| |
|
|
|
| |
|
|
The journal is now published in collaboration
with Lifescience Global
Please visit www.lifescienceglobal.com
for all current and future issues of the journal. |
|
| |
|
| |
|
| A COMPARATIVE STUDY OF ARITHMETIC, OBSERVATIONAL
AND PREDICTED LUNAR CALENDAR FOR PAKISTAN FOR YEARS 2000-2004 |
Muhammad Shahid Qureshi1 and Nasiruddin Khan2
1Institute of Space & Planetary Astrophysics, University of Karachi, Karachi-75270, Pakistan
2Department of Mathematics, University of Karachi, Karachi-75270, Pakistan |
| ABSTRACT |
Arithmetic Lunar Calendar is based on the concept of Leap Years and the average
motion of the Moon. However, the actual motion of the Moon varies greatly due to various factors which cause the
observational calendar to be different from the arithmetic calendar. Whereas, the Calendars based on prediction
criterion of Yallop are the closest to the observational calendar. In this work, we compare these calendars with the
actual observational calendar in practice in Pakistan for the years 2000 to 2004. It is found that on average 95%
observations are according to the Yallop’s criterion. The disagreement is the result of either the bad weather due to
which the new Lunar crescent could not be sighted and the Lunar month began one day late, or too optimistic claims of
observation and the Lunar month began one day earlier than predicted. On the other hand the disagreement between the
Arithmetic Calendar and the observational one is 54%.
|
| INTRODUCTION |
| Reingold and Dershowitz (2001) have given an extensive account of more than 20 different
calendars. This account is based on average motion of the Sun and the Moon and describes the history and practice of each
calendar whether it is Solar, Lunar or Luni-Solar. Starting with the epoch, the sunset of Thursday, July 15, 622 C.E.
(Julian), the year of Prophet Muhammad’s (PBUH) emigration to Madina, the Arithmetic Islamic Calendar, they describe,
has 12 months of alternately 30 and 29 days. The last month of a year is considered as the Leap year if the year number
satisfies the leap-year-criterion. Most of the Islamic countries follow an observational lunar calendar, at least for their
religious purposes. Although substantial work is done to evolve a prediction criterion to develop a universal calendar by
Ilyas (1984, 1988, 1994, 1997) and others, a truly universal calendar could not be developed. As according to common Islamic
belief actual sighting of the new lunar crescent is necessary to begin a Lunar month, such a universal calendar seems to be
impossible. This is true especially because just after conjunction the new lunar crescent is not visible on the same day
throughout the world, even if two places of observation are on same longitude. Yallop’s (1998) single parameter
criterion is the most accepted method of determining whether the new Lunar crescent would be visible on a particular day at a
particular place or not. Based on this criterion accurate lunar calendar for each Islamic country can be developed but are not
generally accepted by various Islamic communities. Shaukat on his website www.moonsighting.com is keeping a track of
this “calendar” along with a number of members of the website.
In Pakistan an Official Committee (Ruet-e-Hilal Committee) decides about when to begin a Lunar month on the basis of
public observations. In this work all these public observation-based dates of start of each Lunar month from year 2000 to
2004 are reproduced and are studied in comparison with the Yallop’s criterion-based calendar and the Arithmetic
calendar (Tables 2 to 6 in appendix). |
| THE ARITHMETIC LUNAR CALENDAR |
The Lunation Period is the time interval between two consecutive conjunctions of the Moon. It is known that due to a number
of perturbations the Moon does not follow a perfect elliptical path around the Earth (none of the planets and their satellites
does). Due to these perturbations, the Lunation period is not a constant. Its average value is 29.530589 days. During the
period of this study (year 2000-2004) it varied from a minimum of 29.295208 days (Rabius Sani 1421 A.H.) to a maximum of
29.822986 days (Shawwal 1421). It should thus be noted that the average of lunation period is considered over a longer
(a century at least) period. Thus in a 12-month Lunar year based on the average value there are 354.367068 days. Whereas,
if alternate months of 30 and 29 days are considered in a Lunar year (6 moths of 30 and 6 moths of 29) it makes a total of
354 days. This makes the average year to be 0.367068 days ahead of the year with alternate 30 and 29 days’ months. If
11 years out of each cycle of 30 Lunar years are considered to be Leap Years (1 day extra in the last month) it makes 10631
days in the cycle. On the other hand 30 years each containing an average of 354.367068 days makes a total of 10631.01204 days.
This causes an excess of 12 days in the average-year cycle of 3000 years as compared to alternate 30-29 days lunar months with
11 Leap Years in every 30 years. The Arithmetic Islamic Lunar Calendar presented by Reingold and Dershowitz (2001) considers 12
Islamic Lunar months of alternately 30 and 29 days as follows:
(1) Muharram 30 days
(2) Safar 29 days
(3) Rabi al-Awwal 30 days
(4) Rabi al Akhir 29 days
(5) Jumada al-Awwal 30 days
(6) Jumada al-Akhir 29 days
(7) Rajab 30 days
(8) Shaaban 29 days
(9) Ramadan 30 days
(10) Shawwal 29 days
(11) Dhul al-Qa’da 30 days
(12) Dhul al-Hijja 29 days {30}
In the Leap Year the 12th month contains 30 days. Starting the first Islamic Year (beginning Muharram 1, the epoch Thursday, July 15,
622 C.E. (Julian)) as the Year Number 1, the rule for the Leap Year is: The year with year-number Y is a leap year if it satisfies the
following condition:
(( 14 + 11*Y) mod 30 ) < 11 (1)
Thus the 12th month contains 30 days in the year numbers 2,5,7,10,13,16,18,21,24,26 and 29 of each cycle of 30 years. Birashk (1993)
has used a variation of this rule. Such simple schemes, known as Istalahi system, were devised to construct long-term calendars
especially to inter-convert Islamic dates with Christian calendars and other luni-solar dates during the medieval times by Muslims and
Arabs (Ilyas 1994b). Within the range of this study (Greg. Years 2000 to 2004), from the Islamic years 1421 to Islamic year 1425 the
years, only 1423 is a leap year according to (1). Table 1 shows the comparison of the Observation based Lunar Calendar of Pakistan for
the years 2000 to 2004 with the Arithmetic Lunar calendar of Dershowitz and Reingold. This table shows (A) the time and date of New
Moon, (B) Gregorian date of the beginning of the new Lunar Month according the decisions of the Ruet-e-Hilal Committee, Pakistan for
the years 2000 to 2004, (C) the name of the Islamic Lunar Month, (D) the number of days in the lunar month (E) the date when the new
lunar month begins according to the Arithmetic Lunar Calendar and (F) whether the observation based lunar month
is “ahead”, “synchronized” or “behind” the arithmetic lunar month. There is a clear trend of
two/three consecutive months with either 29 days each or 30 days each. There can be at most four consecutive months of 30 days each and
three consecutive months of 29 days each (Ilyas 1994). The triplet of months of same duration (29 days), from Rabi al-Awwal, 1421 to
Jumad al Awwal, 1421 (June 5, 2000 to August 30, 2000) occurred due to late sighting on June 4,2000. This natural repetition of 29-days
lunar months and 30-days lunar months clearly contradicts alternate 29-days and 30-days lunar months adopted in the arithmetic lunar
calendar. Out of 62 cases of new moons considered only 28 matches are there between observational and the arithmetic calendar. Thus the
arithmetic calendar has 54% errors. The reason of consecutive lunar months of same duration is linked with the variations in the
Lunation Period and the region of Earth whereas the arithmetic lunar calendar is based only on average motion of the Moon.
|
| OBSERVATION BASED LUNAR CALENDAR |
As mentioned earlier that to make decision about starting new Lunar Month is the responsibility of an Official
Moon-sighting Committee (Ruet-e-Hilal Committee) in Pakistan. This committee gathers information about the claims of sighting
the crescent. The claims are judged on the basis of the directives of the Islamic Laws. Some representatives of various
scientific organizations are also consulted. Once the claim/s is justified religiously and/or scientifically, the announcement
is made about beginning of the next Lunar month. In a way, the beginning of new lunar month is based on “public
observations”. The advantage is that a large number of “observers” take part in the exercise and with it
the probability of sighting new crescent is increased. Moreover, most of these observers are from rural areas where there is
least industrial/traffic and light pollution, and it is highly probable that the observing conditions are near perfect.
Therefore in this study these public observations are considered to have a high degree of authenticity.
The results of the 62 lunation during the years 2000 to 2004 along with observational data is presented in Tables
No. 2 to 6. Out of the 62 public observations reported in this work, there were only three occasions when the sighting was
reported one day late in comparison to the prediction criterion of Yallop according to which the New Crescent was visible on
the previous day but was not reported. There was only one occasion when the early sighting is reported. Thus, there were
only 6.45% errors in the decisions of moon sighting committee of Pakistan during last five years. However, this result is
based on verified claims. The data regarding number of claims not verified is not available. The low percentage of errors
in this observational effort is much more promising as compared to the results of “moon watch” programs conducted
in United States in the late 1980s and reported by Dogget & Schaeffer (1994). According to this report 15% positive errors
(wrong claims of observing the crescent) and 2% negative errors (crescent was visible but the observers missed them) were
found amongst the experienced moon watchers. These experienced moon watchers were generally considered to know where to find
the crescent and what the orientation of the “horns” was.
One of the major causes of false claim of early sighting of new crescent in Pakistan is the keenness of the claimer and
the misconception amongst masses that when the “sighting” has been reported in the Kingdom of Saudi Arabia the
crescent must be sighted the next day in Pakistan. However, the official decision about starting new lunar month in the
Kingdom of Saudi Arabia is not based on actual sighting of the new crescent. These decisions are based on criteria that have
changed three times over the past two decades (Odeh 2000).
i) Up to 1999 the criteria was as follows: If the Moon’s age at the sunset is 12 hours or more after the New Moon, the previous day is the first day of the Islamic month. This actually means that the lunar month begins on the day of conjunction of Moon which occurs one or two days earlier than the time when the new crescent becomes visible to the naked eye.
ii) From 1999 the criterion was changed to the following: The lunar month begins on the evening when the sunset is before the moon set according to Mecca. This was more disastrous as it is possible that the sunset before moonset will occur even before the conjunction. Therefore, the lunar month may begin three days before the crescent becomes visible to naked eye.
iii) From 2003 onwards the criterion is:
a) The geocentric conjunction occurs before Sunset.
b) The Moon sets after the Sun.
This is more realistic but it is scarcely possible that the crescent becomes visible on the day of conjunction.
Tables 2-6, show the crescent visibility on the day on the conjunction and on the day after, for year 2000-2004, for
Pakistan. These tables clearly show that new crescent was never visible on the day of the conjunction in Pakistan. During
last five years (2000-2004) the best condition for crescent visibility on the day of conjunction was on August 9, 2002 but
still the sighting was not reported. On this particular day the moonset occurred 48 minutes after sunset, the age of moon was
around 19 hours, the crescent width 52 arc seconds and Moon was visible under perfect conditions. On three other occasions
(September 28, 2000 and July 21 and October 17 2001) the visibility was very close to naked eye visibility on the day of
conjunction but was not reported in any of these. |
| THE LUNAR CALENDAR FOR PAKISTAN BASED ON YALLOP’S CRITERION |
Since the antiquity, the problem of earliest visibility of the New Lunar Crescent has baffled the
Astronomers as well as the religious leadership. For Astronomers, being explorers of nature it has lead to a better
understanding of the Lunar orbit around the Earth and resulted into good enough prediction criteria. The religious
leadership is still forced to depend on the actual observation (at least amongst various Islamic schools of thought).
Amongst the Astronomers of various eras, Babylonians considered the following conditions for the New Lunar Crescent to be
visible at any place Age > 24 hours and Lag > 48 minutes. The Muslim/Arab astronomers modified this criterion to Altitude >
8 degrees and Lag > 45 minutes. The conditions used by Muslim/Arab Astronomers are still considered authentic. However, over
the past century a number of authors have contributed significantly in the understanding of the problem. A number of
references may be found in Ilyas (1994b) and Yallop (1998).
Two quantities of major concern in the visibility of the new Lunar Crescent are the Altitude (ARCV) of the Crescent
relative that of the Sun (at the time of sunset on the days following a conjunction) and the Width (W) of the Lunar
Crescent at the same time. The importance of the crescent width was realized by Bruin (1977) that others (Rizvi 1974)
claimed to be a rediscovery of the work of al-Beruni (1000). The height above horizon (ARCV) of the crescent is important
in view of the fact that lower the crescent more its visibility is diminished due to bright evening twilight and view
through denser (and more polluted) atmosphere closer to the horizon. However, closer is the Moon to the Earth (us) in its
orbit wider the crescent appears, thus being brighter it has a better chance for being sighted through the dense atmosphere
close to the horizon without any optical aid. The single-parameter criterion considered by Yallop (1998) for visibility of
the New Lunar Crescent is based on the value of q in the following formula:
q = (ARCV – (11.8371 – 6.226W +
0.7319W2 – 0.1018W3))/10 (4)
On the basis of this q-value test Yallop studied the recorded observations over the past 150 years and developed the following
criteria for the visibility of the new lunar crescent:
(A) q > +0•216
Easily visible (ARCL ³ 12°) EV
(B) +0•216 ³ q > -0•014
Visible under perfect conditions VUPC
(C) -0•014 ³ q > -0•160
May need optical aid to find crescent MROA
(D) -0•160 ³ q > -0•232
Will need optical aid to find crescent OAO
(E) -0•232 ³ q > -0•293
Not visible with a telescope ARCL £ 8•5° I
(F) -0•293 ³ q
Not visible, below Danjon limit, ARCL £ 8° I
For any place, just after sunset on a particular day following the conjunction, one requires to determine the coordinates of the Sun
and the Moon on the local horizon and the width of the crescent at the time of local sunset that leads to determination of the q value
for the place. Based on this q value one determines whether the New Crescent would be easily visible to the naked eye or not.
Table 1 . Observation Based Calendar Vrs Arithmetic Lunar Calendar
According to the visibility classification shown above, the surface of Earth is divided into 5 regions by four constant-q values.
As the actual visibility of the crescent depends on the its width and on its altitude above horizon at the time of sunset (4) a constant
q-value describes a curve on the globe indicating similar visibility conditions along all points of the curve. Such a curve is a
pseudo-parabolic curve with vertex on the east-most longitude. The longitudinal position of this vertex varies month to month and the
latitude of the vertex depends on the declination of the Moon on the celestial sphere that also varies month to month without any
seasonal dependence. The parabola opens westward above (northwards) and below (southwards) from the vertex. The Curve A is the
collection of points on the globe for which the q-value is 0.216. All regions within the two branches of the parabola west of the
vertex are the regions where the q-value is greater than 0.216 and the crescent is easily visible to the naked eye in this region.
Curve B is the collection of all points where the q-value is -0.014. In all the regions between curves A and B the crescent is visible
to the naked eye only under perfect visibility conditions. The regions between curve B and C (q-value -0.16) are the regions in which
an observer would require optical aid to locate the crescent and then it may be visible to naked eye. For regions with q-value less
than -0.16 the crescent would not be visible to the naked eye. For a common, untrained observer it is highly unlikely that the crescent
would be seen in regions east of the curve A. The scientifically recorded observations (on which all the study of the twentieth century
is based) do not prohibit observation of crescent with naked eye in region between curves A and C. In such regions, in fact, the
probability of observation increases with the number of keen trained and experienced observers.
The Tables No. 2 to 6 show the following:
i) Time & Date of Conjunction, or the Birth of New Moon.
ii) The Gregorian date of the day of conjunction or the day next to conjunction. In some cases two days after conjunction is also considered in case of very late visibility.
iii) Relative altitude (ARCV) and relative azimuth (DAZ) of the Moon at the time of sunset.
iv) The difference between the sunset and the moon set (LAG).
v) The time elapsed since the last conjunction till the time of local sunset(AGE).
vi) Separation between the Sun and the Moon (Elongation/ARCL).
vii) Width of the crescent (W).
viii) The q-value calculated according to (4).
ix) Visibility as described by (A for Easily Visible EV) to (F for Invisible I) above.
x) The name of the Islamic month, the date (Gregorian) on which it started according to the decision of the Reut-i-Hilal Committee
of Pakistan, the length (number of days) of the month and a comment (PROP for beginning of the month according to Yallop’s
criterion, LATE for starting the month one day late, EARLY for starting the month one day earlier than the Easily Visible criterion.
A close look at this table reveals that for two out of the three occasions when the crescent was sighted late (June 4, 2000 and June
23, 2001), the next lunar crescent was very close to sighting on the 28th day of a lunar month. In fact the conditions on both these
instances were much better than on the day when the sighting was reported early (November 13, 2004). Thereby, the practice amongst
Muslims to complete 30 days if the crescent is not seen on 29th of a lunar month especially due to cloudy season may cause a
discrepancy in the following sense. As mentioned earlier that there is a possibility of 3 consecutive lunar months occurring naturally,
if the first two of them are delayed due to bad weather there is always a chance that the crescent is sighted on 28th or even 27th of
the third month. Such a discrepancy is avoided by following the dates of the full Moon, and Islamic Shariah has a mechanism for
changing dates in the middle of a lunar month (Ilyas 1994b).
The Tables A to E also show that 58 out of 62 decisions for starting new lunar month by the Ruet-e-Hilal Committee, Pakistan are
exactly according to the Yallop’s criterion. The most serious deviation is that of November 13, 2004 which is the only instance
when a claim of early sighting (according to Yallop’s criterion) was accepted. Although early claims are frequently made
by general public but these are not accepted by Ruet-e-Hilal Committee. All these early claims are motivated by the claim of sighting
in Saudi Arabia as mentioned earlier.
On November 13, 2004 the astronomical conditions were very poor. The q-value was around -0.24 almost in the totally invisible range
for most of Pakistan. Altitude of Moon in Karachi was 6.7 degrees (old Muslim criteria required it to be more than 8 degrees). The LAG
was only 35 minutes (again old Muslim criterion required it to be more than 45 minutes). For Karachi the AGE was 22.5 hours. The only
positive factor was its phase that was around 1.2%. The Astronomical Almanac states that the crescent is generally visible when its
phase becomes more than 1%. However the recent understanding of the problem of earliest crescent visibility clearly rejects this
condition. This is simply due to the reason that with varying distances of the Moon from the Earth the brightness of the crescent
required for earliest visibility may be achieved at much smaller phase when the Moon is close and may not be achieved even when the
phase is much greater than 1%. In general none of the parameters from amongst LAG, AGE, ARCV etc. alone is enough for visibility and
the best one is based on the width of crescent, i.e. the one given by Yallop. |
| ANALYSIS AND DISCUSSION |
|
The main parameters significant in the earliest visibility criterion for the lunar crescent are LAG, AGE, ARCV, DAZ, ARCL,
Phase and the width of crescent. As mentioned above none of these parameters alone decide the visibility or non-visibility of
the lunar crescent. Generally the critical value of the Phase is considered to be 1%. During the five years from 2000 to 2004
that were considered in this study there was not a single incidence when the crescent of phase less than 1% was reported and
accepted. There is only one incidence of reported sighting when the AGE was less than 24 hours (22.3 hours) and that was
November 13, 2004, the most doubtful report of the range. Apart from this controversial sighting there was only one incidence
of sighting of AGE less 25 hours (Feb. 6, 2000). Apart from this there are only four occasions when crescent of less than 30
hours was reported and accepted the youngest being on October 7, 2002 of age 25.93 hours. There has been only 4 occasions when
the crescent as low as 11.4 degrees or less was reported and accepted. The lowest (7 degrees) being that of November 13, 2004.
Otherwise the lowest was on December 24, 2003 at 11.2 degrees. Lately on November 3, 2005 the Shawwal crescent was sighted at
8.97 degrees at the Astronomical Observatory of the University of Karachi first through telescope and then with naked eye.
Therefore at Karachi’s latitude (25 degrees) the crescent with ARCV less than 9 degrees can be seen but has not been
reported very frequently. Many authors have indicated that none of these parameters are reliable for earliest crescent
visibility. The Yallop’s criterion has been the most reliable under cloudless skies.
On the basis of the Yallop’s criterion that has proved to be the best in comparison to the decisions of the
Reut-i-Hilal Committee of Pakistan, the lunar crescent reaches visibility generally on the same day in Makkah as in Karachi.
There are only 10 out of 62 occasions during 2000 to 2005 that lunar crescent achieved “EV” the easily visible
conditions one day earlier in Makkah as compared to Karachi. This is indicated as the date of starting lunar month within
parenthesis in the Tables 2-6 below the Gregorian dates of the beginning of lunar months in Karachi.
The public observation and acceptance of the same by the Reut-i-Hilal Committee of Pakistan of November 13, 2004 has
been critically discussed in this work. However, in view of the record observation by Pierce (Schaeffer 1996) on February
25, 1990 (Lat. 35o.6, Long. -83o.5) of the crescent of only 14.8 hours and very low q-value (-0.16 to -0.232), this
observation seems acceptable. According to Yallop’s test the crescent should not have been sighted by Pierce.
For Pierce observation the phase was 0.55%, relative azimuth was 32 arc seconds, relative altitude 7.135 degrees, the
lag was 38 and a half minute and the crescent width was only 0.14 arc minute. Whereas during public observation of
November 13, 2004 the phase was well above 1.1%, relative azimuth was 10.4 degrees, relative altitude 7 degrees, the
width was more than 0.3 arc minute, the lag was 35 minutes and the age well over 22 hours. Such young crescent sightings
are mostly rejected by the Reut-i-Hilal Committee of Pakistan mostly because the claimers are not able to verify the
correct place of crescent and orientation of its horns. On four occasions when the crescent was very close to visibility
on the day of conjunction mentioned at the end of the article 3 above the crescent was not reported to have been sighted
because most of the keen observers try observing crescent mostly for the months of Ramazan, Shawwal and Zil Hajjah. For
the rest of the year common people do not try moon watching. |
| APPENDIX |
Table 2. Year 2000
Table 3. Year 2001
Table 4. Year 2002
Table 5. Year 2003
Table 6. Year 2004
Table 7. Year 2005
|
| REFERENCES |
al-Beruni, Abu Raihan Muhammad, 1000, Al-Athar al-Baqiyah an al-Quran al-Khaliyah. Translated and annotated by Sachau,
C. E. as The Chronology of Ancient Nations”, William H. Allen & Co., London, 1879; reprinted by Hijra International
Publishers, Lahore, Pakistan, 1983.
Birashk, A. 1993. A Comparative study of the Iranian, Muslim Lunar and Christian Eras of Three Thousand Years, Mazda Pub.,
Costa Mesa, CA.
Doggett, L.E. and Schaefer, B.E. 1994. Lunar Crescent Visibility, Icarus, 107, 388-403.
Ilyas, M. 1984. A Modern Guide to Astronomical Calculations of Islamic Calendar, Time and Qibla, Berita Publ. Sdn. Bhd.,
Kuala Lumpur, Malaysia.
Ilyas, M. 1988. Limiting Altitude separation in the Moon’s first visibility criterion, Asronom. Astrophys., 206: 133-135.
Ilyas, M. 1994a. New Moon’s Visibility and International Islamic Calendar (For the Asia-Pacific Region 1407H-1421H), Pub.
COMSTECH, OIC, Da’wah Council of South East Asia and pacific (RISEAP), Malaysia.
Ilyas, M. 1994b. Lunar Crescent Visibility Criterion and Islamic Calendar, Q. J. R. Astr. Soc., 35: 425-461.
Ilyas, M. 1997. Astronomy andf Islamic Calendar, A. S. Noordeen Pub.; Kuala Lumpur, Malaysia.
Maunder, M. 1911. On the Smallest Visible Phase of Moon, J. British Astron. Assoc. 21: 355-362.
Odeh, M. 2000. The Actual Saudi Dating System. The Jordanian Islamic Society, www.jas.org.jo/index.htmi
Reingold, EM. and Dershowitz, N. 2001. Calendarical Calculations. The Millennium Edition, Cambridge University Press, U.K.
Schaeffer, BE. 1996. Lunar Crescent Visibility, Q. J. R. astr. Soc. 37: 759-768.
Shaukat K., www.moonsighting.com
The Astronomical Almanac. 2004. His Majesty’s Stationary Office, London.
Yallop, BD. 1998. A Method of Predicting the First Sighting of New Moon, NAO Technical Note No. 69, HM Nautical Almanac Office, Royal Greenwich Observatory, Cambridge, UK.
|
|
|
|
|
|
|
