SCID002: SOME SCIENCE ISSUES IN CRESCENT SIGHTING

On the occasion of Eid al-Adha, Tuesday 16 November, 2010

Prof S. M. Deen  [University of Keele, UK]

The early Muslim research in Astronomy was prompted by the need to determine the direction of the Qibla and prayer times. Although clocks have been generally used for the determination of not only prayer times but also Suhr and Iftar times, calculations were avoided for the determination of Ramadan and Eid dates. These days it seems the situation is changing even among the Sunnis. There are some Muslims (whom I shall call traditionalists in this document) for whom nothing but the physical sighting of the new crescent will do, and there are others (whom I shall refer to as the modernists) who call for astronomical calculations. Naturally both sides quote theology to support their respective positions. The most curious is the position of Saudi Arabia, which has surprisingly opted for calculations, but being Saudi Arabia, it seems it has a sting, entirely of its own. "Curiouser and curiouser", exclaims Alice.  "Begin at the beginning and continue till to the end", commands the King.  Certainly, "to hear is to obey" but with an Appendix for the detailed bits – says I.

Someone once asked the late physics-genius Richard Feynman to give an example of quantum fuzziness in ordinary human affairs. He cited  precision vs clarity.  That is, if you wish to describe something very precisely, you will have to give up some clarity, and on the other hand if you wish to describe something very clearly, you will have to sacrifice some precision. You can never have a description which is absolutely precise and at the same time absolutely clear.  I turn to Feynman for guidance and opt for clarity in describing this model, but I fear, I might end up being neither precise nor clear, or worse still, being very boring. With this risk, I seek your indulgence.

To start with, as the title suggests, this Scid presents science issues (bypassing theological issues) relating to lunar crescent sighting. The coverage includes conjunction, visibility, and how these issues are interpreted by Muslims to create a lunar calendar. Needless to say that it is largely the modernists who are concerned with such science issues. The Scid ends in a Conclusion, followed by an Appendix, where a new crescent sighting scheme has been presented for both the traditionalists and modernists.

Conjunction   

Imagine you are sitting at the centre of the earth, the sun goes round you in about 365¼  days at a higher orbit and the moon in 29½ days in a lower orbit. The positions of the sun and the moon make an angle at the centre of the earth. This angle is called elongation, which  gives the angular distance between the sun and the moon, as you would see from the centre of the earth.

As we know every 29½ days, the sun, the moon and the centre of the earth fall in a  straight line (approximately), with the moon in between the sun and the earth. This is called conjunction, which signifies the end of the previous lunar month and the beginning of the next. The conjunction is also called new moon, which by the way means "no moon", since we cannot see the moon at all at that time. For the moon to be visible to us, the sunlight must reflect from the lower side of the moon (i.e. the side facing us), which is not possible at that time, since the sun is on the other side.  The time of the conjunction can be calculated with a relatively simple algorithm within an error-margin of ±2 minutes. There are more sophisticated astronomical algorithms for more precise values, with far less error-margin. But for our purpose, the two minute error margin is good enough.  These predictions have been verified for correctness with observations over many decades.

Immediately after the conjunction the moon begins to move away from the sun, gradually permitting the sun's light to reach the lower side of the moon and then to reflect onto the earth. For this to happen the elongation has to be about 10 to 12 degrees, which takes about 13 to 17 hours approximately after the conjunction. That is, the moon is then about 13 to 17 hours old.  The reason for this variation, along with how solar eclipses occur, is given in the Appendix

A conjunction can occur at any time, day or night, different conjunctions (each for a different lunar month) occurring over different locations. Strictly speaking, a conjunction would occur on the sun's apparent annual path over any longitude within the latitude band of 23.5N and 23.5S (which represent the sun's northern and southern most positions from our perspective).  The change in the conjunction location every lunar month, over that latitude band and over all longitudes, affects on crescent visibility from different locations.

Visibility Issues

As indicated earlier, the time taken for a crescent to be visible after conjunction is variable. It depends mainly on elongation and the moon's altitude above the horizon, in addition to other atmospheric factors, such as local weather, clouds, transparency of the atmosphere, twilight, air quality (e.g. dust, too much humidity). Furthermore,  the visibility is better over oceans because of better air transparency than over land. Observe also that in our winter the moon (along with the sun) is over the southern hemisphere, while in our summer it is over the northern hemisphere, and hence the visibility in our winter would be better in the southern hemisphere, where the moon would have generally higher altitude.

One person who has studied the visibility issues of young crescents is Dr Barnard D Yallop of HM Nautical Almanac Office (HMNAO) in 1997/98, who has analysed nearly 300 observations and came out with a quality factor q for visibility [1]. Based on his work visibility maps are produced for the conjunction day and for the two successive days, showing where the moon can be visible, the quality varying from easily visible by naked eyes to possibly visible by big conventional telescope, to not visible at all.  Some further details are given in the Appendix. Their website is [www.crescentmoonwatch.org].

Their website showed that the conjunction for the Zil-Hajj moon would occur at 04:52 am GMT on Saturday Nov 6, 2010, and it gave successive coloured parabolic areas displaying the six visibility ranges. The best (i.e. category A) was in a parabolic region between the latitude band (00, 60S) and longitude band (105W, 180W), beginning with the moon-age of 21 hours.  That region included the Polynesian Islands.  The map also depicted a possible visibility (with optical aid) over an area of the ocean below South Africa, starting from (40S, 120E), the moon aged 14 hours.  The visibility map for the next day (Sunday, Nov 7), showed an easy visibility over a larger area, excluding the northern latitudes of Asia, Europe and Canada (no visibility in the UK either except perhaps in the extreme south-west corner).

Many Muslim groups also produce such maps following the algorithm of Yallop. The most active Muslim website is the www.moonsighting.com managed from North America, with a world wide committee structure. The group also produces visibility maps from Yallop's algorithm.  In addition, the group has many interesting articles. I found an excellent 18-page QA article there by Dr Khalid Shaukat  (www.moonsighting.com/faq _ms.html). He has also produced a list of mistaken moon-sighting in the Middle East. There is a website (www. phys.uu.nl/~vgent/islam/islam_lunvis_main.htm) that provides information on crescent visibility for lunar months during the Prophet's life in Medina between 622 and 632 CE

Muslim Debates

As indicated earlier the modernist Muslims are happy to accept the predicted conjunction times for the start of new lunar months without requiring any physical sighting of the crescent. In fact they assert that it is our religious duty to accept knowledge (here astronomical knowledge) over unreliable individual sightings.  So, if the conjunction is predicted to occur today, say, Sunday, 29th Ramadan, then the Eid would be tomorrow (Monday). But they will usually fix a time gap before which the conjunction must occur. Naturally the traditionalists insist on physical moon-sighting. Both sides quote the Quran and hadiths for their respective point of view.

Apart  from theological arguments, the modernists also say in their general defence, as put forward by Dr Louay Safi in his 22-page well-argued article [2]:

The actual choice is not one in which we are asked to choose between astronomical calculation and moon sighting. The choice is really between calculations and individual testimonies.  .... Those who insist that Muslims abandon the astronomical calculation and rely on individual testimonies, are in actuality asking Muslims to abandon  the certainty of reliable knowledge, for the inconsistencies of unverified individual reports.

On the other hand some traditionalists, concerned about mistaken sightings, say that sighting should be verified for correctness and accepted if sighted only after conjunction. Presumably they will prescribe a minimal age for the crescent and accept sighting only from a location in an area of good visibility, as determined by Yallop's (or equivalent) algorithm. And if so, then reliance on calculations again. For their point of view, see an interesting and informative 24-page article by Dr Naveed Sheikh of Keele University  [3].

Saudi Mystery

It is well-known that Saudi Arabia usually claims moon-sighting before everybody else, sometimes even before the conjunction.  For a long time Saudi Arabia is using astronomical calculations for conjunctions to determine the start of lunar months, without requiring any physical moon-sighting. But they applied the conjunction information in a most peculiar way. Some years ago, the rule was that if conjunction was 12 or more hours old before the sunset in Mecca, then that day is the first of the new lunar month, starting from the previous (I repeat the previous) evening. That is, they started their new month even before the conjunction took place, and therefore, it's no wonder that they were always at least one day ahead of others.  Then a few years ago, they changed their rule (through several stages), delaying the start of the first day of the month by one day. The new rule is that if the conjunction happens before sunset in Mecca on 29th day of a lunar month and if the moon sets after sunset in Mecca on that evening, then this evening is the start of the new lunar month [note moon may not necessarily be visible by its setting time in Mecca, since the moon needs to be 13 to 17 hours old for it to be visible].  This rule that the moon must set after the sun is required, since at the Mecca latitude, if conjunction occurs just before sunset, then in some occasions (when the moon is at its most northerly latitude), the moon can set before the sun, even before the conjunction.  This rule can be discarded if a minimal time-gap (e.g. one hour) is required between the conjunction and the subsequent sunset.

The resulting calendar is used by Saudi Arabia (created and publicised in advance for many years) as the civil calendar for official and other needs (such as airline schedules, school holidays etc).  However, for the dates of religious events, they accept physical moon sighting to "correct" the civil dates, but without establishing the genuineness of the sighting.  For example, if the month of Ramadan was calculated to be a 30-day month with conjunction on the 30th day, but if someone on the 29th evening claims to have seen the crescent, the following day would be declared Eid al-Fitre, even though the conjunction has not taken place. (I can understand the sentiment that a devout Muslim cannot lie, but surely he/she can make mistakes).  There is a story of an 80-year old man claiming to have seen the crescent on a 29th day, and it was reported to the committee late at night, but nevertheless the following day was declared Eid, without verifying the sighting. Therefore, there could be early start of a lunar month (even before conjunction) often in Saudi Arabia [see Uummal Qurra Calendar].The Saudis would not modify their practice, but would ask all Muslims to accept their dates. However this year (2010) the Saudi start-day of the month of Zil-Hajj coincided with that of others.  An impossible Saudi moon sighting in  2005 (for Hajj and Eid al-Adha) has been narrated by a then Saudi-resident Haroon R Choudhary, Edmonton, Canada {haroonc@shaw.ca}.

FCNA [Fiqh Council of North America]: www.fiqhcouncil.org

FCNA has adopted calculations as the basis for a world Islamic calendar. They say, if a conjunction occurs on the 29th of a lunar month before 12 noon GMT, then the new lunar month will start after sunset at Mecca that evening. Observe that 12 noon GMT will be 2:39 pm in Mecca longitude (39.75 E) time, and 3 pm in Mecca official time. Either way, it would be several hours before sunset in Mecca, even on the shortest day (around Dec 21) when the sun sets at about 5:38 pm (official time). Note that by then the crescent will be old enough to avoid the problem of its setting before sunset, as discussed earlier. 

As regards crescent visibility,  FCNA accept that the crescent may not be visible by sunset in Mecca, but it will still be in the Mecca sky before sunset, and additionally it will be visible somewhere in the world in the course of that day. For instance, the crescent would be at least 18 hours old at sunset at the cross point of the equator and the IDL (International Date Line), and therefore it should be visible somewhere there.  [note sunset at the equator is always around 6 pm local longitude time]. Thus, the FCNA argues, that the scheme provides a basis for an international Islamic calendar.  Why did FCNA tie the start date of a lunar month with the Mecca sunset?  Perhaps to show reverence to Mecca, but this tying creates some  problems as covered in the Appendix. A Canadian Muslim group: the Hilal Committee of Toronto, also advocates a calculation-based calendar.  All these groups employ Yallop's algorithm for their calculations.

Conclusion

It was an interesting journey for me. It seems we are divided between sighters and calculators on  lunar calendar. The sighters insist that physical sighting is a religious imperative, while the calculators insist that the acceptance of knowledge (over unreliable sighting) is a religious duty.  However, the sighters (I mean the educated adherents) are not necessarily anti-science – they trust calculated conjunctions and visibility maps, and many of them would like the claims of sighting verified for genuineness before acceptance. In that case, in my opinion, sighting has to happen sometime after the conjunction (when the crescent is at least 13 hours old) and at a location of reasonable visibility, as predicted by calculations. However in the last conjunction on Nov 6 for Zil-Hajj the crescent was not easily visible from most of the inhabited regions of the globe, except the Polynesian Islands (as discussed in the text). So the sighters assumed the crescent was not sighted on Nov 6 and hence they did their Eid al-Adha one day after others.

As for the calculators, they have accepted the calculated conjunction as the signal for the start of a new lunar month from the subsequent evening, generally subject to a time-gap for correctness and standardisation. This time-gap is usually not long enough for the crescent to be visible,  and in those instances, the calculators will begin their lunar months one-day before the sighters. Most astonishing is that conservative Muslim countries, like Saudi Arabia (along with some other Middle Eastern countries), are using calculation-based Islamic calendar for some time, even though there is a quirk in the Saudi practice. The proposal by FCNA for a world Islamic calendar is laudable, but flawed, as discussed in the Appendix, where  a new sighting scheme, longitude-based crescent sighting, has been presented for both the sighters and the calculators.  

This year in the UK, many Muslim groups appear to have celebrated Eid al-Adha on Tuesday 16 Nov, 2010, perhaps because of Saudi Arabia (which had Eid on that day), rather because of any particular preference for any calculation-based approach. This is then I guess our current position.

Finally, I am sure there are mistakes in this presentation, for which I seek your correction. There also some questions placed at the end of the Appendix, which you might like to look at. If you would like others to hear of your comments and suggestions, then please make them also at the blogsite: www.scienceunderislam.blogspot.com. 

Next Blog: Ramadan and Prayer Times in Lands Under Midnight Sun

Acknowledgement: I am indebted to Dr Naveed Sheikh of Keele University and Ms Catherine Hohenkerk of HM Nautical Almanac Office for providing me with articles and related information.

References (only three important ones are listed here)

[1]  B. D. Yallop: A Method for Predicting the First Sighting of the New Crescent Moon, Rep No 69,  updated 1998,  HM Nautical Almanac Office

[2]  Dr Louay Safi:  Reading, Sighting and Calculations: http://Isinsight.org/articles/current/hilal.htm]

[3]  Dr Naveed Sheikh : "And the Moon Rose Over Us" – The Fiqh and the Science of Islamic Moon-Sighting,  Keele University,  Nov, 2010.

APPENDIX

Variation in the Moon Age and Solar Eclipse

The orbits of the sun and the moon are oval, and the moon moves at different rates at different parts of its oval orbit. Also the moon's mountains have an effect on how much sunlight can be reflected onto the earth. Unless the crescent is reasonably bright, we cannot see it. This affect the elongation angle and hence the age of the moon. There is approximately a 5-degree angle between the planes of the orbits of the sun and the moon. Therefore for most conjunctions the centres of the sun, moon and earth align only approximately (providing a closest possible encounter), after which they start to diverge from one another again.  When the centres do align exactly, there will be a total solar eclipse, since the sizes of the lunar and solar discs usually appear to be of the similar angular size from the earth, despite the great distance between the moon and the sun. If the discs overlap each other partially, then there will be a partial solar eclipse, but most times they do not touch each other. Nevertheless we cannot see the moon, even on those untouched conjunctions, since there would really be no sunlight to reflect to us from the lower surface of the moon (i.e. the surface facing the earth). For a lunar eclipse, the moon and the sun have to be on the opposite sides of the earth, as happens at full-moons, and it is the earth's shadow which makes the moon invisible.

Further on Crescent Visibility

Dr Yallop  has since retired, but his work is still being continued at the NAO (HM Naval Almanac Office), the relevant NAO website is  www.crescentmoonwatch.org  [not to be confused with moonwatch.org, which is different]. It is his work that most Muslim modernist organisations, such as www.moonsighting.com,  cite and use. He has produced six categories of visibility, A to F,  in terms of q values  These ranges are: 

A (Easily visible by naked eyes),

B (easily visible to the naked eye with perfect atmospheric conditions) 

C (may need optical aid),

D (can only be visible with a small conventional telescope (inc binoculars)),

E (below the limit of small telescope) 

F (not visible even by large conventional telescope) .

He has also determined the best time for a crescent observation after sunset, as the 4/9th of the time interval between the sunset and moonset. For example if the local time for the sunset is 18:00, and that for moonset is 19:30, then the best time to observe the crescent is 18:40.  His group has generated global crescent visibility maps from the year 2009 to 2019 for every lunar month – three maps for each month, one for the conjunction day and the other two for the successive two days. These maps give world-maps, showing  the areas of these visibility categories (different categories in different colour), along with the age of the moon, and latitudes and longitudes of the visibility locations. The NAO  website that presents all these maps is: www.crescentmoonwatch.org/nextnewmoon.htm. 

Their website showed that the conjunction for the Zil-Hajj moon would occur at 04:52 am GMT on Saturday Nov 6, 2010, and it gave successive coloured parabolic areas displaying the six visibility ranges. The best (i.e. category A) was in a parabolic region between the latitude band (00, 60S) and longitude band (105W, 180W), beginning with the moon-age of 21 hours.  That region included the Polynesian Islands.  The map also depicted a possible visibility (with optical aid) over an area of the ocean below South Africa, starting from (40S, 120E), the moon aged 14 hours.  The visibility map for the next day (Sunday, Nov 7), showed an easy visibility over a larger area, excluding the northern latitudes of Asia, Europe and Canada (no visibility in the UK either except perhaps in the extreme south-west corner).

Comment on the FCNA Proposal

However, on closer examination there seems to be one or two problems with this FCNA proposal.  Assume it is Sunday, 29 Ramadan in Mecca, where conjunction occurs, either (i) just 30 seconds before 12 noon GMT , or (ii) just 30 seconds after 12 noon GMT. We shall now examine what happens in Mecca, IDL (International Date Line), Auckland (New Zealand), Jakarta and Kuwait in these two cases. In each case we shall apply their longitudinal times (i.e. the local times), except where indicated otherwise.

Case (i): The Eid would be on Monday in Mecca and also on all places east of IDL  But on which day would the Eid be on locations east of Mecca and west of IDL?  Consider for example, Auckland (36.9 S, 174.7 E), which has a longitudinal difference of over 11½  hours from GMT and where sunset time is say 6 pm (at its longitudinal time). The 12 noon GMT (the conjunction time) on Sunday would be after 11 pm on Sunday in Auckland, and therefore naturally the Eid there would be on Tuesday, which is fine and would follow from the IDL as well. But what about Kuwait (29.5 N, 45.75 E),  which is also east of Mecca with a longitudinal time difference of some 24 minutes from Mecca. Would the Eid be in Kuwait on Monday as in Mecca or Tuesday as in Auckland? I presume it has to be on Monday, but under what rules?

Now the case (ii). The conjunction has occurred just after 12 noon GMT on Sunday, and therefore the new month would start in Mecca on the Monday evening instead of the Sunday evening. So, the Eid would take place on Tuesday in Mecca and in all places right up to the IDL. But what about Auckland? Would the Eid be on Wednesday, the day after Mecca as was in case (i)?  In the Auckland (longitudinal) time, the conjunction would have taken place at about 11 pm on Sunday, hence by the Monday evening before sunset at 6 pm, the moon would be over 17 hours old. And at Jakarta (06S, 106.45 E), the conjunction would have taken place at 7 pm on Sunday, and  the moon would be 23 hours old at the sunset time of 6 pm at Jakarta longitudinal time. So in both places moon could be seen on Monday, hence the Eid should be on Tuesday, the same day as in Mecca, not the day after, as was the case in the previous example and as the current rule seems to suggest. I have been unable to get a response from FCNA on my criticism.

Therefore in case (i), some of the places east of Mecca and west of IDL would (or should) have Eid on the same day as in Mecca, while some other of these places would (should) have the Eid  day after, but without any rules to tell us how to decide. In case (ii), all these places (east of Mecca, west of IDL) should have Eid on the same day as in Mecca, but the rule will probably make it the day after.  Something seems to be seriously deficient. Clearly tying the start point to any particular location (e.g Mecca) creates an artificial boundary problem, on the top of the natural one (see below). I think the Longitude-based Crescent Sighting scheme proposed below is a better solution.

Longitude/Latitude Issues

It seems there is an assumption in Muslim theology that if the new crescent is sighted on one longitude, then it is right to believe that it would be sighted (naturally subject to atmospheric conditions) over all longitudes west. Is it correct, given that the sun sets much later, or much earlier on higher latitudes, depending on whether it is summer or winter? There is also in addition the polar effect at very high latitudes (above 66N and below 66S) when the sun and the moon do not rise or do not set, for one day to 6 months, as the latitudes increase to 90 deg (at the poles).

Longitude Time: First we define the longitude (or longitudinal) time, which is the local time over a longitude and it has the same value at all points (i.e. all latitudes) on that longitude. It is found for a longitude by multiplying the longitude value by 4 minutes, and then by adding it to GMT if East, or subtracting it from GMT if West. For example for Mecca (39.75 E), the longitude time should be 39.75×4 = 2h 39m to be added to GMT. It is thus (GMT + 2h 39m), whereas the Mecca official time is (GMT + 3 h).  The GMT is the longitude time for the zero longitude. The time used below is longitude time, unless indicated otherwise.

 

Now, ignoring the polar effect for the moment, let us take an example of London (50.5 N, 00) and another place X at (50.5 S, 00).  If the sun sets in London at 8pm GMT on a June day, it would set at about 6 pm at the equator on zero longitude, and at about 4 pm GMT at the place X. Therefore the London sunset allows extra 2 hours over the equator and 4 hours over the place X, to be added to the crescent's age, and hence the crescent could be visible in London, but not at those two other places.  Therefore the assumption that if the crescent is sighed on one longitude, it would be sighted on all longitude west cannot be true, when it is not true even for all latitudes of the same longitude.  We can have a solution if we agree on a concept of what I would call longitudinal sighting.

Longitudinal Sighting: which states that if the crescent is sighted (physically or logically) at any point (i.e. any latitude) on a longitude, then it should be accepted as sighted at all points of that longitude. For the physical sighters, it would mean that the people at place X may have to wait for many hours after their sunset to hear news of physical sighting, if any,  from say London. For calculation-based sighting (to be called logical sighting) people would not have to wait, since the predicted conjunction times would be known in advance.

Midday Rule: For a conjunction-based solution, we need to accept a midday rule that states:  if the conjunction occurs by 12 noon on a longitude (in its longitude time), then the new lunar month will start for this longitude from sunset times that evening. Although the 12 noon in longitude time is the same time at all latitudes on this longitude, the sunset times will vary on different latitudes, as we have shown earlier in our example of London, place X and the equator, all on the same zero longitude.  Islamic day begins from sunset and this rule allows different latitudes on this longitude to start their new month from their respective sunsets, but from midnight at this longitude, all of them will have the same date (since all sunsets on this longitude must occur by its midnight).  If the conjunction takes place after 12 noon, then the month will start for this longitude from the next evening. We have chosen 12 noon as the last conjunction time for a subsequent sunset, so that we can avoid the possibility of conjunction after sunset, or moonset before sunset, as we encountered in the Saudi case. Since a longitude spans over all latitudes, we need to take into account the very high latitudes as well, where the day length sometimes could be very short (even zero), and hence 12 noon is the best choice to avoid the Saudi problem. Furthermore, we can employ the midday rule to resolve the polar effect at very high latitudes, since we can apply the sighting or conjunction information from any convenient lower latitude of a longitude to a higher latitude (where the sun/moon do not rise or set) of the same longitude. If we agree to this rule, then the first day of a new month started at a longitude should be valid for all longitudes west of it, until reached a longitude where the conjunction occurred at its midday.

Example: Next let us consider an example for the clarification of some issues, for which we shall use longitudes 90 E and 91 E, around Dhaka (23.72 N, 90.43 E) in Bangladesh.  Let us assume that on a Sunday, 29th Ramadan the conjunction is to take place just at 12h 00m (longitude time) on longitude 90 E (which would be some 30 miles west of Dhaka). Since the conjunction would occur by midday, the Eid on that longitude would be on Monday, but what about longitude 91 E, some 30 miles east of Dhaka, still in Bangladesh? There the conjunction time would be at 12:04 pm on Sunday (again at longitude time), and therefore Eid there would be on Tuesday. Is it right that Eid should be held on two separate days over such a short distance, and besides within the same country?  How is it that we have ended up having Eid over two different days within such a short distance?  Let us take a pause before considering this locality problem.

Boundary Problem: Our rule for conjunction is based on middays for a good reason (given earlier), but whatever rule we make there will be a boundary problem, in the west of which Eid will be on one day, and in the east of which the next day. This happens naturally also when physical sighting is required. However, the boundary will be on different longitudes at different conjunctions, but only one boundary at each conjunction. The first day of the month will start from the west-side of the boundary longitude and end on the east-side, via the International Date Line (IDL). If we take the above example, where the boundary is the longitude 90 E, the Eid will be on Monday on longitude 90E and on all longitudes west of it, until the IDL is passed when the day name will change to Tuesday (by the IDL rule) until the longitude 90 E is touched from the east. If you think about it, you will observe that the midday of the Eid day will be within the same 24 hour period (in the westerly direction) beginning at 90 E, and ending at just east of 90 E, even though the Eid day passes through two daynames. We cannot make Eid to take place on a single dayname across the whole globe.

Conjunction Longitude: We shall define a conjunction longitude for a lunar month as the longitude where the conjunction occurs exactly at midday (12 noon longitude-time) for that new crescent.  Thus, following from the preceding paragraph, the first day of the lunar month will begin from the evening at its conjunction longitude.  This rule can be used by the physical sighters as well, if they accept the concept of longitudinal sighting, defined earlier. However, they will start, not from the conjunction longitude for that new crescent, but from a different longitude which we shall call the (physical) sighter's longitude, where the first physical sighting of that new crescent is made in the evening. Therefore for the (physical) sighters the Eid day can sometimes begin one day later, since the crescent has to be minimally 13 to 17 hours old before it becomes visible. As against the (physical) sighter's longitude, we can call the conjunction longitude as the calculator's longitude.

Now returning to the locality problem of 90E and 91E. This is not a science issue, it is up to the community to decide how they want to deal with the boundary problem in the same country (for both the calculators and the sighters).  A typical solution is the policy "one country, one Eid day", thus leaving the choice of the day to the community. However, this policy could be difficult to follow in a large country, such as Russia which spans over some 6000 miles and 11 time zones from east to west. But again it would be up to the community to decide, whether the Eid is to be held over one day or over two separate days.

A Longitude-based Crescent Sighting Scheme

Recapitulating the concepts developed above: We have defined a concept of longitudinal sighting, which states that if the crescent is sighted (physically or logically) at any point on a longitude, then it should be accepted as sighted at all points of that longitude. This concept can be used by both the (physical) sighters and the calculators (who are the logical sighters). Based on this concept, we have defined (physical) sighter's and calculator's longitudes, the former is the eastern-most longitude in which the new crescent is physically sighted, and the latter is the longitude where the conjunction for this new crescent takes place exactly at 12 noon (longitude time) and hence the eastern-most longitude for the logical sighters (i.e. the calculators) for that new crescent.  Furthermore the crescent would be deemed sighted (physically or logically as the case may be) on all longitudes west of it, until the east side of the sighter's or the calculator's (as the case may be) longitude is reached. As discussed above this scheme will work for both sighters and calculators and also at high latitudes (polar latitudes) where sun/moon may not even rise or set for days.  Observe that the Saudi rule – of conjunction before sunset with moonset after sunset – will have latitude problems even on the same longitude (not to speak of the polar-latitude problem), because of different sunset times at different latitudes, as discussed earlier.  As also shown above, the FCNA scheme is seriously flawed. Therefore we conclude that the longitude-based crescent sighting scheme proposed here provides a sounder alternative.

SOMETHING TO PONDER

1.  Should we insist on physical moon sighting? If yes, then

 (a) how to ascertain the genuineness of the sighting?

      (b) how to rectify the calendar in a formal way after several successive 29-day months become 30-day months?

      (c) do we insist on local sighting for every place, or some kind of global sighting will do (if yes then how)?

      (d) if local sighting is essential, then what to do with the regions where the crescent is not easily sightable, or not sightable at all (as shown by visibility maps). Also what is to be done in very high-latitude regions where  the moon (let alone the crescent) may not rise or set for days, in winter or summer times?

3.  Is it right to have a conjunction-based lunar dates?

4. Is FCNA right to tie the start date tied with Mecca, if yes, how would you solve the problems discussed?

5.  Do you have any view on the idea of conjunction longitude for defining start of lunar months?

© S. M. Deen, 2010.

END