On 12/20/2010 09:57 AM, Mauro Lacy wrote: > On 12/19/2010 05:01 PM, Mauro Lacy wrote: >> On 12/19/2010 04:44 PM, Mauro Lacy wrote: >>> On 12/19/2010 01:28 PM, Mauro Lacy wrote: >>>> Here's an open version of the same database: >>>> http://www.hermit.org/Eclipse/when_search.shtml >>>> I've downloaded the raw file, and after searching for total lunar >>>> eclipses from Dec 19 to Dec 23, post Oct 15 1582(before that, Julian >>>> dates are used), I've found the following "solstice eclipse" candidates: >>>> >>>> 1638|12|21|01:59|L|T|N-|119||-0.139|2.632|1.605|12960|5760||| >>>> 1703|12|23|06:30|L|T|S-|120||0.025|2.891|1.763|14160|6360||| >>>> 1768|12|23|15:07|L|T|S-|121||0.060|2.770|1.757|12840|6000||| >>>> 1945|12|19|02:20|L|T||124||-0.284|2.355|1.348|12360|4800||| >>>> 1964|12|19|02:37|L|T||134||0.380|2.171|1.180|11760|3600||| >>>> 2010|12|21|08:17|L|T||125||0.321|2.306|1.261|12600|4440||| >>> Wolfram Alpha gives solstice dates for each year easily. According to >>> wolframalpha, the (northern hemisphere) winter solstice for the year >>> 1703 occurred Saturday, December 23, 7:04 am LMT. >>> http://www.wolframalpha.com/input/?i=1703+northern+hemisphere+winter+solstice+date >>> >>> LMT stands for Local Mean Time(an old form of timezone, it seems), >>> because wolfram alpha likes to give local times, based on the location >>> of the questioner. Searching on how to convert from LMT to GMT(UT), for >>> western latitudes you have to add the local latitude in degrees divided >>> by 15 degrees. So, 7:04 am LMT in my latitude is around 11:04 am GMT. >>> >>> The last time an eclipse coincided with a (northern hemisphere winter) >>> solstice, then, was December 23, 1703. Not that this is important, of >>> course, but is in the name of precision, and of course, of being picky. >> In the name of precision (and of being picky) that is wrong. I misread >> the date of the solstice, which is December 22, not 23. This is off then >> by around 20 hours. >> So, neither of those dates coincide with a solstice inside the 24 hours >> range, and the closer one is December 21, 1638. >>> According to the same, the winter solstice date for 1638 was 12:20 pm >>> LMT, Tuesday, December 21. That date is around 16 pm GMT for my >>> latitude, so the lunar eclipse of that day is out of the 24 hours rule >>> established before(by a margin of about 2 hours), even when it happened >>> on the same calendar day. >>> >>> Calculating the precise solstice time for the year 1554 is left as an >>> exercise for the picky. > Above I meant longitude, not latitude, or course. > > Using wolfram alpha again(which is a wonderful tool), I've got the > following for 1554: > http://www.wolframalpha.com/input/?i=december+1554+lunar+eclipse > A partial lunar eclipse on 9:38 pm LMT, December 8, 1554, Julian calendar. > > The solstice that year occurs on: > http://www.wolframalpha.com/input/?i=1554+northern+hemisphere+winter+solstice > Wednesday, December 12, 1554, Julian calendar. > > There's a relatively close match that year, but the eclipse is partial, > and the difference is 4 days > > It seems that a difference of +/- 12 hours is too narrow. Not even > tomorrow's eclipse qualify to that. I'll now look for coincidences in > the 24 hour range(+/- 24 hours) to finally settle how rare is tomorrow's > eclipse. Well, here are the solstice eclipses for year 0 to 3000. This is, total lunar eclipses separated by less than 24 hours from the winter solstice. Dates are gregorian or extrapolated gregorian. 0093|12|19|14:51|L|T|S-|65||0.100|2.753|1.628|14040|6120|||23.4 0158|12|22|01:59|L|T|N-|66||-0.168|2.568|1.562|12600|5640|||17.13 0875|12|20|10:43|L|T||97||-0.341|2.245|1.249|12000|4200|||23.71 1247|12|20|18:53|L|T|S-|103||0.093|2.698|1.707|12600|5760|||23.11 1638|12|21|01:59|L|T|N-|119||-0.139|2.632|1.605|12960|5760|||14.33 1703|12|23|06:30|L|T|S-|120||0.025|2.891|1.763|14160|6360|||19.5 2010|12|21|08:17|L|T||125||0.321|2.306|1.261|12600|4440|||16.35 2029|12|20|22:42|L|T||135||-0.381|2.227|1.122|12840|3240|||16.65 2094|12|21|19:53|L|T|S-|136||0.202|2.539|1.467|13320|5520|||9.85 2401|12|21|01:39|L|T|S-|141||0.130|2.693|1.576|13920|6000|||20.91 2466|12|22|01:01|L|T||142||-0.273|2.398|1.346|12840|4920|||7.78 2485|12|21|22:02|L|T||152||0.413|2.116|1.116|11640|3000|||14.11 2857|12|22|05:21|L|T|N-|158||-0.037|2.801|1.810|12720|5880|||14.5
The last added column is the difference in hours between solstice and eclipse. The mean in years for the occurence of an eclipse of this kind is of around 250 years, but they tend to group sometimes, separated by 19 or 65 years. In fact, there will be another in the year 2029, and another in 2094. They can also be separated by 717 years, and probably more. It was fun to calculate this. I've done similar calculations in the past, by example to determine the epoch in which solstice and perihelion coincided. That was in the XIII century, the coincidence averaging around the year 1260 AD. That coincidence is a one in 25000 years event, by the way.
