Annual Calendars for Germany 1400-1449 AH

To the German version of this article

Here for the first time calculated annual calendars for Germany will be presented on the following pages, which cover a period of 50 hijric years. These annual calendars may serve for the planning of events in the nearer future, but also to check past dates. Of course there is also the possibility to do comparisons with otherwise published annual calendars with insufficient information about their method of calculation.

Links to the calendars:

Annual calendar 1400-1409 AH / 1979-1989 CE

Annual calendar 1410-1419 AH / 1989-1999 CE

Annual calendar 1420-1429 AH / 1999-2008 CE

Annual calendar 1430-1439 AH / 2008-2018 CE

Annual calendar 1440-1449 AH / 2018-2028 CE

Translation for the colum titles in the calendars:

Here once again shall be mentioned that the Islamic day starts already with sunset of the previous day. An Islamic day therefore comprises firstly the whole night (layla), then the whole illuminated day (nahār). In the annual calendars the entry under “Erster Tag des Hijriyy-Monats fällt auf” always indicates the date on which the illuminated day (nahār) of the Islamic day falls. In the case of Ramaḍān this corresponds with the first day of fasting.

On the Calculation of the Calendars

The annual calendars that are presented on the following pages were all derived in a uni-form manner. All data are based on calculation, no observation results were incorporated, not even in the annual calendars for past years. The method of calculation shall be described here in a clear and reproducible way. Moreover, some essential points regarding the applicability of the annual calendars have to be observed:

The annual calendars are in a narrower sense only valid within the region of Germany, respectively Central Europe. Any application to other regions of the Earth is therefore not valid! In consequence this is also valid for the statistics that were derived from it.

• For the determination of the beginnings of the Islamic months the principle of local sighting (Ikhtilāfu l-maṭ̣āli`) was used, i.e. only the occasions for sighting within a restricted horizon (Maṭ̣la`) were used for the determination, but not sightings anywhere in the world.
• As sightings within Germany are usually only possible during a couple of months in the year because of the meteorological circumstances, it was made use of the whole of Europe as Maṭ̣la`. This corresponds to an application of the fiqh rule “Difficulty brings alleviation” (al-mašaqqa tajlibu l-taysīr). Moreover, the restriction upon a certain state (e.g. Germany) doesn’t make sense islamologically, too. Because of different reasons it seems more reasonable to use a wider region as Maṭ̣la`, a region that is defined by geography and not by historically founded boundaries of national states.
• By “Europe” here the continental part including the British Isle and Ireland will be understood. This region also forms a unit geologically. Not included are Iceland and the Atlantic archipelagos that are counted among Europe politically (Azores, Madeira, Canaries, etc.), because they don’t belong geologically to the European continent.
• The possibility of sighting was deduced from the Yallop criterion D. The criterion D corresponds to a visibility with binoculars or telescope only. The Yallop criterion was empirically derived from several hundreds of observations or non-observations of the Hilāl during the past 150 years. It proved to be an extremely reliable criterion. It was published in 1997/98 by B.D. Yallop in NAO Technical Note No. 69 of the HM Nautical Almanac Office.
• The Yallop criterion was applied at the moment of best visibility for the Hilāl (“Best Time”). The usual definition for it is: Best Time = Sunset Time + 4/9 Lag Time, with Lag Time = Moonset Time – Sunset Time. A topocentric calculation was used, and a correction for refraction (temperature 15°C, atmospheric pressure 1010 hPa) was applied.

On this basis all month beginnings during a period of 50 hijric years were examined with regard to a theoretical visibility of the Hilāl within the assumed Maṭ̣la`. The next day was accepted as the first day of the new hijric month only when any part of Europe (as defined above) fell into the zones A-D according to the Yallop criterion.

Whenever the zone of visibility of the Hilāl is just grazing Europe, especially southern Spain, southern Portugal, and in rare cases also Ireland and Scotland (this was for example the case in Šawwāl 1412/April 1992), are favoured within Europe to be those locations where a sighting might just still be possible. In those cases a special attention was turned to the visibility conditions in the vicinity of Tarifa (most southerly city in Spain) and the Cabo de São Vicente (most south-westerly point of land of Portugal), where sometimes a decision was rather tight. Yet, within the examined period of 600 hijric months were only 13 cases, i.e. about 2 %, where the limit of visibility passed so close to these locations that a decision could only be made after a very exact and detailed re-examination. However, when these locations were found to be outside the limits of the zone of visibility, the beginning of the month was not taken for granted, even when the limit was only very closely off in northern Morocco, or off the Portuguese coast.

All examinations were done twice to exclude errors. The result is displayed in tables on the following pages. In due time annual calendars for other periods will be added, in šā’a-Llāh.

Statistics

The gained data were used to do some statistical investigations. The results are listed and commented here:

• During the entire examined period of 600 hijric months only month lengths of 29 or 30 days do occur. There was no single case where the above described method to derive the beginnings of the months yielded months of 28 or 31 days, so that a perforce correction of the derived date would have been needed.
• During the entire examined period of 50 hijric years only year lengths of 354 (common year) or 355 days (leap year) do occur. There was no single case where the above described method to derive the beginnings of the months yielded years of 353 or 356 days.

These results show that the applied method to determine the beginnings of the months doesn’t cause gross errors through impermissible month or year lengths. Other methods will still have to be subject to this criterion. The results of such a comparison will be appreciated.

• Number of 29-day months in the examined period: 281
• Number of 30-day months in the examined period: 319
• Average month length in the examined period: 29.53 days. This corresponds exactly with the length of the synodic month.

The following statistic is interesting here: Although over a longer period each month should have a length of 29 days in 47 % of all cases and of 30 days in 53 % of all cases, the month of Ramaḍān shows a significant deviation from this distribution within the examined period of 50 years:

• Number of years with a 29-day month of Ramaḍān: 20 cases = 40 %
• Number of years with a 30-day month of Ramaḍān: 30 cases = 60 %

The interpretation of this result is left to everyone alone, for a statistical significance a much longer period than only 50 years would have been necessary to examine. However it should make us reconsider that this special month (at least in our epoch) so often has its full length of 30 days and thereby offers us the opportunity to more `Ibāda. Unfortunately one has often to realize that many fasting people take every unconfirmed or incredible information (prayer tables of unknown origin, spread reports of “sightings”) to break their fast after 29 days. Allāhu a`lam.

The mathematically “idealized” sequence of month lengths in the Islamic calendar would correspond with an alternating succession of months with 30 and 29 days, starting with 30 days for Muḥarram and ending with 29 days for Dhū l-hijja in common years, respectively 30 days for Dhū l-hijja in leap years. However, such an “idealized” sequence does occur in reality rather seldom because of the varying orbit of the Moon around the Earth. Within the examined period only the two years 1406 AH (leap year) and 1430 AH (common year) follow this pattern. This is also due to the fact that rather often series of months with the same length interrupt this “idealized” succession:

• Two months of 29 days in immediate succession: 46 cases
• Three months of 29 days in immediate succession: 8 cases
• Four months of 29 days in immediate succession: 0 cases
• Two months of 30 days in immediate succession: 44 cases
• Three months of 30 days in immediate succession: 17 cases
• Four months of 30 days in immediate succession: 7 cases
• Five months of 30 days in immediate succession: 0 cases

Sometimes the cumulated succession of months with the same length is taken as an argument to mistrust the accuracy of calculated calendars. Just as the same argument is used to shorten or lengthen months artificially, because one erroneously acts on the assumption that there must not be series of months with equal length.

But this is not correct: the above result shows that a repeated succession of months with 29 or 30 days is nothing particular. Thus it is rare but not impossible that series of three months with 29 days, or even four months with 30 days occur. This will happen on the average in each case once every 6 to 7 years, and still this doesn’t cause the whole calendar to get out of step.

Even longer series didn’t occur in the examined period, but cannot be excluded in principle for other epochs.

Remark: Prof. Dr. Iraj Malakpur of the University Tehran conducted an investigation comprising 65,000 months resp. locations, where he found also a maximal number of 3 successive months with 29 days and 4 successive months with 30 days. This investigation was published in the Autumn 1385 edition of Našr e-Daneš (in Farsi).

• Number of common years with 354 days in the examined period: 31
• Number of leap years with 355 days in the examined period: 19

• Average year length in the examined period: 354.38 days. This corresponds nearly exactly with the length of 12 synodic months.

• The new month begins with the first sunset after geocentric conjunction of sun and moon (New Moon), i.e. while moon age < 24 h: 136 cases (23 %)

• The new month begins with the second sunset after geocentric conjunction of sun and moon (New Moon), i.e. while moon age 24-48 h: 439 cases (73 %)
• The new month begins with the third sunset after geocentric conjunction of sun and moon (New Moon), i.e. while moon age > 48 h: 25 cases (4 %)

(Remark: here the moment of sunset in southwest Germany was assumed) This result shows on one hand that in Europe normally and in most cases the hijric month begins with the second sunset after New Moon, and on the other hand that it is nothing extraordinary when the hijric months begins even with the third sunset after New Moon. This case happens cumulatively in each of the years 1988-91, 1995-97, 2006-08, 2011-15, and 2024-27, only during the months of July to November. This is caused by the variable orbit of the Moon around the Earth, which yields especially unfavourable sighting conditions on the northern hemisphere of the Earth, such that the Hilāl is not visible before the third sunset after New Moon in Europe.