In the recent times, the term "blue moon" has come to mean having two
full moons in a month. The term "once in a blue moon" implies some kind
of a rarity. The year 2018 is in that sense even more rare in the sense
that there are two blue moons in the same year. But is it that much of a
rare phenomenon?
Having two full moons in a calendar month occurs due to a mismatch in the lunar calendar and our standard calendar. But before going there, let's get some basics in. What is actually the lunar calendar? or what is a lunar month?
There are two ways to define the periodicity of a body like the Moon. This occurs because Moon revolves around the observer while the observer also revolves around another object. If we measure the time taken to do a full 360 degree cycle around the axis of the Earth, that period is called the sidereal period (or month). It takes 27.3 days for the Moon to complete this revolution. However there is a slight problem here. Since the Earth is also moving, by this time, the Moon is not in the same "phase" as we started measuring it from. I.e. if you started measuring when it was the full moon, by the end of the sidereal period, it will not be a full moon. The reason for this is that the phase of the moon depends on the angle between the moon, the observer and the sun.
However, it is much easier for us to measure periodicity of the moon by measuring it phase-to-phase, for example, from one full moon to another full moon. This time period is slightly longer than the sidereal period and is called the synodic period. This takes 29.5 days as the Moon has to "catch up" with the Earth.
Now that we got the basics in place, let's look at why a blue moon occurs. As we stated at the begining, a blue moon is an occurence of two full moons in a calendar month. If you look at the numbers again, you will see immediately that this is not a very rare incident. The Moon takes 29.5 days to complete a synodic cycle, if you have a full moon on the 1st of a month, then 30.5th day, i.e. the 31st day, you will have another full moon! Given that 7 months of the year has 31 days, this doesn't seem to be a rare occurence at all. But wait, what's the probablity of a full moon coming up on the 1st of a month? There are many ways to look at this problem and get confused. The question should be thus made clear as "Given any full moon day, what is the probability of it being a 1st of a month?"
We have 365.25 days in an year. Out of that 12 are 1st of a month. Therefore the straightforward evaluation gives us a value of 12/365.25 or 3.28%. Is this correct though (because it looks like we skipped a lot of related info)? A study over the full moons from 1901 to 2000 does reveal that in fact, this is likely to be the answer. Between 1901 Jan 1st to 2000 Dec 31st (inclusive of both days), there were a total of 1237 full moon days. Out of which 40 have fallen on a 1st of a month yielding a probability of 3.23%.
That does look like pretty small odds right? But is it really? If you consider a period little over 2.5 years (i.e. 31 full moons), you are very likely to get a month with a 1st being a full moon day.
But this is still only part of the puzzle. For a blue moon phenomenon, it is not enough for a full moon day to be a 1st of a month, it also needs to be a month with 31 days. What's the probability of this happening? Going by our previous data, we can arrive at a probability of 12/365.25 for any 1st to be a full moon. Out of the 12 dates which are 1sts, 7 are months with 31 days. Therefore the probability is (12/365.25)*(7/12) = 1.91%. Now again if we look at the actual data within the century considered before, we get 20 full moon days which fall on a 1st of a 31 day month yielding a probability of 1.61%.
So how rare is this? If you take a period of over 4.33 years (or roughly over 53 full moons), you are likely to have at least one month with a blue moon.
Is it really rare then? Once in 4 something years does sound kind of rare, but in reality that's only slightly less rare than a leap year. Now next time you hear some one says "Once in a blue moon", you know how rare that is.
This article will however continue to it's part two, to discuss about the second important factor that fell on the blue moon this time, the lunar eclipse.
Having two full moons in a calendar month occurs due to a mismatch in the lunar calendar and our standard calendar. But before going there, let's get some basics in. What is actually the lunar calendar? or what is a lunar month?
There are two ways to define the periodicity of a body like the Moon. This occurs because Moon revolves around the observer while the observer also revolves around another object. If we measure the time taken to do a full 360 degree cycle around the axis of the Earth, that period is called the sidereal period (or month). It takes 27.3 days for the Moon to complete this revolution. However there is a slight problem here. Since the Earth is also moving, by this time, the Moon is not in the same "phase" as we started measuring it from. I.e. if you started measuring when it was the full moon, by the end of the sidereal period, it will not be a full moon. The reason for this is that the phase of the moon depends on the angle between the moon, the observer and the sun.
However, it is much easier for us to measure periodicity of the moon by measuring it phase-to-phase, for example, from one full moon to another full moon. This time period is slightly longer than the sidereal period and is called the synodic period. This takes 29.5 days as the Moon has to "catch up" with the Earth.
Now that we got the basics in place, let's look at why a blue moon occurs. As we stated at the begining, a blue moon is an occurence of two full moons in a calendar month. If you look at the numbers again, you will see immediately that this is not a very rare incident. The Moon takes 29.5 days to complete a synodic cycle, if you have a full moon on the 1st of a month, then 30.5th day, i.e. the 31st day, you will have another full moon! Given that 7 months of the year has 31 days, this doesn't seem to be a rare occurence at all. But wait, what's the probablity of a full moon coming up on the 1st of a month? There are many ways to look at this problem and get confused. The question should be thus made clear as "Given any full moon day, what is the probability of it being a 1st of a month?"
We have 365.25 days in an year. Out of that 12 are 1st of a month. Therefore the straightforward evaluation gives us a value of 12/365.25 or 3.28%. Is this correct though (because it looks like we skipped a lot of related info)? A study over the full moons from 1901 to 2000 does reveal that in fact, this is likely to be the answer. Between 1901 Jan 1st to 2000 Dec 31st (inclusive of both days), there were a total of 1237 full moon days. Out of which 40 have fallen on a 1st of a month yielding a probability of 3.23%.
That does look like pretty small odds right? But is it really? If you consider a period little over 2.5 years (i.e. 31 full moons), you are very likely to get a month with a 1st being a full moon day.
But this is still only part of the puzzle. For a blue moon phenomenon, it is not enough for a full moon day to be a 1st of a month, it also needs to be a month with 31 days. What's the probability of this happening? Going by our previous data, we can arrive at a probability of 12/365.25 for any 1st to be a full moon. Out of the 12 dates which are 1sts, 7 are months with 31 days. Therefore the probability is (12/365.25)*(7/12) = 1.91%. Now again if we look at the actual data within the century considered before, we get 20 full moon days which fall on a 1st of a 31 day month yielding a probability of 1.61%.
So how rare is this? If you take a period of over 4.33 years (or roughly over 53 full moons), you are likely to have at least one month with a blue moon.
Is it really rare then? Once in 4 something years does sound kind of rare, but in reality that's only slightly less rare than a leap year. Now next time you hear some one says "Once in a blue moon", you know how rare that is.
This article will however continue to it's part two, to discuss about the second important factor that fell on the blue moon this time, the lunar eclipse.
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