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Sample Polynomials
From: Gordon Talge
Date: 2002 Oct 23, 22:39 -0700

```Hi,

Here are some Sample polynomials calculated by me from DE200/LE200
for Nov. 2002.

They are evaluated as follows:

f(x) = a0+a1x+a2x^2+a3x^3+a4^x4+a5x^5

Evaluate with Horner's Method:

b5=xa5

b4 = x(a4+b5)
b3 = x(a3+b4)
b2 = x(a2+b3)
b1 = x(a1+b2)
f(x) = a0 + b1

d = day of month
UT = Univ Time ( GMT ) in hours

t = d + UT/24

x = ((t-W)/A)-1

W = weight for Sun.

A = 16 .0  1/2 way mark

Example:

GHA and Dec Sun Nov 11, 2002 at 11h 11min 11 sec UT

t = 11.4661

x = -0.3459

GHA Sun = 3951.17852 degs
Remove multiples of 360 degs

--> GHA Sun = 351.7902 or 351 degs 47.4 min

--> Dec Sun = -17.4393 degs or S 17 degs 26.4 mins

--> SD = .2695 and .2695 x 60 = 16.1725 or 16.2 mins.

Nautical Almanac gives:

Nov 11 at 11h

348 degs 59.6 mins     Dec S 17 degs 26.2 mins  SD 16.2 mins

d correction  +0.7

Correction 11 min 11 sec 2 degs 47.8 min for GHA and +0.1 for Dec

--> GHA is 351 degs 47.4 mins and Dec S 17 degs 26.3 mins SD 16.2 min

I tried to get the polynomials to match the Almanac to 0.1 min of Arc.

The NA does say that "The tabulated hourly values of the Sun's GHA have
been adjusted to reduce to a minimum the error caused by treating v as
negligible".

I have generally found that the polynomials match better to the "Air
Almanac"
then the "Nautical Almanac". I do not have a 2002 copy of the "Air
Almanac"
to Check however.

The Polynomials are valid for 32 days, starting at Nov 1, 2002 0h 00m
00s UT.

The Polynomials for the Navigation Planets are all valid for 1 month
each,
For the Moon, 8 days with 8 terms. Includes polynomial for H.P.

-- Gordon

Dates:  Nov.  1 - Nov. 32

A = 16.0   W = 1

Aries        Sun          Sun           Sun
GHA          GHA          Dec.          S.D.
Term              �            �            �            �
0           5815.8788    5943.7870     -18.8849        .2699
1           5775.7703    5759.2473      -3.9398        .0010
2               .0001       -.4415        .7179       -.0001
3               .0008        .0066        .0687        .0000
4               .0000        .0090       -.0040        .0000
5              -.0006        .0034        .0008        .0000

Sums         11591.6494   11702.6118     -22.0413        .2708

```
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