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--- Begin Message ---Dear Frank, I am asking for more clarification, confident that we will get some useful replies, from the astronomers at least. Taking the three sets of solutions, should we not inject some slide-rule realism? Or figuratively, where are the error bars? Taking a very simple thought process, can we check these results by observation? Regrettably there is no gossamer-fine grid in the sky, so that the virtual grid is derived by other observations and mathematical construction. The logical questions are: who is making the observations? Are they recent? Do they have any errors? I assume that wide-field photography of the stars is the basis of the observations and hence the derivation of the constants in the formulae. I assume that the data is fed into the Bureau Internationale de l’Huere. Finally, why do the three ’solutions’ give different results? Or, should we take an arithmetic mean and do some rounding? In general I remind myself that Kepler used Brahe’s naked eye observations to show that the earth has an elliptical orbit when it is damn-near circular! Regards, Doug > On 4 Oct 2019, at 13:58, Frank King <[email protected]> wrote: > > Dear Hervé, > > Congratulations on your comments on my > puzzle about the September Equinox last > month... > >> It seems that the answer to your question >> can be found in the attached picture >> inclosed in a recent information letter >> issued by the French IMCCE institute >> specialised in celestial mechanics and >> ephemerides calculations > > This gives us three times of interest on > 23 September 2009: > > 07:49:51.80 Right Ascension = 12h > > 07:50:11.81 Solar Longitude = 180 > > 07:50:15.58 Solar Declination = 0 > > Call this the FRENCH solution. > > If you have an Android cell 'phone you > can look at Sol et Umbra which gives > these times on 23 September 2009: > > 07:49:49.40 Solar Declination = 0 > > 07:50:09.25 Solar Longitude = 180 > > 07:50:32.50 Right Ascension = 12h > > Note that the events occur in reverse > order! Call this the ITALIAN solution. > > Now use the JPL Horizons program: > > https://ssd.jpl.nasa.gov/horizons.cgi > > I don't have a proper computer at the > moment but here are three values I found > (using my 'phone) for the single time: > > 23 September 2019 07:50:12.00 > > Solar Declination = 00:06:13.3 > > Solar Longitude = 180.0019964 > > Right Ascension = 11:59:01.94 > > The declination has not yet dropped to > zero. > > The longitude has gone past 180. > > The Right Ascension has not yet > reached 12h. > > Call this the U.S. solution. > > Moral: never believe a single source > of information :-) > > If you think you can see the pattern, > try using the Horizons program to > investigate the March Equinox in > 1718. Using the Gregorian Calendar, > we find: > > The Right Ascension went to zero > late on 16 March (just before > midnight). > > The declination went through zero > about the same time on 16 March. > > The solar longitude reached zero > on 21 March. FIVE DAYS LATER!!! > > So you see: there is still a little > bit more of my puzzle to unravel!! > > Very best wishes > Frank > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial >
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