Hi all, in a private message Mario Catamo has remarked that in the table of the Sun's declination calculated by Thibaud Taudin-Chabot, and from him published in his URL http://www.chabot.demon.nl/sundials/SunMeanGMT.htm, there are some values different from those that are found on many books on Sundials.
Since, time ago, I had interested in this matter for the search of a development of the declination in Fourier serie (perhaps some old member of this list remembers this) I have printed and checked with attention the Thibaud's table comparing his values with mine. I have also calculated again the mean values of the Sun's declination for the years 2000-2099 with the methods described in "Astronomic Algorithms" of J. Meeus and with the programs of Jeffrey Sax, sold with the book. On the basis of my results I think that in the calculation of Thibaud ...... there is an error (perhaps in transcribing a formula). In fact the values that I've found are different (and in some cases enough different) from those of the Thibaud Table (from now shortened in TT) . I make some examples: - From TT I've found (with interpolation) that the Spring Equinox (Decl. =0) is on 22 Mar at 23h (about). Now between 2000 and 2099 the Equinox will be between the 21.04 Mar (on 3/21 only in 2003 and in 2007) and on 19.58 Mar: The mean is 20.4 Mar (from Astronomical Tables of J. Meeus) >From the values calculated by me the instant in which Decl=0 is on 20 Mar at 7.2h GMT The error from TT is greater then 2 days - From TT the Summer Solstice (the Decl. is maximum) happens on 19 Jun. According to Meeus it will happen instead between 21.8 (in 2004) and 20.27 Jun (in 2096), with a mean on 21.0 Jun - on 20 Mar : from TT we have a Decl = -0.9939d, I find -0.1194d with a difference of 52.5 ' - on 1 Jan : from TT we have a Decl. = -23.1027d, I find -23.0077d with a difference of 5.7 ' - on 15 Aug : from TT we have a Decl. = 12.9008d, I find 14.0003 with a difference of 1d 6 ' - on 1 Oct : from TT we have a Decl. = -4.3394, I find -3.2306 with a difference of 1d 7 ' etc. I invite others to verify these data to reach some correct results ------------------------------------------------- I would like to notice that the use of mean values of the Sun's Decl. calculated on a very long period can give the feeling of a great precision , but this it is not always true. The precision comes also from the local instant of calculation (the hour 12h GMT is the 24h in Australia !), from the period of time in which we think our sundial will work and obviously from the dimension of the dial. If we think to make a very great sundial that will remain for one century or more, then we can use a table of mean values made on a period of 100 or more years, but if our sundial will have a duration only of 20-40 years (or it is of small dimensions) I think it's (perhaps) better to use a table of mean values done on a period of 10-20 years (at most). For dials of small dimensions the tables with the mean values on only 4 years are enough. For example ; the mean values from the 2000-2099 give a maximum error on the real value of the Sun's Decl. (at local 12h in a whatever day of the same period) of about 18 ' The mean values - done at the local 12h - for the period 2000-2003 (4 years) give a maximum error in a whatever day of the next 50 years inferior to 17' (the error can arrive to 27 ' if we extend the period till the year 2100) We can have the greatest errors using the tables calculated about in 1980 at 0h GMT and not at the 12h (local) (published in several books): in this cases for the next 50 years the maximum error can reach 31 ' Best Gianni Ferrari P.S. In my opinion for the calculation of the sundials the values of the Time Equation should be given with the sign changed in comparison to the Thibaud's table (for instance positive on1 Jen) even if the astronomers use them with this sign
