BackEveryone will have heard of the phrase "once in a Blue Moon", meaning very rarely, but how many people know what it actually means? It is of course possible for the Moon to look blue in a literal sense, if its light has passed through a smoke haze, for example. However, the usual meaning is the one taken from folk-lore where a Blue Moon is an "extra" Full Moon in some way. One early usage was to refer to the thirteenth Full Moon in a year - about one year in three has such an "extra". Years were divided into Quarters (and still are for some religious and legal purposes) with the Quarters starting on each equinox and solstice. One Quarter would usually have three Full Moons: the first one after the start of the Quarter was called the "early" Moon, the next after that the "mid" Moon and the one just before the end of the Quarter the "late" Moon. If a fourth Full Moon appeared it was deemed a Blue Moon: by the above definitions it would be the third one in the sequence. Now, if twelve months contain thirteen Full Moons at least one of them must have two Full Moons. Due to a misinterpretation of the original meaning, Blue Moon came to refer to this second Full Moon in a (calendar) month - in the Quarter-year sense a Blue Moon could in fact have been the only one in that month.
But why a "Blue" Moon specifically? There seems to be no good answer to this, but Wikipedia suggests a derivation from the Old English word "belewe", meaning "to betray". The "betrayal" came about because the date of Easter is determined by Full Moons, being the Sunday after the first Full Moon which falls on or after the spring equinox. The way to calculate this date in advance was only known to the educated clergy but because the equinox marked the end of the first Quarter of the year, which began at Christmas, people knew to look out for the "Easter moon" one Quarter after Christmas i.e. after three Full Moons. However, if an "extra" Full Moon occurred in this time it would be necessary to count four of them, not three. The third Full Moon thus "betrayed" the people by not being the one which indicated that Easter was near. In addition, it meant they had to continue their Lenten fast for another month! The "betrayal" idea was then extended to an extra Full Moon in any Quarter (as it would also "betray" the start of the planting or harvesting seasons, for example), leading to the usage detailed above.
Given the association with rarity I was intrigued to know how often a Blue Moon (in the modern sense) would actually happen, so I started by doing some rough calculations to find out.
The average time interval between two Full Moons, called a lunation, is 29.53days. Purely statistically, there is thus a (31-29.53)/31 probability of there being a second Full Moon in a 31-day month - 4.74%. In a 30-day month the probability is (30-29.53)/30, 1.57%, and of course there can be no second Full Moon in 29 or 28-day months. Over a full year, therefore, the combined probability is (7*4.74+4*1.57+1*0)/12 or 3.29%. This was a sufficiently small number to justify the "happens rarely" description so I decided to improve upon the rough estimate, mainly because Full Moons do not of course happen at random, as would be presumed by a statistical approach, but at totally correlated intervals: about every 29.53days, in fact! I thus wrote a computer program which simulated a long series of Full Moons, noting whether they fell in the same month. When writing the program I made allowance for the fact that the duration of lunations varies quite a lot - from 29.27 to 29.83days in fact, in a cyclic fashion. This variability does affect the overall numbers quite significantly.
From the data generated by the program I derived figures for all sorts of related statistics, which are summarised below:-
In more detail, the chance of a given Full Moon being Blue and also falling in a given month varies from about 1 in 250 for months with 31days to about 1 in 835 for those with 30 days. The chance is precisely zero for February, as the lunar cycle is longer than even a leap year February.
The question as to when these statistics will next translate themselves into reality has a perhaps unexpected twist - it all depends on where you are! A Moon that is apparently Full can be seen at some time during the relevant night from an entire hemisphere of the Earth, but the exact instant of "astronomical Full Moon" (by which Blue Moons must be defined) could be before or after midnight local time for a given observer. The day in which the Full Moon falls thus depends on your timezone. For example, a Full Moon at 10pm GMT on 31st January will actually fall on 1st February for an observer whose local time is more than 2hrs ahead of GMT, and thus possibly prevent a Blue Moon happening. The dates quoted in this article are therefore only guaranteed for the GMT+0 timezone.
While Blue Moons have no astronomical or observational significance they are interesting to note, so if you missed the double occurence in January & March 2018 the next times a month will have a Blue Moon are October 2020, August 2023 and May 2026: the Full Moons fall on the 1st & 31st on these occasions. In the case of 2018, the first Full Moon in January was very close to lunar perigee, so the Moon appeared to be much larger than usual (though you might have had difficulty actually noticing this - see my article on Supermoons!), and in 2023 both Full Moons are quite close to perigee (just 10hrs off) and so both will look somewhat larger than usual. Interestingly, the second Full Moon in December 2009 was also a (very small!) lunar eclipse, so for a brief moment the Moon was red, white and blue simultaneously! (I will deal more fully with the concept of eclipsed Blue Moons later on in this article).
It is clearly impossible to have two consecutive "Blue Moon months", as this would require Full Moons on the 30th or 31st of one month and the 1st or 2nd of the next. However, because even a leap-year February is shorter than one lunation (29.53 days), there are two ways in which Blue Moons can be separated by one month: if Full Moons fall on 1st & 30th January then 1st & 30th March, or 2nd & 31st January then 2nd & 31st March (the former only in a non-leap year, of course). Due to the effect of leap-years and the exact time of the Full Moon, the overall likelihood for this is about 1 in 330 lunations: the last time it happened was in 1999, with 2018 and 2037 after that (starting on 2nd January on each occasion). A gap of 2 months is also possible (1st or 2nd & 31st January then 1st & 30th April, or 2nd & 31st December then 1st & 31st March) but with much lower probability (1 in 1530) as the timing is critical: it did happen in Dec 1933 / Mar 1934 and Jan/April 1961 though and will do so again in Jan/April 2094. It is just possible for three long lunations in a row to give a sequence of Full Moons falling on 2nd & 31st Jan, 2nd March, 1st April, 1st & 30th May, which has a gap of 3 months between the Blue Moons in January and May. We are now not just talking rare but very rare (1 in 9400 lunations, or 760yrs, on average) but in fact there will be an event of this type in 2113.
Note, by the way, that the interval between all the above Jan/Mar events is a multiple of 19yrs. This is the Metonic cycle, after which the Moon's phases repeat on the same calendar dates and thus make Blue Moons more likely. There is not a double Blue Moon in every cycle though (1980, for example) mainly due to the effect of leap years, which disturb everything by a critical day.
The above are the only cases when a month (February) can have no Full Moon at all, at a combined probability of 4.69% per annum i.e. 4 or 5 times a century: all other months must always have at least one Full Moon. It is not possible to have a gap of between 4 and 29 lunations, and the longest period with no Blue Moons is 36 lunations (about 2yrs 11mths). The most common gap is 34 lunations: this can be understood from a theoretical standpoint as it takes an average of 33.6 lunations for a Full Moon to move through all the days in a [mean] month and get back to the beginning again, thus making a Blue Moon likely once more.
So, that's clear then - "once in a Blue Moon" means once every 2yrs 8months! (on average)
There is, of course, nothing statistically significant about Full Moon - one could just as well repeat the above analysis for any other phase of the Moon. In particular, two New Moons happen in a given month with the same frequency as Full Moons. One might think this wasn't very interesting though, as a New Moon isn't actually visible, but New Moon is when solar eclipses occur! The question thus arises as to the frequency of two solar eclipses in the same calendar month. Roughly, this should be the Blue Moon probability (3.28%) multiplied by the percentage of pairs of solar eclipses one lunation apart (10.33%), giving 0.34% of all eclipses. In fact there are six occasions in the 1645 solar eclipses from 1900 to 2599AD, or 0.36%: pretty darn close to the estimate! The last time it happened was July 2000 but the next is not until December 2206. On all these occasions both eclipses are partial, however - in fact this is generally true for almost all pairs separated by one lunation. There are only 15 cases from 2000BC to 3400AD where one of the eclipses is not partial (next in July/August 2195) but none of these cases is within the same calendar month and the partial of each pair is of very small magnitude (no more than 0.061, where 1.000 would be just total).
I would suggest that a new saying be invented "once in a double black Sun", meaning about once a century, but I don't think it would catch on somehow!!
We now know that a Blue Moon is quite unusual, and of course a lunar eclipse is relatively unusual, so how about the two happening together? I already knew that 31st December 2009 was one such occasion so I checked for instances after that and found that the next times a Blue Moon would be eclipsed were 31st January 2018, 31st December 2028 & 31st January 2037 - but these will all be total eclipses. There is then a very long gap, as the next eclipsed Blue Moons after that are not until 31st July 2129 (which is the next partial) & 30th August 2137 (total). A partially eclipsed Blue Moon is thus quite a rare event - maybe even more so than the "double black Sun" mentioned above!
But there's more, as I also investigated the circumstance mentioned at the end of the first section above: a Full Moon in a Blue Moon month being close to perigee. Both investigations turned out to be a bit complicated so, as ever, I've put them on a separate page - click here to read all about it.