In 2016, the summer solstice will coincide with a full moon. How often does this happen?

• 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?

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

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.

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.

@KeithThompson, so if I wanted to calculate the closest those two occur to each other, which two formulas would I use?

@FlorinAndrei, I see your point. The solstice is by definition a day, correct? Then I guess I'd be looking for the 24 hour period including both the solstice and the full moon

@Bishop: The solstice is a single moment. For example, this year's summer solstice occurs at about 10:51 UTC on June 21.

Since the summer solstice and full moon are pretty much independent, the chance there will be a full moon on the summer solstice (to the nearest day) is about 1 in 29.5, the same as it would be for any other randomly chosen day.

If you're REALLY curious, you can see a list of moon phases at http://eclipse.gsfc.nasa.gov/phase/phasecat.html and the length of the year (time between solstices) at http://en.wikipedia.org/wiki/Tropical_year#Mean_tropical_year_current_value combined with http://www.erh.noaa.gov/box/equinox.html to compute more exact answers.

I'm no statistician but I would think a full moon being on the summer solstice would be about 1 in 28 years. The lunar cycle is about 28 days. But most sites I've seen say it happens once in 70 years.

8 years ago

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.