005      -0.0009       0.0000
    
    Sums         11801.1178   11698.9671      22.9709       0.2625
    
                             Dates:  Jul.  1 - Jul. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           6054.9169    5938.4742      21.2173       0.2626
      1           5775.7705    5759.6584      -2.7037       0.0003
      2              0.0003       0.2879      -0.7651       0.0001
      3              0.0000       0.0258       0.0427       0.0000
      4             -0.0003      -0.0133       0.0030       0.0000
      5              0.0001       0.0022      -0.0008       0.0000
    
    Sums         11830.6875   11698.4352      17.7934       0.2630
    
                             Dates:  Aug.  1 - Aug. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           6085.4722    5938.9684      13.4571       0.2636
      1           5775.7703    5760.8532      -5.1015       0.0008
      2             -0.0001       0.2779      -0.4523       0.0001
      3              0.0000      -0.0390       0.0571       0.0000
      4              0.0001      -0.0089      -0.0013       0.0000
      5              0.0000       0.0038       0.0008       0.0000
    
    Sums         11861.2425   11700.0554       7.9599       0.2645
    
                             Dates:  Sep.  1 - Sep. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           6116.0272    5941.3466       2.3018       0.2655
      1           5775.7704    5761.4320      -6.1798       0.0012
      2             -0.0002       0.0021      -0.0973       0.0000
      3             -0.0003      -0.0657       0.0586       0.0000
      4              0.0002      -0.0024      -0.0003       0.0000
      5              0.0001       0.0037       0.0020       0.0000
    
    Sums         11891.7974   11702.7163      -3.9150       0.2667
    
                             Dates:  Oct.  1 - Oct. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5785.5964    5943.6421      -9.2079       0.2678
      1           5775.7704    5760.8271      -5.8549       0.0012
      2              0.0001      -0.3139       0.2820      -0.0001
      3             -0.0002      -0.0578       0.0682       0.0000
      4             -0.0001       0.0030       0.0012       0.0000
      5              0.0000       0.0041       0.0019       0.0000
    
    Sums         11561.3666   11704.1046     -14.7095       0.2689
    
                             Dates:  Nov.  1 - Nov. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5816.1515    5943.7747     -18.9534       0.2699
      1           5775.7704    5759.2319      -3.9153       0.0009
      2              0.0001      -0.4464       0.7189      -0.0002
      3              0.0001       0.0054       0.0689       0.0000
      4             -0.0001       0.0126      -0.0020       0.0000
      5              0.0000       0.0043       0.0004       0.0000
    
    Sums         11591.9220   11702.5825     -22.0825       0.2706
    
                             Dates:  Dec.  1 - Dec. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              ?            ?            ?            ?
      0           5845.7213    5941.0152     -23.3515       0.2712
      1           5775.7705    5758.0535      -0.5973       0.0004
      2             -0.0001      -0.1069       0.9951      -0.0002
      3              0.0000       0.0841       0.0153       0.0000
      4              0.0001       0.0050      -0.0096       0.0000
      5              0.0001       0.0018      -0.0003       0.0000
    
    Sums         11621.4919   11699.0527     -22.9483       0.2714
    
    -------------------------------------------------------------------------------
    These are the output of a small Pascal program (I wrote a few years ago)
    for July 2005 at 00h 00m 00s UT for each day of the month using the
    above table. (ie the program actually reads the ascii table)
    
    I do not have a current 2005 Nautical Almanac so I have not been able
    to check the values.
    
    1
    
    GHA Aries 279? 8.8'
    Equation of Time - 3m 45.0s
    GHA Sun 179? 3.7'   Dec. N23? 7.0'   SD 15.7'
    
    2
    
    GHA Aries 280? 7.9'
    Equation of Time - 3m 56.6s
    GHA Sun 179? 0.9'   Dec. N23? 2.8'   SD 15.7'
    
    3
    
    GHA Aries 281? 7.1'
    Equation of Time - 4m 7.8s
    GHA Sun 178? 58.0'   Dec. N22? 58.2'   SD 15.7'
    
    4
    
    GHA Aries 282? 6.2'
    Equation of Time - 4m 18.9s
    GHA Sun 178? 55.3'   Dec. N22? 53.3'   SD 15.7'
    
    5
    
    GHA Aries 283? 5.3'
    Equation of Time - 4m 29.6s
    GHA Sun 178? 52.6'   Dec. N22? 47.9'   SD 15.7'
    
    6
    
    GHA Aries 284? 4.5'
    Equation of Time - 4m 40.0s
    GHA Sun 178? 50.0'   Dec. N22? 42.1'   SD 15.7'
    
    7
    
    GHA Aries 285? 3.6'
    Equation of Time - 4m 50.0s
    GHA Sun 178? 47.5'   Dec. N22? 35.9'   SD 15.7'
    
    8
    
    GHA Aries 286? 2.8'
    Equation of Time - 4m 59.7s
    GHA Sun 178? 45.1'   Dec. N22? 29.3'   SD 15.7'
    
    9
    
    GHA Aries 287? 1.9'
    Equation of Time - 5m 8.9s
    GHA Sun 178? 42.8'   Dec. N22? 22.4'   SD 15.7'
    
    10
    
    GHA Aries 288? 1.0'
    Equation of Time - 5m 17.7s
    GHA Sun 178? 40.6'   Dec. N22? 15.0'   SD 15.7'
    
    11
    
    GHA Aries 289? 0.2'
    Equation of Time - 5m 26.1s
    GHA Sun 178? 38.5'   Dec. N22? 7.3'   SD 15.8'
    
    12
    
    GHA Aries 289? 59.3'
    Equation of Time - 5m 34.0s
    GHA Sun 178? 36.5'   Dec. N21? 59.2'   SD 15.8'
    
    13
    
    GHA Aries 290? 58.5'
    Equation of Time - 5m 41.5s
    GHA Sun 178? 34.6'   Dec. N21? 50.7'   SD 15.8'
    
    14
    
    GHA Aries 291? 57.6'
    Equation of Time - 5m 48.4s
    GHA Sun 178? 32.9'   Dec. N21? 41.8'   SD 15.8'
    
    15
    
    GHA Aries 292? 56.7'
    Equation of Time - 5m 54.9s
    GHA Sun 178? 31.3'   Dec. N21? 32.6'   SD 15.8'
    
    16
    
    GHA Aries 293? 55.9'
    Equation of Time - 6m 0.8s
    GHA Sun 178? 29.8'   Dec. N21? 23.0'   SD 15.8'
    
    17
    
    GHA Aries 294? 55.0'
    Equation of Time - 6m 6.2s
    GHA Sun 178? 28.5'   Dec. N21? 13.0'   SD 15.8'
    
    18
    
    GHA Aries 295? 54.2'
    Equation of Time - 6m 11.0s
    GHA Sun 178? 27.2'   Dec. N21? 2.7'   SD 15.8'
    
    19
    
    GHA Aries 296? 53.3'
    Equation of Time - 6m 15.3s
    GHA Sun 178? 26.2'   Dec. N20? 52.0'   SD 15.8'
    
    20
    
    GHA Aries 297? 52.4'
    Equation of Time - 6m 19.1s
    GHA Sun 178? 25.2'   Dec. N20? 41.0'   SD 15.8'
    
    21
    
    GHA Aries 298? 51.6'
    Equation of Time - 6m 22.3s
    GHA Sun 178? 24.4'   Dec. N20? 29.7'   SD 15.8'
    
    22
    
    GHA Aries 299? 50.7'
    Equation of Time - 6m 24.9s
    GHA Sun 178? 23.8'   Dec. N20? 17.9'   SD 15.8'
    
    23
    
    GHA Aries 300? 49.9'
    Equation of Time - 6m 27.0s
    GHA Sun 178? 23.3'   Dec. N20? 5.9'   SD 15.8'
    
    24
    
    GHA Aries 301? 49.0'
    Equation of Time - 6m 28.4s
    GHA Sun 178? 22.9'   Dec. N19? 53.5'   SD 15.8'
    
    25
    
    GHA Aries 302? 48.1'
    Equation of Time - 6m 29.3s
    GHA Sun 178? 22.7'   Dec. N19? 40.8'   SD 15.8'
    
    26
    
    GHA Aries 303? 47.3'
    Equation of Time - 6m 29.6s
    GHA Sun 178? 22.6'   Dec. N19? 27.7'   SD 15.8'
    
    27
    
    GHA Aries 304? 46.4'
    Equation of Time - 6m 29.4s
    GHA Sun 178? 22.7'   Dec. N19? 14.4'   SD 15.8'
    
    28
    
    GHA Aries 305? 45.6'
    Equation of Time - 6m 28.5s
    GHA Sun 178? 22.9'   Dec. N19? 0.7'   SD 15.8'
    
    29
    
    GHA Aries 306? 44.7'
    Equation of Time - 6m 27.1s
    GHA Sun 178? 23.2'   Dec. N18? 46.7'   SD 15.8'
    
    30
    
    GHA Aries 307? 43.8'
    Equation of Time - 6m 25.1s
    GHA Sun 178? 23.7'   Dec. N18? 32.4'   SD 15.8'
    
    31
    
    GHA Aries 308? 43.0'
    Equation of Time - 6m 22.5s
    GHA Sun 178? 24.4'   Dec. N18? 17.7'   SD 15.8'
    
    
    
    
    

       
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