A WORLD-WIDE, PREDEFINED ISLAMIC CALENDAR
David L. McNaughton –
Introduction
Most Muslim communities commence a new month only when the New Moon is observed and identified by reliable observers. However, there are several exceptions: in particular the Bohras follow a predetermined calendar based on a 10631-day cycle, such that they never bother about looking for the newly born crescent.
Calendar systems determined by crescent-sighting will not usually adopt the same date all around the world, because of the variation in the onset of dusk when expressed in Universal Time. Between eastern Asia and California, for example, that time-lag is 16 hours, and during that interval the distance between the migrating moon and the sun can increase by eight or nine degrees. It would of course be impractical for Malaysia to wait for news from America before declaring the beginning or end of Ramadan, say, because (due to the solar time difference) the report would not be received until mid-morning on the next day.
Unacceptable 28-day months through visual sighting
An Islamic calendar which insists that the commencement of a lunar month may be declared only when the young crescent is positively identified by reliable observers – could occasionally result in a28-day month…How and when might that problem occur?
Suppose the beginning of Ramadan is postponed at a place where dust-haze obscures what would otherwise be an obvious New Moon. There is then a definite possibility that the air will become quite clear for the subsequentEid sighting. If that particular Ramadan would normally have lasted only 29 days, then the delay in its start – will result in an "incorrect" end after just 28 days.
An example is provided by 13th June and then the 12th of July 1991 at 25ºS, 65ºE. The crescent could have been disguised by local haze on that first date, when the sun-moon configuration resembled observations 273 and maybe 262 listed by Schaefer (1996)in his Table I. Extending the earlier month into a 30th day (thus ending it at dusk on 14th June 1991) would have cut the following month to 28 days upon a sighting on 12th July – which was certainly feasible there in clear conditions.
Admittedly, those were not Ramadan dates, but they demonstrate that the anomaly could be encountered during any Islamic month.
Note that this was an occasion where haze (not cloud) could have obscured the crescent. If the poor visibility is just due to haze, then a correct start-date could be missed without ever suspecting the error. If the sky is overcast, on the other hand, people are more likely to ask whether the moon might have been spotted in the absence of cloud.
It is of course a well-known fact that two successive 29-day months are often experienced in a lunar calendar which is based strictly on astronomical criteria. (Table 1 gives examples of that; indeed, there would have been three consecutive short months after Rajab 1438 if a slightly lower decision-threshold had been chosen).
A calendar defined according to prior calculation
There are obvious advantages to prescribing the beginning of Ramadan and Eid al-Fitr several months in advance.
In addition, it would be neater and less confusing if the entire world could be persuaded to follow a universalIslamic calendar – such that its festivals are celebrated on thesame date in every country.
Here then is a suggested algorithm for designing an Islamic calendar system which would satisfy both the above requirements:
When dusk commences at 0ºN, 180ºW– the geocentric celestial separation between the New Moon and the Sun must exceed 12 degrees. If prior calculations show that this is going to happen, then the new month will start all over the world with that particular evening – adopting the date prevailing on the eastern side of the International Date Line.
If the above criterion is fulfilled, then the crescent will definitely be sightable from somewhere in the world on the critical day–although occasionally the only such ‘favoured place’ will be in the central Pacific Ocean. The chance of success is greatest at a location where the New Moon appears vertically above the Sun (Ilyas, 1988)– which could easily be well north or well south of the equator: it is determined by the season of the year and the lunar celestial latitude.
The "onset of dusk" could be defined as sunset, or (probably better) as the instant when the centre of the sun is six degrees below the horizon (at that zero-latitude location on the Date Line)– ignoring refraction.
The Sun-Moon "separation" is of course determined by their celestial latitudes as well as by their longitudes. It is alsoknown as the Arc of Light (Ilyas, 1988, Schaefer, 1988, Odeh, 2006). It measures the apparent distance between the centres of the two discs from a geocentric perspective, such that topocentric diurnal parallax need not be considered. From the point of view of a terrestrial observer, the “Arc of Light” is not usually a vertical line.
The above test should be applied (in advance)for the 29th of every Islamic month. Some examples are presented in Table 1 below.Whenever the "threshold” is not achieved, then it will of course become a 30-day month – but you might nevertheless find it reassuring to go forward 24 hoursand calculate the new lunar-solar celestial separation.
Similarly (as illustrated here in Table 1) it is sometimes illuminating to compute this “Arc of Light” value on the 28th of a month – even if it will never surpass the twelve-degree threshold.
Résumé
The decision-process presented here is unambiguously laid down, and the essential, basic concept is not difficult to understand and appreciate.
Also, the verdict is absolutely clear-cut: i.e., the computations yield either a firm "Yes" or a firm "No", with no grey area of uncertainty. In particular, it does not depend on a (sometimes controversial) evaluation of whether or not a particular moon-sighting report was genuine.
This algorithm will almost always provide several years’ advance notice ofRamadan and Eid dates. In extremely rare instances (normally, when attempting to look some decades into the future)it may be necessary to estimate the likely decrease in Earth’s rotation-speed: (in astronomy, this relates to the “Delta-T”correction-factor: a few examples were discussed by McNaughton, 1997).
REFERENCES
Ilyas, M. 1988. "Limiting altitude separation in the New Moon's first visibility criterion".Astron.Astropys.206,133-135. Online:
McNaughton, D.L., 1997. "A universal Islamic Calendar".Hamdard IslamicusXX(1), 77-85. Diagram misprints corrected:Hamdard IslamicusXX(3), 101. This proposed calendar uses a very simple decision-criterion, but it also illustrates the importance of correctly estimating future values of “Delta-T”. Online: ‘English papers’ in
Odeh, M.S., 2006. “New Criterion for Lunar Crescent Visibility,” Experimental Astronomy 18, 39-64. Online: ‘English papers’ in
Schaefer, B.E., 1988."Visibility of the lunar crescent".Q.J.R. Astron. Soc.29,511-523.
Schaefer, B.E., 1996. "Lunar crescent visibility".Q.J.R. Astron. Soc.37,759-768. Online:
TABLE 1 - RESULTS OF CALCULATIONS,
SHOWING ISLAMIC MONTH STARTING DATES
1 2 3 4 5 6 7 8
Islamic New Date Corres- Long Lat Arc of New
month Moon to be ponding Diff Diff Light month
& year birth tested UT/date M-S M-S (degs.) starts
Ramadan 14:06:28 16 June 06:27 8.427 -5.015 9.80 18/06/2015
1436 16/06/15 2015 17/06/2015 NO
Shawwal 1:25:29 16 July 06:32 14.087 -4.133 14.67 17/07/2015
1436 16/07/15 2015 17/07/2015 YES
Dhul Qa'dah 14:54:32 14 Aug 06:29 7.225 -2.755 7.73 16/08/2015
1436 14/08/15 2015 15/08/2015 Far below
DhulHijjah 6:42:24 13 Sept 06:20 10.660 0.077 10.66 15/09/2015
1436 13/09/15 2015 14/09/2015 NO
Muharram 0:06:41 13 Oct 06.10½ 13.662 2.890 13.96 14/10/2015
1437 13/10/15 2015 14/10/2015 YES
Safar 17:48:16 11 Nov 06.09 5.799 4.213 7.16 13/11/2015
1437 11/11/15 2015 12/11/2015 Far below
Rabi’ I 10:30:32 11 Dec 06.19½ 9.867 4.998 11.05 13/12/2015
1437 11/12/15 2015 12/12/2015 NO
Notes on Table 1 – with more explanation of each column
Column:
1. Islamic month which is due to commence (either this night or the next).
2. Lunar Birth – in Universal Time, with its dd/mm/yy.
3. Test-date (in the Gregorian calendar)– in order to decide whether this particular evening will start the new Islamic month.
4. Universal Time when it is dusk (Sun at minus 6 degrees) on the equator on or just east of the International Date Line on the date given in 3. (UT makes it the day after column 3).
5 & 6. Celestial Longitude difference,andCelestial Latitude difference (Moon minus Sun), in degrees.
7. Calculated using cos (ArcLight) = cos (LongDiff).cos(LatDiff). "YES" means it passes the necessary 12-degreethreshold.
8. Gregorian dd/mm/yyyy, denoting the first morning of the new Islamic month. Occurs immediately after the (evening) date listed in column 3 whenever 7 gives "YES" (in which case the previous month finished after only 29 days).
TABLE 1 (continued)
1 2 3 4 5 6 7 8
Islamic New Date Corres- Long Lat Arc of New
month Moon to be ponding Diff Diff Light month
& year birth tested UT/date M-S M-S (degs.) starts
Rabi’ II 1:31:40 10 Jan 06:33½ 15.419 3.758 15.86 11/01/2016
1437 10/01/16 2016 11/01/2016 YES
Jumada I 14:40:03 8 Feb 06:39 8.932 2.054 9.16 10/02/2016
1437 8/02/16 2016 9/02/2016 NO
Jumada II 1:55:37 9 Mar 06:34 16.698 -1.378 16.75 10/03/2016
1437 9/03/16 2016 10/03/2016 YES
Rajab 11:24:47 7 Apr 06:26 11.310 -3.266 11.77 9/04/2016
1437 7/04/16 2016 8/04/2016 Not quite
[+28 days] 19:30:38 6 May 06:21½ 6.438 -4.553 7.88 8/05/2016
1437 6/05/16 2016 7/05/2016 Far below
Sha’ban 19:30:38 7 May 06:21½ 20.523 -4.986 21.09 8/05/2016
1437 6/05/16 2016 8/05/2016 YES
Ramadan 3:00:43 5 June 06:25 15.666 -4.856 16.38 6/06/2016
1437 5/06/16 2016 6/06/2016 YES
Shawwal 11:02:09 4 July 06:30½ 10.606 -3.900 11.29 6/07/2016
1437 4/07/16 2016 5/07/2016 NO
[+ 28 days] 20:45:41 2 Aug 06:31 5.019 -2.332 5.53 4/08/2016
1437 2/08/16 2016 3/08/2016 Hopeless
Dhul Qa'dah 20:45:41 3 Aug 06:31 17.126 -1.217 17.17 4/08/2016
1437 2/08/16 2016 4/08/2016 YES
Dhul Hijjah 9:04:14 1 Sept 06:24 10.266 0.717 10.29 3/09/2016
1437 1/09/16 2016 2/09/2016 NO
Muharram 0:12:30 1 Oct 06.13 13.808 3.408 14.21 2/10/2016
1438 1/10/16 2016 2/10/2016 YES
Safar 17:39:18 30 Oct 06:08½ 5.658 4.508 7.23 1/11/2016
1438 30/10/16 2016 31/10/2016 Far below
For possible interest, somecalculations havebeen included after only 28 days of an Islamic month. More often than not, the "Date being tested" (column 3) is the date of birth of the New Moon – but there are exceptions, for example whenthe moonis born comparatively late in the evening, and when the start of the preceding month had been delayedafter the Arc of Lightjust failed toattainthe 12-degree threshold.These 28th-day calculations (together with those for the following day)show how the Arc of Light increases during a period of 24 hours.
TABLE 1 (continued)
1 2 3 4 5 6 7 8
Islamic New Date Corres- Long Lat Arc of New
month Moon to be ponding Diff Diff Light month
& year birth tested UT/date M-S M-S (degs.) starts
Rabi’ I 12:19:21 29 Nov 06:14½ 8.179 4.928 9.54 1/12/2016
1438 29/11/16 2016 30/11/2016 NO
Rabi’ II 6:54:19 29 Dec 06:28½ 11.128 3.573 11.68 31/12/2016
1438 29/12/16 2016 30/12/2016 Not quite
Jumada I 0:08:10 28 Jan 06:38 15.221 0.789 15.24 29/01/2017
1438 28/01/17 2017 29/01/2017 YES
Jumada II 14:59:31 26 Feb 06:37 8.269 -1.257 8.36 28/02/2017
1438 26/02/17 2017 27/02/2017 Far below
Rajab 2:58:21 28 Mar 06:29 15.545 -4.049 16.05 29/03/2017
1438 28/03/17 2017 29/03/2017 YES
Sha’ban 12:17:17 26Apr 06.22½ 10.652 -4.913 11.72 28/04/2017
1438 26/04/17 2017 27/04/2017 Not quite
[+ 28 days] 19:45:36 25May 06:23 6.368 -4.871 8.01 27/05/2017
1438 25/05/17 2017 26/05/2017 Far below
Ramadan 19:45:36 26May 06:23 20.665 -4.391 21.11 27/05/2017
1438 25/05/17 2017 27/05/2017 YES
Shawwal 02:31:51 24 June 06:29 16.456 -2.937 16.71 25/06/2017
1438 24/06/17 2017 25/06/2017 YES
Dhul Qa'dah 09:46:43 23 July 06:32 11.805 -0.994 11.85 25/07/2017
1438 23/07/17 2017 24/07/2017 Not quite
[+ 28 days] 18:31:19 21 Aug 06:27½ 6.478 1.066 6.56 23/08/2017
1438 21/08/17 2017 22/08/2017 Far below
Dhul Hijjah 18:31:19 22 Aug 06:27 19.246 2.266 19.37 23/08/2017
1438 21/08/17 2017 23/08/2017 YES
Muharram 5:31:00 20 Sep 06.17 12.605 3.808 13.16 21/09/2017
1439 20/09/17 2017 21/09/2017 YES
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