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I found that the solstices work on a 400 year cycle based on this. I can't find anything similar for the lunar cycle. Is there a formula I can use to calculate the date of the full moon?

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is that good enough for you? en.wikipedia.org/wiki/Full_moon#Formula –  DrCopyPaste Jun 13 at 13:43
    
14.5 hours is a pretty large margin of error. Easily enough to give a false positive or negative. If there isn't a better formula, I can make do, but I was hoping for something more accurate –  Bishop Jun 13 at 14:42
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Beware of media-defined notions such as "coincide". This is similar to the "alignment of planets" - they are aligned only according to some lax definition. So, regarding your coincidence, what is the margin of error? One day? And if it's one day, in what time zone? As you can see, these are complex questions in reality. It's just the profit-driven media that dumbs them down and makes them into seemingly simple soundbites. –  Florin Andrei Jun 13 at 16:12
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If you're talking about an exact coincidence, it virtually never happens. If you're willing to accept a two-week margin of error, it happens almost every year. The 400-year cycle is an artifact of the Gregorian calendar, which has no effect on when or how closely the solstice and the full moon coincide. –  Keith Thompson Jun 13 at 18:19
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@Bishop: The solstice is a single moment. For example, this year's summer solstice occurs at about 10:51 UTC on June 21. –  Keith Thompson Jun 13 at 20:18

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Florin Andrei what evidence can you supply to charge the oldest scientific body on this planet (The Royal Society at Greenwich) to be a profit-driven media entity.

Bishop, if you are asking when the 2 specific points in time match, it is true that they have a 'astronomical' infrequency to look at. But if you look at what the common terms for the definition of a solstice and full moon occurring at the same time, then it is not too infrequent. Matching a 24 hour period (solstice day) against a 72 hour period (a full moon) then they occur with a much more reasonable frequency. There are lots of lunar cycle calculators around. The current cycle we are in has the same middle day of the full moon period In 2004, 2007, 2015, 2026, 2034, 2042 and 2045. further dates can be found using this http://aa.usno.navy.mil. Just chose any date, calculate the drift on your 400 year cycle then calculate how often that drift occurs at the same time as the 3 day phase of the full moon drift. There will be large periods when the match occurs rarely (The center point of each phase occurring furthest apart). As the centre points close on each other the Frequency will increase. The recurring pattern of all astronomic movements.

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Exactly what I as looking for. Thanks! –  Bishop yesterday

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