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Re: Sample Polynomials
From: Vic Fraenckel
Date: 2002 Oct 24, 10:17 -0400

```Gordon,

I was delighted to see your post concerning your computations using the JPL
Ephemerides. It has been a goal of mine to write software to have the
equilvalent of the Nautical Almanac available in machine readable form on MY
computer. To that end, I purchased the JPL Planetary and Lunar Ephemerides
CD and the book "Fundamental Ephemeris Computations for use with JPL data"
by Paul Heafner from Willmann-Bell, Inc. The CD contains DE200, DE405 and
DE406 data files.

I have worked thru the programming examples in the book and would now like
to begin developing a program that would extract data from the data files
and get the same values as the Nautical Almanac has. Your post encourages me
that it can be done. Have you any advice for me as I work on this?

Any enlightenment will be appreciated.

TIA

Vic
________________________________________________________

Victor Fraenckel - The Windman                 vfraenc1@nycap.rr.com
KC2GUI                                                      www.windsway.com

Home of the WindReader Electronic Theodolite

"Victory at all costs, victory in spite of all terror, victory however long
and hard the road may be; for without victory there is no survival."
- Winston [Leonard Spencer] Churchill (1874 - 1965)

Dost thou not know, my son, with how little wisdom the world is governed?
-Count Oxenstierna (ca 1620)

----- Original Message -----
From: "Gordon Talge" <        >
To:
Sent: Thursday, October 24, 2002 1:39 AM
Subject: Sample Polynomials

| 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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