Gianni and others, As a long-time academic and scientist, I am acutely aware of the principles and practice of giving credit for previous work. Given the recent exchanges on calculating declination, I have sent a copy of Spencer's original paper where he published for the first time the Fourier series for declination and EoT. I had posted this to the Sundial List several years ago, but in a slightly different format. I assume this is the origin of the entry in the BSS Glossary.
I am sure that no disrespect was intended when the BSS Glossary was complied, but it would be nice if these equations were quoted as coming from Spencer. In science, this is polite, expected, and considered basic good practice. Doing otherwise is commonly known as plagiarism at worst, bad manners at best. One reply I have received in the last day or so said that he had always wondered at the source of the Fourier series for declination. He now knows. By giving the sources of equations, etc. (unless they are lost in the mists of time), people can track back to the original publication and check the mathematics or logic used to derive the information. In the case of the Spencer equations, reading the original paper in the (now defunct) journal Search would NOT pick up a typographic error in one of the equations. This was noted as an erratum in a subsequent issue of the journal. However, I have made the correction in the version I posted a day or so back. It would be nice to see the work of Spencer remembered in the BSS Glossary, perhaps as "the Spencer Fourier series to calculate declination and EoT". Cheers, John [EMAIL PROTECTED] ----- Original Message ----- From: "Gianni Ferrari" <[EMAIL PROTECTED]> To: "LISTA INGLESE" <[email protected]> Sent: Sunday, March 21, 2004 4:51 AM Subject: Re: Declination approximation? Some years ago also I have tried to find the Fourier trasform for the mean values of the Time Equation and of the Sun's Declination for each day of the year; I remember to have sent a long message to this list in the February 1998. Subsequently I have calculated the exact values of the quantities (at 11.00 UT) in each day for the years 2000 - 2047 and, from the mean values obtained from them, I have calculate the coefficients of the Fourier series. The values of the coefficients were also published in a book and in an article (about 1999-2000) These values are slightly different (but very similar) to those in John Davis' Glossary. After I have found the maximum errors in such a way : I have calculated, with these series, the Declination and the Time Equation on each day of the 48 years (2000-2047) and after I have compared the values obtained with the exact mean values calculated with the complete Meeus method. The maximum errors found in this experimental way result = ± 15 ' for the declination and ± 18 sec for the Equation of the time. For this reason I think that the error of 0.0006 rads ( = 2.1 ') is very optimistic. The Fourier transform that I have gotten ( with the quantities in degrees) is the following: D=0.3831+23.2600cos(w-169.785)+0.3551cos(2w-175.6692)+0.1342cos(3w-148.0399) + +0.0326cos(4w+2.9524) w=(N)*360/365.2421897 = 0.98564736*(N) N=1 for 1/1 ; 32 for 2/1, etc. In radians and with sin and cos : D=0.006686 - 0.399528 cosw + 0.071997 sinw - 0.006180 cos2w + 0.000468 sin2w -0.001987 cos3w + 0.001240 sin3w + 0.000568 cos4w - 0.000029 sin4w Some examples for Sun's Declination : March 21 - N=80 Davis =18.48 ' My result = 22.20 ' Mean value of the exact values (calculated on 3/21 in the years 2000-2047) = 22.44 ' 3/ 31 - N=90 Davis= 4d 13.15 ' My result = 4d 18.92 ' Exact mean value= 4d 17.48 ' 6/1 - N=152 Davis = 22d 4.43 ' My result = 22d 6.08 ' Exact mean value = 22d 6.0 ' For the calculation of the exact values I have used my program SUNEPH_0103 , distributed as bonus with "The Compendium", and that can be downloaded from our site : http://www.gnomonicaitaliana.it/index.php?area=15&article=57 To calculate the declination in hours different from 11.00 UT, it is necessary to take N = Number of the day + (Hour_UT - 11) / 24 and to use the decimal number so obtained. For instance wanting the values for 5 pm UT (noon at New York) we have to take N= Number of the day +0.25 Gianni Ferrari P.S. If someone is interested I can send the Fourier transform for of the Equation of the Time - -
