By Duncan Steel 05/06/2019

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The Islamic fast of Ramadan has come to an end, marking the beginning of the tenth month of the religion’s twelve-lunation year and therefore Eid al-Fidr, the ‘Festival of Breaking the Fast’. How the decision is made when each of those months begins and ends depends upon the actual sighting of the crescent new moon in the sky, a highly-complicated matter that is briefly explained here. 

Most of us are habituated to the use of a calendar based on how long it takes the Earth to orbit the Sun (for present purposes, a ‘solar year’), and it is such a system that is used as the global standard in all but a few places (such as North Korea) for ease of international communications. Very often people refer to this as the ‘Gregorian calendar’, but it is not. It seems self-evident that the Gregorian calendar is that instigated by Pope Gregory XIII in 1582, through the papal bull normally termed the Inter gravissimas (a Latin pair of words with which the bull begins, meaning “amongst the most important/grave”). What is laid down therein are the Catholic rules for computing the date of Easter each year, and so clearly both the year (hence Earth’s orbit around the Sun) and the month (hence the Moon’s orbit around the Earth) are involved. Each Gregorian year (from Easter to Easter) contains either twelve or thirteen lunar months (synodic months, or lunations).

The Gregorian calendar, therefore, is a luni-solar calendar. Other luni-solar systems include the Chinese calendar, which has variants used in other parts of Eastern Asia, the Diwali festival in one type of Hindu calendar, and the Buddhist calendar.

The international standard we use for everyday dating, which I prefer to term the ‘Western calendar’, is a purely solar calendar. If I were pushed to say how that calendar is defined, I would point to Lord Chesterfield’s Act of 1750, because it was that Act of Parliament which stipulated the new calendar to be used in Britain and its Dominions (including being inherited by the United States, Canada, Australia, New Zealand, and so on), including the swap to January 1st as being the start of the year – an alteration that the Gregorian reform did not include, as such, because the Feast of the Circumcision was already part of the Catholic liturgical year.

In a previous blog post I have written in some detail about how long a solar calendar year should be; for present purposes, let’s just say it’s a little less than 365.25 days. One might also think of this as being a seasonal year: the cycle of the seasons.

Some religions and peoples use a purely lunar calendar. That is, they define their year in terms of a number of lunar months (as opposed to our calendar months of January through December, which have been disconnected from the phases of the Moon for rather more than two millennia, since the time of the Roman Republic). Whether any particular lunar year contains twelve lunations (about 354/355 days) or thirteen (about 383/384 days), clearly it cannot have the same duration as a solar year.

Examples of purely-lunar calendars include the Hebrew or Jewish calendar, which contains either twelve or thirteen lunations in accord with a pre-ordained cycle (and may last 353, 354, 355, 383, 384 or 385 days), and the Hijra, Muslim or Islamic calendar, which contains twelve lunations. It is the latter that is the main focus of this blog post.



In recent days and weeks the Islamic calendar has received some mention in the world’s mass media, including in New Zealand. Let us start with developments elsewhere, before turning to NZ.

In Pakistan the government, through its Ministry of Science and Technology, has recently established a website entitled Moon Sighting Pakistan where calculations are presented of when the new moon should be visible, and so a new month proclaimed on the Islamic calendar. This, apparently, has infuriated a number of conservative clerics, who have warned the relevant government minister to “stay in his lane”.

What is the problem?” many readers might ask. The problem is this. According to the calendar rules and tradition, a new lunar month can only be declared by the mullahs when the slender crescent new moon is actually observed in the western sky soon after sunset, and prior determinations of when that will occur are not allowed, as such. What this implies is that important religious events such as the beginning of Ramadan (which lasts throughout the ninth of the twelve months of the Islamic lunar year), and its ending (and therefore the start Eid al-Fitr, the ‘Festival of Breaking the Fast’), cannot be definitively known in advance. An indicative date might be calculated, but it is possible that poor sky clarity might delay the lunar crescent sighting and therefore the declaration of the new month (or year) by a day, or even two. It is also feasible (though unlikely) that the new moon might be spotted a day earlier than anticipated.

Here in New Zealand, preparations for the end of Ramadan have been in process for some time. In Auckland, twenty men have been living in a mosque for ten days, as they are in mosques all around the world, as a form of service to their fellow Muslims. In Christchurch, the terrible events of March 15th led to consideration of some of the normal practices of Ramadan being abandoned for this year. A front-page story in The Press today (June 5th) concerned a false report of the lunar crescent having been sighted on the evening of Tuesday the 4th, implying that Eid al-Fitr would come a day earlier than had been expected.

Obviously-enough, what might appear to many as being a straightforward thing – the question of when the new moon can be observed – must be more complicated than they had thought. How come?



When you fly with Air New Zealand from Auckland to Los Angeles, one can find it confusing that you land earlier than you took off. You can leave Auckland on Monday evening and land in California on Monday morning. The thing is, you’ve crossed the International Date Line, which divides one day from the next. Cross it flying west to east and you gain a day; cross it flying from east to west and you lose a day. Returning from Los Angeles you can depart on a Tuesday evening and twelve hours later you land in Auckland on Thursday morning.

Despite the fact that it wiggles around rather than following the meridian 180 degrees away from Greenwich, the International Date Line is easy to understand. It divides one day from another. The Lunar Date Line, however, is far more complicated, in that it divides one lunar month from another, and it is far from being a straight line, and it is forever shifting and changing shape.

The simplest way to think of the Lunar Date Line is that it is a line across Earth’s surface to the east of which you are highly unlikely to see the thin crescent Moon within a day or so of passing closest to the direction of the Sun, and if you are to the west of it you are much more likely to do so. It’s a curve, but that curve moves east and west depending upon the particular new moon that is in question (and they are never the same), and it moves north and south depending on the season. Plus it is affected by other things like the sky clarity, which obviously varies from place to place.

Now you are utterly confused, let me try to make things more understandable by showing an example. Below is a diagram taken from a paper by Mohammad Ilyas from the University of Science of Malaysia, published in the Journal of the Royal Astronomical Society of Canada in 1986.

Lunar Date Lines for the new moons of January and February in 1986, from a paper by Mohammad Ilyas. That for January indicates the calendar dates on which it is likely that the crescent moon could be seen, as a function of latitude and longitude: the far-easterly region of that curve is across the International Date Line meaning that the new moon might be sighted from there whilst it was still January 10th. To the west of there it would be January 11th when the spotting occurred. The Lunar Date Line for January is near-symmetric about a latitude around 25S because this is soon after the December solstice and the Sun is a long way south. The Lunar Date Line for February (mostly over the Atlantic) is symmetric about a latitude of about 10S because by then the Sun has moved further north. Clearly the Lunar Date Line is far more complicated than the International Date Line, in that it depends on the season and also your latitude and longitude. Thus Islamic clerics in California might see the new moon and so call an end to Ramadan on a different day to those in (say) London or Cairo.

In another paper published in the same journal in 1986, Ilyas presented the following diagram. Here he was indicating relative likelihoods of the crescent new moon being observed for different positions east-west compared to a particular Lunar Date Line (i.e. for one specific month). Dark circles (to the east) mean seeing the new moon on the evening in question is unlikely, larger black circles implying reduced probabilities. White circles (to the west of the Lunar Date Line) imply increasing probabilities of the new moon being seen, larger circles meaning a better chance.

A graphical representation of the probability of the new moon being seen from different locations for one specific occasion marking the start of a month. Black circles imply lower probabilities, white circles mean a better chance of the crescent moon being observed.



So how long is a lunar year of twelve lunations? Well, the average length of a synodic month is 29.530589 days, and is very slowly increasing as the Moon recedes from the Earth due to tidal drag. Any particular lunation, however, can range between 29.268 and 29.838 days – close to half a day – due to the fact that the Moon’s orbital speed varies between perigee and apogee.

If we take a lunation to last typically for 29.5 days, for ease of arithmetic, then twelve such months last for 354 days, which is about eleven days short of a solar year. In consequence the date of Ramadan shifts earlier from year to year on the Western calendar by about eleven days per year. That is, Ramadan is not fixed in terms of the seasons, but rather follows a cycle of around 33 years across the seasonal year.

As I’ve written previously in these blog posts, I do have a particular interest in calendars, and how they are based on astronomy plus historical contingencies. Their sheer variety I find highly intriguing.



You might think that the above is more than enough, in terms of our understanding of when a new moon might be seen in the evening sky, soon after passing by the Sun in the sky and so being visible shortly after sunset. But there is a lot more to be said, and a huge amount has been written about the subject by astronomers in recent decades. There are good reasons for this, entirely separate from anything to do with the Islamic calendar. Principally, the interest has been in deciphering ancient recordings of celestial events, such as the Crucifixion of Jesus and therefore perhaps its dating, though there are many other historical records that might be dated if we are better able to work out what the ancients could have seen, and what they could not.

One of the undoubted leaders in this regard is Bradley Schaefer, now at Louisiana State University, who has been awarded a range of major prizes for his work in astrophysics quite separate from his research on historical astronomy. For those who are interested, here is a link to a paper he published in 1988 on the visibility of the lunar crescent, in which he discusses the various factors that control whether it might be seen on any date (including not only astronomical and geographical parameters but also the influence of the weather/sky clarity and the physiology of the human eye); in the paper linked here Schaefer discusses the duration of the lunar month and how this affects calendars; and here is a paper Schaefer published in 1996 in which he reported not only on the theoretical side of lunar crescent visibility specifically with regard to its significance for the Islamic calendar but also on a large experimental programme in which observers charted when they could first see the slender lunar crescent following its conjunction with the Sun. The ‘quickest’ recordings were 15 hours post-conjunction with the naked eye, and 12 hours using a telescope. The general rule in terms of angular separation between Sun and Moon is that seven degrees is the minimum feasible, though of course meteorological conditions and other factors usually imply that a larger angle of separation is necessary.



What I hope I have managed to convey in all the above is that deciding when the new moon will be seen is not at all as simple as one might imagine, prior to examining all the factors involved. It is entirely possible that two observers spaced by only a few hundred kilometres might see the crescent moon first on separate evenings. This has major consequences for religions in which the actual sighting of the new moon is necessary for the calling of a new month/a new year.

Lest any members of distinct Christian denominations think that the way their ecclesiastical year is defined is superior to the above, might I remind all that in a previous post I described how Easter this year was marked a month later than it should have been, if the Easter mnemonic (“Easter is the first Sunday after the first full moon after the vernal equinox“) were correct; it’s not, obviously.

The moral: religion and strict science don’t mix. All I have been trying to do here is to outline some of the astronomical (and other) matters that might be pondered. In the diverse human world, other considerations than simple science greatly affect how different peoples decide to divide their daily, weekly, monthly and yearly activities.



The photograph at the head of this blog post shows the crescent Moon above the Sea of Japan, taken from the International Space Station early in May. The dark area at the bottom is the night-time Earth; the blue band is our atmosphere; above it the Moon and the blackness of space; the orange structure on the left is part of the exterior of the Space Station. 



Addendum, June 6th: As I wrote the post above concerning lunar calendars and their complexities, I knew that I would want to append this note today, the 75th anniversary of the Allied landings in Normandy. The decision on the date was closely linked to astronomical factors: a full moon was needed to aid the airborne assaults during the night, but a low tide was necessary for the landing craft pilots to see the underwater defensive barriers set just off the beaches, and the tide needed to be soon rising so that those craft would not be stranded. Only June 5th, 6th or 7th would do, else a one-month postponement would be necessary. Bad weather on the 5th led to the 6th being selected.

In terms of the scientific matters involved, I cannot do better than the description in the article Astronomy and D-Day: The Sun, Moon, and Tides at Normandy by Donald Olson, published a few days ago in Sky & Telescope magazine. Personally, I read and weep. On the beaches, 130,000 men were landed; from the skies, 24,000 arrived by glider or parachute; a large fraction never made it home again.

14th June: Olson’s analysis has also been discussed in Cosmos magazine.

0 Responses to “The problem of knowing when a lunar year begins and ends”

  • All of which just goes to show what garbage religion is. Thanks Duncan.

    • Well, I am not religious myself (apart from believing in the huge potential of humanity*), but I respect that other people have their own thoughts, and reasons for those thoughts. Because of that I try to keep religion and science separate, just as there are many clubs in which discussion of politics or religion is prohibited: those broad subjects are likely to cause destructive arguments rather than reasoned debate. The one thing that I would hope that readers take away from the blog post above is a realisation that being able to state in advance when a crescent new moon is going to be visible is not as simple as it might seem at first consideration, even if the best methods of science are applied.

      *I would have to count that as being a ‘belief’ rather than a matter of confident prediction, because of humanity’s dismal record of achieving all that it might. So much strife, so much hatred, so much violence and sheer nastiness.

  • Another intriguing piece. Thank you Duncan.
    The addendum prompted me to comment. We spent some time in France 4 years ago and visited some of the beaches in Normandy. I understand the desire to commemorate the allied landings, but we were not impressed with the proliferation of the (Allied) memorials throughout the area. We weep for the French whose towns and cities were practically obliterated in the process, yet there is little evidence of memorials commemorating their suffering.

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