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. For most countries, such a situation will not be acceptable. However, for Eid al Adha, Russia and China constitute exceptions that we will discuss later.
We now invite the reader to consult the visibility curves for the beginning of Dhul-Hijjah 1434 (Dhul-Hijjah 2013). The pertinent visibility curve is that of 5th October 2013. The new moon is born on 5th October at 00 hours and 34 minutes in Universal Time UTC. 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 of 5th October shows that the blue zone covers a good part of the South American continent and the green zone the Pacific Ocean. We thus have to examine which countries can begin Dhul-Hijjah on 6th October 2013.
According to our usual methodology, we have to choose a point of visibility, and basing ourselves on the visibility at this point, check whether Fajr in the country under consideration is before or after the visibility of the crescent.
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 5th October 2013, we find that the first point of visibility in the blue zone is situated at a latitude of 34° S and 21° 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 34° S and 24° W. 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 realised. 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, Dhul-Hijjah 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 before visibility. Dhul-Hijjah 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 %. The reader interested in the details of the calculation can refer to our example for the end of Ramadan 2013 (link) taking care to change the data to suit the case of Dhul-Hijjah.
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 5th October 2013 at 00H34M Universal Time (UTC) at our point of observation at 34° S and 24° W:
Once we decided upon the point and time of visibility, we chose 4 cities situated in Oceania, 16 in Asia, 5 cities in Africa and in Europe and 7 cities in North, Central and South America.
The results are depicted in the following table.
We invite the reader to consult this table carefully. The content of the columns is explicit. The 5th and 6th columns compare the times of Fajr in the selected cities with the best time of visibility at the point of observation, both times being expressed in the local time of the city. If these Fajr times occur after the time of best visibility in the Atlantic Ocean, then Dhul-Hijjah will start on 6th October 2013, as explained in the last two columns.
It is easy to see that all the countries in Africa and Europe as well as in North, South and Central America will start Dhul-Hijjah on 6th October 2013. All countries in Oceania except French Polynesia will start Dhul-Hijjah on 7th October 2013. In Asia the countries are divided as the table shows. Most countries start Dhul-Hijjah on 6th October, whereas some like Korea and Japan on 7th October.
Normally, there cannot be two dates for major festival in the same country. But we cannot reason in the same manner for a small country and one as huge as Russia or China. In both cases, the zone of visibility includes the greatest part of each country on the evening of 5th October 2013. Dhul-Hijjah will begin there on 6th October 2013. However, a small part of each country – to the east of Yakutsk in the case of Russia and to the east of Harbin in the east of China – are not covered by the visibility zone on 5th October 2013 and will start Dhul-Hijjah on 7th October 2013.
We used the results obtained for establishing a list of countries according to the date of Dhul-Hijjah, either on 6th or on 7th October 2013. The reader can consult this by clicking here. The results are also depicted on the map that can be consulted on the following link.
Eid al Adha is celebrated on the 10th of Dhul-Hijjah. For most countries in the world, Dhul-Hijjah starts on 6th October 2013. Thus they will celebrate Eid al Adha on 15th October 2013. This is particularly true for Saudi Arabia.
Wuquf Arafat, the major event of Hajj, is proper to Saudi Arabia. Wuquf Arafat is celebrated on the day before Eid al Adha. Since Eid al Adha in Saudi Arabia is on 15th October 2013, Wuquf Arafat is on 14th October 2013. This concerns millions of pilgrims who will celebrate Hajj this year.
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 Dhul-Hijjah 2013 for the different countries of the world and thus the date of Eid al Adha and of Wuquf Arafat for Saudi Arabia.
In future we intend to integrate this concept of the extension of the zone of observation in our visibility curves themselves. This will lead us to an authentic, legitimate and rigorously exact calendar for all places in the world.