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