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We recall to the visitor our methodology for calculating the beginning of the month for establishing the calendar for Makkah.
After the new moon is born, we first look for the earliest crescent in the evening sky of Makkah. If it is visible, then the new month starts the next day. If not, we look further and further west until the time of fajr in Makkah. If the crescent is visible anywhere to the west before fajr in Makkah, then the new month starts on the next day, exactly as if the crescent had been visible in the evening in Makkah itself. We call this concept that of the extension of the observational zone.
The methodology for calculating the beginning of the month in Makkah can be applied to any place on earth. The month will begin next day if: (1) the new moon is born (2) if the young crescent is visible in the evening sky of the place considered, or (3) if it is visible at somewhere to the west of the place before fajr there. Otherwise the month will last 30 days.
We follow this methodology in order to determine the beginning of important Islamic dates for the various countries of the world. For several strategically chosen countries on different continents we select a town towards the eastern limit of the country. We use the eastern limit because fajr in the east is earlier than fajr in the west. If visibility is acquired for the east, then it will also be acquired for the west where fajr is even later. We avoid situations where there is visibility for the west but not for the east, because in such cases, the country will be divided into two for celebrating the feast day.
We now invite the reader to consult the visibility curves for the beginning of Ramadan 1435 (Ramadan 2014). Two visibility curves are pertinent: that of 27th June 2014 and that of 28th June 2014 (Link). The new moon is born on 27th June 2014 at 08 hours 08 minutes Universal Time. The blue and green zones represent the areas of the world where the crescent can be seen with the naked eye, blue under good atmospheric conditions, green representing easy visibility.
The visibility curve for 27th June 2014 shows most of the earth in a non-visibility zone. Thus there will be no direct sighting on the various continents. However, a blue zone covers a part of the Pacific Ocean towards the west. Thus it becomes essential to calculate whether fajr in some countries – with no direct visibility on the evening of 27th June 2014 – is not after the visibility of the crescent in the Pacific Ocean, thus insuring visibility to the west of the country under consideration, before fajr in the country. These countries can thus start the fasting of Ramadan on 28th June 2014.
For the other countries the visibility curve for 28th June 2014 will apply. Here most of the world is in a green or blue zone, especially in the southern hemisphere. Thus all countries that cannot start Ramadan 2014 on 28th June 2014 will start fasting on 29th July 2014.
For calculating the time of Fajr with respect to the first visibility of the moon, the choice of the point of observation is important. Looking at the visibility curve for 27th June 2014, we find that the first point of visibility in the blue zone is situated at 26° S and 146° W.
We select as our point of observation not the first point of visibility, but a point situated in the interior of the blue zone, 3° further west in longitude. Our point of observation is situated at 26° S and 149° W. This point is in the ocean. However it corresponds to a real possibility – and not a theoretical or supposed possibility – of observing the new crescent. Let us call this point of observation the point P. The choice in the interior of the blue zone is dictated by the following reason:
The blue zone represents naked eye visibility under perfect observational conditions. For an individual point, such as the first point of visibility, it is not certain that such conditions will be realized. But if we place ourselves within the blue zone, we take advantage of visibility not only at the selected point of observation, but also of the probability of observation in the whole of the blue zone situated to the east of our point of observation P. Indeed, to the east of P, the crescent will be visible before it is visible at the point P itself. If Fajr in a given locality is after visibility at the point P, it will be even more so if the visibility occurs earlier than at the point P.
Let us take an imaginary example in order to clarify this point. Let us say that the visibility at the point P occurs at 04H45 in universal time UTC. Let us say that Fajr in a given locality is at 04H50, also in UTC. Since Fajr is after visibility, Ramadan will start in the place under consideration. Now, as we said before, visibility to the east of the point P will occur before that at the point P. Let us say that visibility occurs at 04H40 UTC, somewhere to the east of the point P, always in the blue zone. Fajr in the place under consideration will still be after visibility. Ramadan will start in this place.
The detailed calculation shows that the blue zone towards the east of the point P covers an area of roughly 450 000 km2. This is 67 % of the surface area of France. Within such an extensive area, the probability of sighting the crescent with the naked eye within the blue zone is almost 100 %.
Whenever possible, we ask people in whom we have confidence – astronomical observatories or groups of astronomers in different countries of the world – to photograph the young crescent for us, according to our visibility predictions based on the visibility curve of the month. The photo gallery on our site bears testimony to the exactness of our predictions and the seriousness of our calculations. Month after month, we publish photographical evidence of the very young moon. We might add that all our photographs are without optical aid.
In his paper “A Method for predicting the first sighting of the New Crescent Moon”, the British astronomer B. D. Yallop gives the following formula for determining the best time for sighting the new moon after sunset in a given place (HM Nautical Almanac Office NAO, NAO Technical Note, Updated April 1998):
Best time of visibility of the new moon = Sunset time + 4/9 * (Difference between sunset and moonset time)
Let us now examine the situation after birth of the new moon (conjunction) on 27th June 2014 at 08H08M Universal Time (UTC) at 26° S and 149° W:
Once the place and time of visibility were determined, we chose 15 strategically situated cities in Africa and Europe and 7 in the Americas and two in Asia.
The results of the calculation are reproduced in the following table.
The concept of the extension of the zone of observation to the west of a place before fajr in the place has allowed us to publish the dates of the beginning of Ramadan 2014 for various countries. Soon we will publish visibility curves with integrated concept of the extension of the zone of observation. This will lead us to an authentic, legitimate and rigorously exact calendar for all places in the world.