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Pocket Calculator Almanac
From: Gordon Talge
Date: 2005 Feb 12, 00:58 -0800
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 |
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(_/
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'
