Thank you, Frank, for that comprehensive analysis of the problem. However, I wonder if the errors might be masked by the 32 arc minute solar penumbra.
Best wishes, Geoff On 19 January 2017 at 16:33, Frank King <f...@cl.cam.ac.uk> wrote: > Dear John, > > I wondered when someone would spot that there is a > whole can of worms waiting to be opened here... > > > Won't the factors that necessitate the addition > > of a leap day prevent this alignment from > > happening at exactly 11/11 11:11 every year? > > Quite so. No doubt you looked at the time-lapse > video and spotted that the circle of light DIDN'T > properly centre itself on the Great Seal of the > United States. This is surely only one step less > sinful than being disrespectful to the US flag? > > OK, take a deep breath and see what we are up > against... > > First we need to be clear what is meant by the > time 11:11? I assume this is clock time in > Anthem, Arizona, and a little research suggests > they are on Mountain Time there and that they > don't observe Daylight Saving. [Just think how > the whole scheme could be wrecked if they did > go over to Daylight Saving and the clocks didn't > go back until after 11 November!] > > To me, their interest is at 18:11:00 UTC but that > is a detail. > > The big difficulty is that, at this exact time of > day, the solar declination varies with the leap > year cycle and there is a steady drift. As a > result both the solar altitude and solar azimuth > vary from one year to the next. Let's see by > how much... > > I'll take it that the Geographical Coordinates > of Anthem are: > > 33° 51' 15" N 112° 7' 30" > > Using GCstudio I determined the following data > for 10 years starting in 2016, a leap year: > > 2016 -17°41'09" +36°25'01" +161°40'45" > 2017 -17°37'11" +36°28'55" +161°39'53" > 2018 -17°33'13" +36°32'52" +161°39'05" > 2019 -17°29'12" +36°36'55" +161°38'33" > 2020 -17°41'38" +36°24'36" +161°41'11" > 2021 -17°37'47" +36°28'23" +161°40'14" > 2022 -17°33'48" +36°32'21" +161°39'31" > 2023 -17°29'52" +36°36'14" +161°38'36" > 2024 -17°42'18" +36°23'55" +161°41'16" > 2025 -17°38'23" +36°27'48" +161°40'23" > > The four columns show: year, declination, alt, az > as they are at Anthem at 11:11:00 Mountain Time > on 11 November in the 10 years shown. > > Take declination first. You see that starting in > 2016 the declination gets about 4 minutes less > negative on successive years until there is a > sudden jump back which is A LITTLE TOO BIG. > This sets the pattern. We become less negative > until 2024 when there is another jump. > > The jumps back over-compensate because the tropical > year is slightly less than 365.25 days. > > You will see that the solar altitude increases by > just under 4' a year before falling back just over > 12' in a leap year. You will see that even in this > little table the range of altitudes is about 11' > and this will be noticed by careful observers. > > The azimuth varies too of course but by not so > much and its main effect is to make you have to > worry about just how to align the slabs. > > OK, what should they have done? > > Well one approach is to settle on the 2016 figures > and note that over the next 36 years the data for > 2016 will be somewhere near the middle. After > that the drift will become more noticeable but the > designer will probably be dead and won't care. > > Things gradually get worse and worse until The > Great Correction over the years 2096 to 2004 > when the omission of a leap year in 2100 will > reverse some of the damage. > > Most people know that the Gregorian Calendar > was an improvement over the Julian Calendar but > almost all readers of this list will live their > entire lives enduring pure Julian Drift. > > This is a massive imposition and we should all > be lobbying for a much better 33-year Calendar > originally designed by Omar Khayyam in 1079, > long before John Dee and others rediscovered > it. This was over 500 years before Pope > Gregory's tinkering in 1582. Why didn't > Pope Gregory do a proper job then? > > That's a long story but the result is that we > are lumbered with an unhelpful calendar which > is, I suppose, upward-compatible with its > predecessor. > > I share the view that "upward-compatibility is > the business of deliberately not putting right > someone else's mistakes". > > Many apologies. Another rant I fear! > > Very best wishes > > Frank > > Frank King > Cambridge, U.K. > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > >
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