Bismillah hir-Rahman nir-Rahim

(In the Name of ALLAH, THE MOST BENEFICENT, THE MOST MERCIFUL)

THE RULES OF THE UMMUL QURA ISLAMIC CALENDAR ?

1 Jan 1998

Dr.Mohib.N.DURRANI, E-Mail: mnd0@columbia.edu
North American Coordinator (Since 1987), for Astronomical Information
Islamic Society of North America (ISNA), Copyright (c) 1997

       THE MUSLIM STUDENTS ASSOCIATION (MSA) OF COLUMBIA UNIVERSITY 
          102 Earl Hall, Columbia University, New York, NY 10027

              THE RULES OF THE UMMUL QURA ISLAMIC CALENDAR ?
              **********************************************
                                                         2 Ramadan 1418 AH
                                                         1 January 1998 AD
                                                  [11 Jan '98,Small revisions]
                            Dr.Mohib.N.Durrani
                             mnd0@columbia.edu
                      http://www.Hilal-Sighting.Com

                            Copyright (c) 1998
            [Permission for free distribution granted to all]
                                                         
As Salam alikum and Ramadan Mubarak to all.

I am very grateful to Br.Bushair Thayyil (from Saudi Arabia) for the 
explanation of the RULES of the "UMMUL QURA ISLAMIC CALENDAR" of Makkah. 

I would like to first repeat what Br.Thayyil had mentioned, so that we 
can be sure that we have understood what he has stated. Then, if these  
rules are the ones used for the Ummul Qura Islamic Calendar, I would like 
to share some extensions of the explanation and hence some implications 
of the rules of the calendar. These implications would give some idea of 
the strengths and limitations of this system for determining the 
"Ummul Qura Islamic Calendar", inshallah. This is accomplished by 
considering actual examples of lunations, specifically chosen, to 
highlight the implications. Examples for Shaban 1418 AH (Nov 1997), 
Ramadan 1418 AH (Dec 1997), and Shawwal 1418 AH (Jan 1998) are also given.

Ofcourse, an Islamic Month starts only after the actual sighting, in the 
Western direction, of the Hilal (Crescent Moon), in the evening, and 
after sunset.

IF the rules given by Br.Thayyil do NOT apply to the Ummul Qura Islamic 
Calendar, the following article can be considered as an explanation of 
the strengths and limitations of a calendar based on the Time of an 
Astronomical New Moon, with a built-in phase shift. 

A summary of the results is provided at the beginning of the analysis, 
after the graphical representation of the Hijri/Gregorian Days.

If any of you feel that I could learn more about the "Ummul Qura Islamic 
Calendar" from anyone else, please forward my message to them and/or 
forward their address (preferably email) to me. 

I seem to recall that Islamic Calendars are based on a thirty (30) year 
cycle with eleven (11) leap years in the cycle. The year has twelve (12) 
months with odd-numbered months having thirty (30) days and even-numbered 
months having twenty-nine (29) days. During leap years the twelfth month 
(Dhul-Hijjah) has thirty days. In the thiry year cycle the leap years are 
designated as year 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29.

The Islamic months are in the following order:

 1.  Muharram           2. Safar                3. Rabi-ul-Awwal
 4.  Rabi-ul-Thani      5. Jummah-dhul-Awwal    6. Jummah-dul-Thani
 7.  Rajab              8. Shaban               9. Ramadan
10. Shawwal            11. Zul-Qada            12. Zul-Hajj

I STRONGLY feel that an Islamic attitude of mutual respect and 
understanding can go a long way in the exchange of critical information. 
Since we are blessed with various email lists and newsgroups, I would 
request those of us who have additional technical astronomical 
information on the subject to help me in the understanding of the 
rules of the "Ummul Qura Islamic Calendar", Jazakumullahu Khairun.


Your brother in Islam,

Dr. Mohib.N.Durrani

North American Coordinator for
Astronomical Information
Islamic Society of North America (ISNA)
E-Mail: mnd@columbia.edu
Homepage  http://www.columbia.edu/~mnd

PS: The full article could not be posted at some places, due to length 
    restrictions, hence I request you to please visit my homepage 
    (address mentioned above) for the complete article with the 
    background calculations.

***********************************************************************

Br.Thayyil stated on Thu Jan  1 07:08:15 1998
> Subject: msa-net: Ramadan
> Message-Id: (99801011205.GAA29057@msa-natl.org)
> From: Bushair Thayyil, JEDDAH-21432, SAUDI ARABIA.
... .. .
> The world lunar calendar always agrees with the 'Ummul Qura Calendar' 
> and in turn with the announced dates in Makkah. (Or the dates are
> always announced based on the Ummul qura calendar.)

> The following are the rules to calculate the 'World Lunar Calendar'.. .

> 1. Hijra Date Line. Assuming Makkah (40E) as the zero line instead 
>    of Greenwich, the Hijra date line is fixed on 140w line which 
>    pass through the border of Canada and Alaska (US).

> 2. If the new moon falls in a hijra day the current day is the first 
>    day of the new hijra month.

> 3. Only when the New moon is after 21:00 hrs (greenwich) the date is 
>    not changed. (Since based on the Hijra date line 21:OO hrs fall in 
>    the next day )

> Thanks and Regards
> Bushair Thayyil

PS: Brother Thayyil has mentioned (in personal communications) that 
    the above rules are "expected" rules. The actual rules of the 
    Ummul Qura Calendar are known only to the creators of the calendar. 
    Please inform me if anyone knows the actual rules used to generate 
    the Ummul Qura Calendar, Jazakumullahu Khairun.

***********************************************************************
                 
I will first try and "draw" an approximate Longitude Grid of the world 
as this may help in crystalizing the concepts, inshallah.


                   HIJRI      Dr.Mohib.N.DURRANI       HIJRI
                    Date      Copyright (c) 1998        Date
                    Line             MAKKAH             Line
                     |                 |                 |
  REF: UMMUL QURA    |+++++++++++ HIJRI Date ++++++++++++| MAKKAH Centered 
                     |                 |                 |
  LONGITUDES:  -180-140            0  +40          +180+220 Degrees
                 W   W                 E             E   E
                 |   |             |   |             |   |
     |----|----|----|----|----|----|----|----|----|----|----|----|----|
                 |   |             |   |             |   
      Examples:  | 3 | 2           |   |           1 | Examples
                 |   |             |   |             |   
UNIVERSAL TIME: 24  21            12   9             0 [Noon at Greenwich]
Relative Hours:-12  -9             0  +3           +12 
                 |                 |                 |
                 |========= GREGORIAN Date ==========| GREENWICH Centered
                 |                 |                 |
           INTERNATIONAL       GREENWICH       INTERNATIONAL
                Date                                Date
                Line                                Line
                   ^   ^                           ^
                   |   |                           |
                   |   |    Examples 1A and 1B  =  1
                   |   2 =  Examples 2A and 2B
                   3     =  Examples 3A and 3B

                       E = East of Greenwich
                       W = West of Greenwich

        International    Date line: -180 deg W (same as +180 deg E)
        Ummul Qura Hijri Date Line: -140 deg W (same as +220 deg E)
                                   [Phase Shift of 40 Deg E, from Greenwich]

The following is a short description of the dynamics of the Sun-Earth-Moon 
system. The Earth revolves around the Sun in one year (Tropical Year, 
equinox to equinox: 365Days 05Hrs 48Min 45.19Sec). The Moon revolves 
around the Earth in about one month (Synodic Month, new moon to new moon: 
29Days 12Hrs 44Min 03Sec). The Earth rotates on its axis once a day 
(mean solar day: 24Hrs 00Min 00.0084Sec of mean sidereal time). Mean 
inclination of the path of the Moon around the Earth to the apparant 
path of the Sun around the Earth (Ecliptic) is 5.145396 Degrees. The 
mean obliquity of the ecliptic is 23Deg 26Min 21.4Sec to the equator. 

The International Date Line is an artificial line at around 180 deg 
Longitude (opposite to Greenwich Longitude of 0 degrees). 
The date increases by one while traveling west across the date line. 
The date decreases by one while traveling east across the date line.

If the Hilal (Crescent Moon) is first sighted at a location on the 
Earth, then all locations to the west of that location, on the same 
latitude, would be able to see the Hilal. In fact, places to the 
west of the location of first world-wide sighting would see the hilal 
more easily since it would be higher in the twilight sky and would 
also be thicker.

There exists a Zone-Of-Uncertainty (ZOU) around the locations of 
the first sightings of the Hilal (east and west of the location, 
at the same latitude) where the Hilal may or may not be seen, because 
of variations in the optical clarity of the atmosphere.

The first sighting of the Hilal could occur at any point on the globe and 
the loction of the first sighting varies from lunar month to lunar month.
Based on reported sightings of the Hilal, there exists a combination of  
minimum values of parameters when the Hilal could be PREDICTED AS VISIBLE.
The predominant factor is the altitude (height) of the Hilal relative to 
the Sun. The next predominant factor is the elongation of the Hilal (the 
angular separation of the Moon from the Sun, as viewed from the 
Earth).

SUMMARY OF IMPLICATIONS OF THE RULES OF UMMUL QURA ISLAMIC CALENDAR:
********************************************************************

The RULES OF UMMUL QURA CALENDAR state (?) that the Ummul Qura Calendar 
    ****************************
Month starts on the SAME DATE as the Astronomical New Moon (ANM) Date (ANMD) 
IF the Astronomical New Moon Time (ANMT) is LESS than 21 Hours Universal 
Time (UT). The Calendar Date is the DATE AFTER the Astronomical New Moon 
Date (ANMD) Date, IF the Astronomical New Moon time (ANMT) is GREATER than 
21 Hours Universal Time (UT). THEN such a calendar is expected to be 
ACCURATE FOR VISUAL SIGHTING OF THE CRESCENT MOON, AT MAKKAH, ONLY FOR 
**********************************************************************
ABOUT TWENTY PERCENT (20%) OF ITS PREDICTIONS !!!
*************************************************
 
Most of the sighting probabilies indicate "IMPOSSIBLE" for sightings on 
the date of the Astronomical New Moon. As will be shown later, only very 
few of the dates of the Astronomical New Moon have sighting probabilties 
of at least "Very Difficult" !!

 
 HENCE, SUCH A SET OF RULES ARE INADEQUATE FOR AN ISLAMIC CALENDAR, BASED 
 ************************************************************************
 ON PREDICTIVE VISUAL SIGHTINGS OF THE HILAL, AT MAKKAH. 
 *******************************************************
 
 Please see the examples shown below. The examples are given for the 
 following Astronomical New Moon Times:

 1. Astronomical New Moon Time of CLOSE TO     00 Hours (with ANMT>0 Hrs)
 2. Astronomical New Moon Time of LESS    THAN 21 Hours
 3. Astronomical New Moon Time of GREATER THAN 21 Hours
 4. Sighting Probabilities for the months of SHABAN, RAMADAN, 
    SHAWWAL, AND ZUL-HIJJ, 1418.

When we look at the conditions of the Sun and Moon AT MAKKAH on that evening 
of 1997 Dec 29 (Mon), for the month of Ramadan 1418, the Moon had set BEFORE 
the Sun had set making it IMPOSSIBLE for the Hilal to be seen. In addition 
to the above, the Astronomical New Moon Time was about 2 hours AFTER the the 
local sunset time!! 

The predicted visibility of the Hilal, at Makkah, on the evening of 
29 December 1997 was IMPOSSIBLE.

Please also note that the rules of the Ummul Qura Calendar would predict 
the Islamic month of RAMADAN 1418 to start on evening of 1997 Dec 29 (Mon) 
since the Astronomical New Moon occured on 1997 Dec 29d 16h 56m (Mon)!

Similarly, the start of Shaban 1418 would be predicted by the rules of Ummul 
Qura to be on the evening of 1998 Jan 28 (Wed) since the Astronomical New 
Moon Time is 1998 Jan 28d 06h 01m. 

The predicted visibility of the Hilal, AT MAKKAH, based on astronomical and 
atmospherical information, on the evening of 28 Jan 1998, is IMPOSSIBLE.

The following are some summarized details of the examples considered:

 ****************************************************************************
 
 EXAMPLE  ISLAMIC         SIGHTING DATE       ASRONOMICAL NEW MOON (UT)
   No.    Year Month      (Evening of)        Year Mth Dte Hr  Min (Day)

          Astronomical New Moon near 00 Hours Universal Time (UT)  
   1A     1418 SHABAN     1997 Nov 30 (Sun)   1997 Nov 30d 02h 14m (Sun) 
   1B     1416 SAFAR      1995 Jun 28 (Wed)   1995 Jun 28d 00h 50m (Wed)
 
          Astronomical New Moon less than 21 Hours Universal Time (UT)  
   2A     1411 SHAWWAL    1991 Apr 14 (Sun)   1991 Apr 14d 19h 38m (Sun)
   2B     1413 JUMMAH-1   1992 Oct 25 (Sun)   1992 Oct 25d 20h 34m (Sun)
   
          Astronomical New Moon greater than 21 Hours Universal Time (UT)  
   3A     1416 SHAWWAL    1996 Feb 18 (Sun)   1996 Feb 18d 23h 30m (Sun)
   3A1                    1996 Feb 19 (Mon)
   3B     1412 RABI-2     1991 Oct 07 (Mon)   1991 Oct 07d 21h 39m (Mon)
   3B1                    1991 Oct 08 (Tue)

          Examples for 1418 AD of SHABAN, RAMADAN, SHAWWAL, ZUL-HAJJ
   4A     1418 SHABAN     1997 Nov 30 (Sun)   1997 Nov 30d 02h 14m (Sun) 
   4B     1418 RAMADAN    1997 Dec 29 (Mon)   1997 Dec 29d 16h 56m (Mon)
   4C     1418 SHAWWAL    1998 Jan 28 (Wed)   1998 Jan 28d 06h 01m (Wed)
   4D     1418 ZUL-HIJJA  1998 Mar 28 (Sat)   1998 Mar 28d 03h 14m (Sat)

=============================================================================
A summary of the results of the predicted sighting of the Hilal, based 
on the Rules of the Ummul Qura Calendar is presented below.

 The following Symbols are used:

 * = Moonset BEFORE Sunset, Impossible to see Hilal
 $ = Hilal could be seen with Optical Aids
 @ = Hilal may not be seen even on the next date
 
=============================================================================
  
  Examples:         2A           2B                 1A           1B
IslamicMonth      1411Shw      1413Jm1            1418Shb      1416Sfr
AstroNewMoon      91Apr14      92Oct25            97Nov30      95Jun28
UniversalTime     19Hr38M      20Hr34M            02Hr14M      00Hr50M
SightinfDate      91Apr14      92Oct25            97Nov30      95Jun28
                SIGHTING ?   SIGHTING ?         SIGHTING ?   SIGHTING ?

.MAKKAH-SArb    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE$  IMPOSSIBLE
%ISTNBUL-Trk    IMPOSSIBLE   IMPOSSIBLE@        IMPOSSIBLE$  IMPOSSIBLE
.CAIRO-Egypt    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE$  IMPOSSIBLE
.CPETOWN-SAf    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   VERY DFCLT$
.ALGIERS-Alg    IMPOSSIBLE   IMPOSSIBLE@        VERY DFCLT$  IMPOSSIBLE
%GRENWCH-Eng    IMPOSSIBLE   IMPOSSIBLE@        IMPOSSIBLE$  IMPOSSIBLE
.DAKAR-Sengl    IMPOSSIBLE@  IMPOSSIBLE@        DIFFICULT $  IMPOSSIBLE
 
%RIOJNRO-Brz    IMPOSSIBLE@  IMPOSSIBLE         VERY DFCLT$  DIFFICULT $
.SnTIGO-Chle    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE$   PROBABLE $
.GUYQIL-Ecdr    IMPOSSIBLE   IMPOSSIBLE          PROBABLE    DIFFICULT $
%MIAMI---USA    IMPOSSIBLE   IMPOSSIBLE@         PROBABLE    IMPOSSIBLE
%SnDIEGO-USA    IMPOSSIBLE   IMPOSSIBLE          MOST PROBL  IMPOSSIBLE
.DWSONyk-Cnd    IMPOSSIBLE   IMPOSSIBLE         IMPOSSIBLE   IMPOSSIBLE
%ANCHORG-Als    IMPOSSIBLE   IMPOSSIBLE         IMPOSSIBLE$  IMPOSSIBLE
.HONOLU--Hwi    IMPOSSIBLE   IMPOSSIBLE          VISIBLE     VERY DFCLT$

              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.TOKYO-Japan    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.PERTH-Austr    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.JAKARTA-Ind    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
 
.KULALMP-Myl    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.DHAKA-BngDs    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.AGRA--India    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.PESHAWR-Pks    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.KABUL-Afghn    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE
.TEHRAN-Iran    IMPOSSIBLE@  IMPOSSIBLE@        IMPOSSIBLE   IMPOSSIBLE

=============================================================================
  
  Examples:         3A           3A1                3B           3B1     
IslamicMonth      1416Shw      1416Shw            1412Rb2      1412Rb2 
AstroNewMoon      96Feb18      96Feb18            91Oct07      91Oct07 
UniversalTime     23Hr30M                         21Hr39M
SightinfDate      96Feb18      96Feb19            91Oct07      91Oct08 
                              (NextDay)                       (NextDay)
                SIGHTING ?   SIGHTING ?         SIGHTING ?   SIGHTING ?

.MAKKAH-SArb    IMPOSSIBLE@  VERY DFCLT$        IMPOSSIBLE@   IMPOSSIBLE
%ISTNBUL-Trk    IMPOSSIBLE@  DIFFICULT $        IMPOSSIBLE@   IMPOSSIBLE
.CAIRO-Egypt    IMPOSSIBLE@  DIFFICULT $        IMPOSSIBLE@   IMPOSSIBLE
.CPETOWN-SAf    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE@    PROBABLE $
.ALGIERS-Alg    IMPOSSIBLE@   PROBABLE $        IMPOSSIBLE@   IMPOSSIBLE
%GRENWCH-Eng    IMPOSSIBLE@  DIFFICULT $        IMPOSSIBLE@   IMPOSSIBLE
.DAKAR-Sengl    IMPOSSIBLE@   PROBABLE $        IMPOSSIBLE@   IMPOSSIBLE
 
%RIOJNRO-Brz    IMPOSSIBLE@  IMPOSSIBLE$        IMPOSSIBLE@   MOST PROBL
.SnTIGO-Chle    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE     VISIBLE
.GUYQIL-Ecdr    IMPOSSIBLE@   PROBABLE          IMPOSSIBLE@    PROBABLE
%MIAMI---USA    IMPOSSIBLE    VISIBLE           IMPOSSIBLE@   IMPOSSIBLE
%SnDIEGO-USA    IMPOSSIBLE    VISIBLE           IMPOSSIBLE    IMPOSSIBLE
.DWSONyk-Cnd    IMPOSSIBLE   MOST PROBL         IMPOSSIBLE    IMPOSSIBLE
%ANCHORG-Als    IMPOSSIBLE    VISIBLE           IMPOSSIBLE    IMPOSSIBLE
.HONOLU--Hwi    IMPOSSIBLE    VISIBLE           IMPOSSIBLE    VERY DFCLT$
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE@   IMPOSSIBLE
.TOKYO-Japan    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE@   IMPOSSIBLE
.PERTH-Austr    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE@   IMPOSSIBLE$
.JAKARTA-Ind    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE@   IMPOSSIBLE
 
.KULALMP-Myl    IMPOSSIBLE@  IMPOSSIBLE         IMPOSSIBLE@   IMPOSSIBLE
.DHAKA-BngDs    IMPOSSIBLE@  IMPOSSIBLE$        IMPOSSIBLE@   IMPOSSIBLE
.AGRA--India    IMPOSSIBLE@  VERY DFCLT$        IMPOSSIBLE@   IMPOSSIBLE
.PESHAWR-Pks    IMPOSSIBLE@  VERY DFCLT$        IMPOSSIBLE@   IMPOSSIBLE
.KABUL-Afghn    IMPOSSIBLE@  VERY DFCLT$        IMPOSSIBLE@   IMPOSSIBLE
.TEHRAN-Iran    IMPOSSIBLE@  VERY DFCLT$        IMPOSSIBLE@   IMPOSSIBLE
 
=============================================================================
=============================================================================
EXAMPLE 1A: (Detailed Outputs)
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1418 SHABAN [8th Islamic Month]
    Astronomical New Moon Date    1997 Nov 30d 02h 14m (UT) (Sun) [INVISIBLE]
    Sighting Date, Evening of     1997 Nov 30 (Sun) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 17:39 18:12  12: 25  +7<+7  +1 IMPOSSIBLE$
%ISTNBUL-Trk  41.0   28.9  +2 16:39 17:20  12: 25  +7<+7  -2 IMPOSSIBLE$
.CAIRO-Egypt  30.1   31.3  +2 16:55 17:32  12: 41  +7 +7  -0 IMPOSSIBLE$
.CPETOWN-SAf -33.8   18.6  +2 19:41 20: 0  15: 27  +9 +4  +8 IMPOSSIBLE
.ALGIERS-Alg  36.8    3.0  +0 16:33 17:16  14: 19  +8<+8  -2 VERY DFCLT$
%GRENWCH-Eng  51.5    0.0  +0 15:56 16:47  13: 42  +8 +6  -4 IMPOSSIBLE$
.DAKAR-Sengl  14.7  -17.5  +0 18:38 19:17  16: 24  +9 +9  +1 DIFFICULT $
 
%RIOJNRO-Brz -22.9  -43.2  -3 18:23 18:56  19:  9 +10<+7  +7 VERY DFCLT$
.SnTIGO-Chle -33.2  -71.0  -4 19:38 20:10  21: 24 +11 +6  +9 IMPOSSIBLE$
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:19 19: 3  21:  5 +11+10  +4  PROBABLE
%MIAMI---USA  25.8  -80.2  -5 17:30 18:20  20: 16 +10+10  -2  PROBABLE
%SnDIEGO-USA  32.7 -117.1  -8 16:43 17:41  22: 29 +11+11  -4 MOST PROBL
.DWSONyk-Cnd  64.1 -139.4  -8 15:39 17: 6  21: 25 +11 +5 -10 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 15:54 17:15  22: 40 +12 +6 -10 IMPOSSIBLE$
.HONOLU--Hwi  21.3 -157.5 -10 17:46 18:47  25: 32 +13+13  -2  VISIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 17:37*17:27   3: 23  +5 -2  +5 IMPOSSIBLE
.TOKYO-Japan  35.7  139.7  +9 16:30 16:55   5: 16  +5 +5  +1 IMPOSSIBLE
.PERTH-Austr -31.8  116.2  +8 19: 5 19: 9   8: 51  +6 +1  +6 IMPOSSIBLE
.JAKARTA-Ind  -6.3  106.9  +7 17:56 18:12   8: 42  +6 +4  +5 IMPOSSIBLE
 
.KULALMP-Myl   3.1  101.7  +8 19: 2 19:21   8: 48  +6 +4  +4 IMPOSSIBLE
.DHAKA-BngDs  23.8   90.3  +6 17:12 17:39   8: 58  +6<+6  +2 IMPOSSIBLE
.AGRA--India  27.2   77.9  +6 17:56 18:25  10: 12  +6 +6  +1 IMPOSSIBLE
.PESHAWR-Pks  33.6   71.4  +5 17: 7 17:40   9: 53  +6 +6  +0 IMPOSSIBLE
.KABUL-Afghn  34.5   69.2  +5 17:14 17:47  10: 30  +6 +6  +0 IMPOSSIBLE
.TEHRAN-Iran  35.7   51.4  +3 16:23 16:59  11:  9  +7<+7  -1 IMPOSSIBLE

=============================================================================
EXAMPLE 1B:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1416 SAFAR     [ 2nd Islamic Month]
    Astronomical New Moon Date    1995 Jun 28d 00h 50m (UT) (Wed) [INVISIBLE]
    Sighting Date, Evening of     1995 Jun 28 (Wed) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 19: 8 19:23  15: 18  +8 +3  -7 IMPOSSIBLE
%ISTNBUL-Trk  41.0   28.9  +2 19:42 19:45  16: 52  +9 +1  -9 IMPOSSIBLE
.CAIRO-Egypt  30.1   31.3  +2 19: 0 19:12  16: 10  +9 +2  -8 IMPOSSIBLE
.CPETOWN-SAf -33.8   18.6  +2 17:48 18:29  14: 58  +7 +7  -0 VERY DFCLT$
.ALGIERS-Alg  36.8    3.0  +0 19:10 19:20  18: 20  +9 +2  -9 IMPOSSIBLE
%GRENWCH-Eng  51.5    0.0  +0 20:20*20:13  19: 30 +10 -1 -10 IMPOSSIBLE
.DAKAR-Sengl  14.7  -17.5  +0 19:42 20: 7  18: 52  +9<+6  -7 IMPOSSIBLE
 
%RIOJNRO-Brz -22.9  -43.2  -3 17:19 18: 3  19: 29  +9 +9  -1 DIFFICULT $
.SnTIGO-Chle -33.2  -71.0  -4 17:47 18:40  20: 57 +10+10  +1  PROBABLE $
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:19 19: 1  22: 29 +11 +9  -5 DIFFICULT $
%MIAMI---USA  25.8  -80.2  -5 19:15 19:42  23: 25 +11<+6 -10 IMPOSSIBLE
%SnDIEGO-USA  32.7 -117.1  -8 18:59 19:26  26:  9 +13 +5 -11 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 23:47*22:51  30: 57 +15 -4 -15 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 22:39*22:13  30: 49 +15 -2 -15 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 19:15 19:54  28: 25 +13 +8 -10 VERY DFCLT$
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 15: 2 15:24   2: 12  +4 +4  -2 IMPOSSIBLE
.TOKYO-Japan  35.7  139.7  +9 19: 1*18:56   9: 11  +6 -1  -6 IMPOSSIBLE
.PERTH-Austr -31.8  116.2  +8 17:22 17:47   8: 32  +5 +5  -2 IMPOSSIBLE
.JAKARTA-Ind  -6.3  106.9  +7 17:50 18: 7  10:  0  +6 +4  -4 IMPOSSIBLE
 
.KULALMP-Myl   3.1  101.7  +8 19:26 19:41  10: 36  +6 +3  -5 IMPOSSIBLE
.DHAKA-BngDs  23.8   90.3  +6 18:50 18:57  12:  0  +7 +2  -7 IMPOSSIBLE
.AGRA--India  27.2   77.9  +6 19:48 19:55  13: 28  +8 +1  -8 IMPOSSIBLE
.PESHAWR-Pks  33.6   71.4  +5 19:29 19:33  13: 39  +8 +1  -8 IMPOSSIBLE
.KABUL-Afghn  34.5   69.2  +5 19:40 19:43  14: 20  +8 +0  -8 IMPOSSIBLE
.TEHRAN-Iran  35.7   51.4  +3 18:54 18:59  15:  4  +8 +1  -8 IMPOSSIBLE
 
=============================================================================
EXAMPLE 2A:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1411 SHAWWAL   [10th Islamic Month]
    Astronomical New Moon Date    1991 Apr 14d 19h 38m (UT) (Sun) [INVISIBLE]
    Sighting Date, Evening of     1991 Apr 14 (Sun) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 18:41*18:26  -3: 57  +6 -3  +5 IMPOSSIBLE@
%ISTNBUL-Trk  41.0   28.9  +2 18:44*18:39  -2: 54  +5 -1  +5 IMPOSSIBLE
.CAIRO-Egypt  30.1   31.3  +2 18:22*18:12  -3: 16  +6 -2  +5 IMPOSSIBLE@
.CPETOWN-SAf -33.8   18.6  +2 18:26*17:55  -3: 12  +6 -6  +1 IMPOSSIBLE@
.ALGIERS-Alg  36.8    3.0  +0 18:21*18:19  -1: 17  +5 -0  +5 IMPOSSIBLE
%GRENWCH-Eng  51.5    0.0  +0 18:54 19: 3   0:-44  +5 +1  +5 IMPOSSIBLE
.DAKAR-Sengl  14.7  -17.5  +0 19:23*19:15   0:-15  +5 -2  +5 IMPOSSIBLE@
 
%RIOJNRO-Brz -22.9  -43.2  -3 17:41*17:22   1:  3  +6 -4  +4 IMPOSSIBLE@
.SnTIGO-Chle -33.2  -71.0  -4 18:23*18: 2   2: 45  +6 -4  +4 IMPOSSIBLE@
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:21*18:15   3: 43  +6 -1  +5 IMPOSSIBLE
%MIAMI---USA  25.8  -80.2  -5 18:43 18:51   4:  5  +5 +2  +5 IMPOSSIBLE
%SnDIEGO-USA  32.7 -117.1  -8 18:17 18:36   6: 39  +6 +4  +4 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 20:47 21:58   9:  9  +6 +6  -0 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 20:19 21:23   9: 41  +6 +6  +0 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 18:48 19: 7   9: 10  +6 +4  +5 IMPOSSIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 15:54*15: 6 -15: 44 +11 -8  -7 IMPOSSIBLE@
.TOKYO-Japan  35.7  139.7  +9 18:14*17:46 -10: 24  +8 -5  +6 IMPOSSIBLE@
.PERTH-Austr -31.8  116.2  +8 17:57*17:17  -9: 41  +8 -8  -1 IMPOSSIBLE@
.JAKARTA-Ind  -6.3  106.9  +7 17:54*17:21  -8: 44  +8 -8  +2 IMPOSSIBLE@
 
.KULALMP-Myl   3.1  101.7  +8 19:20*18:51  -8: 18  +8 -7  +3 IMPOSSIBLE@
.DHAKA-BngDs  23.8   90.3  +6 18:20*17:57  -7: 18  +7 -5  +5 IMPOSSIBLE@
.AGRA--India  27.2   77.9  +6 19:13*18:54  -5: 55  +6 -3  +6 IMPOSSIBLE@
.PESHAWR-Pks  33.6   71.4  +5 18:44*18:28  -5: 54  +6 -3  +6 IMPOSSIBLE@
.KABUL-Afghn  34.5   69.2  +5 18:54*18:39  -5: 14  +6 -2  +6 IMPOSSIBLE@
.TEHRAN-Iran  35.7   51.4  +3 18: 7*17:55  -4: 31  +6 -2  +5 IMPOSSIBLE@
 
=============================================================================
EXAMPLE 2B:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1413 JUMMAH-1  [ 5th Islamic Month]
    Astronomical New Moon Date    1992 Oct 25d 20h 34m (UT) (Sun) [INVISIBLE]
    Sighting Date, Evening of     1992 Oct 25 (Sun) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 17:50*17:22  -5: 44  +6 -6  -1 IMPOSSIBLE@
%ISTNBUL-Trk  41.0   28.9  +2 17:11*16:36  -5: 23  +6 -6  +1 IMPOSSIBLE@
.CAIRO-Egypt  30.1   31.3  +2 17:14*16:44  -5: 20  +6 -6  -0 IMPOSSIBLE@
.CPETOWN-SAf -33.8   18.6  +2 19: 8*18:58  -3: 26  +5 -2  -4 IMPOSSIBLE@
.ALGIERS-Alg  36.8    3.0  +0 16:59*16:30  -3: 35  +5 -5  -1 IMPOSSIBLE@
%GRENWCH-Eng  51.5    0.0  +0 16:46*16: 8  -3: 48  +6 -5  +1 IMPOSSIBLE@
.DAKAR-Sengl  14.7  -17.5  +0 18:44*18:26  -1: 50  +5 -4  -3 IMPOSSIBLE@
 
%RIOJNRO-Brz -22.9  -43.2  -3 18: 1*17:59   0: 27  +4 -1  -4 IMPOSSIBLE
.SnTIGO-Chle -33.2  -71.0  -4 19: 5 19:12   2: 31  +4 +1  -3 IMPOSSIBLE
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:11*18: 9   2: 37  +4 -1  -4 IMPOSSIBLE
%MIAMI---USA  25.8  -80.2  -5 17:44*17:30   2: 10  +5 -3  -4 IMPOSSIBLE@
%SnDIEGO-USA  32.7 -117.1  -8 17: 4*16:51   4: 30  +5 -2  -4 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 17:21*16:29   4: 47  +5 -5  -3 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 17:17*16:34   5: 43  +6 -4  -4 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 17:57*17:56   7: 23  +5 -0  -5 IMPOSSIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 16:54*16:16 -15: 40 +10 -8  -7 IMPOSSIBLE@
.TOKYO-Japan  35.7  139.7  +9 16:55*16:11 -12: 39  +9 -8  +3 IMPOSSIBLE@
.PERTH-Austr -31.8  116.2  +8 18:34*18: 6 -10:  0  +8 -5  -5 IMPOSSIBLE@
.JAKARTA-Ind  -6.3  106.9  +7 17:47*17:15  -9: 47  +8 -7  -3 IMPOSSIBLE@
 
.KULALMP-Myl   3.1  101.7  +8 18:59*18:27  -9: 35  +8 -8  -2 IMPOSSIBLE@
.DHAKA-BngDs  23.8   90.3  +6 17:25*16:50  -9:  9  +8 -8  +1 IMPOSSIBLE@
.AGRA--India  27.2   77.9  +6 18:12*17:38  -7: 52  +7 -7  -0 IMPOSSIBLE@
.PESHAWR-Pks  33.6   71.4  +5 17:30*16:54  -8:  4  +7 -7  +1 IMPOSSIBLE@
.KABUL-Afghn  34.5   69.2  +5 17:38*17: 2  -7: 26  +7 -7  +1 IMPOSSIBLE@
.TEHRAN-Iran  35.7   51.4  +3 16:48*16:13  -6: 46  +7 -7  +1 IMPOSSIBLE@
 
=============================================================================
EXAMPLE 3A:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1416 SHAWWAL   [ 9th Islamic Month]
    Astronomical New Moon Date    1996 Feb 18d 23h 30m (UT) (Sun) [INVISIBLE]
    Sighting Date, Evening of     1996 Feb 18 (Sun) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 17:50 17:56  -8: 40  +7 -6  +4 IMPOSSIBLE@
%ISTNBUL-Trk  41.0   28.9  +2 18:21*17:22  -7:  9  +6 -3  +5 IMPOSSIBLE@
.CAIRO-Egypt  30.1   31.3  +2 17:43*17:23  -7: 47  +7 -5  +5 IMPOSSIBLE@
.CPETOWN-SAf -33.8   18.6  +2 17:46 19: 4  -7: 44  +7 -7  -1 IMPOSSIBLE@
.ALGIERS-Alg  36.8    3.0  +0 19:36*17:14  -3: 54  +5 -2  +5 IMPOSSIBLE@
%GRENWCH-Eng  51.5    0.0  +0 17:31*17: 7  -5: 59  +6 -2  +5 IMPOSSIBLE@
.DAKAR-Sengl  14.7  -17.5  +0 17:20 18:58  -6: 10  +6 -4  +5 IMPOSSIBLE@
 
%RIOJNRO-Brz -22.9  -43.2  -3 19:15*18: 9  -1: 15  +5 -4  +2 IMPOSSIBLE@
.SnTIGO-Chle -33.2  -71.0  -4 18:30 19:12  -1:  0  +5 -4  +2 IMPOSSIBLE@
.GUYQIL-Ecdr  -4.5  -80.0  -5 19:33*18:30   1:  3  +4 -2  +4 IMPOSSIBLE@
%MIAMI---USA  25.8  -80.2  -5 18:41*18:12   0: 11  +4 -1  +4 IMPOSSIBLE
%SnDIEGO-USA  32.7 -117.1  -8 18:16*17:41   2: 46  +4 +1  +3 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 17:36 18:28   2:  6  +3 +3  +2 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 18: 0 18:22   3: 30  +3 +3  +1 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 17:55 18:37   4: 25  +4 +2  +4 IMPOSSIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 18:29*16:30 -17:  1 +12-10  -6 IMPOSSIBLE@
.TOKYO-Japan  35.7  139.7  +9 17:23*16:44 -15:  7 +10 -8  +7 IMPOSSIBLE@
.PERTH-Austr -31.8  116.2  +8 17:26 18:19 -14:  4 +10-10  -3 IMPOSSIBLE@
.JAKARTA-Ind  -6.3  106.9  +7 19: 3*17:37 -11: 27  +9 -9  +0 IMPOSSIBLE@
 
.KULALMP-Myl   3.1  101.7  +8 18:16 18:52 -13: 14 +10 -9  +2 IMPOSSIBLE@
.DHAKA-BngDs  23.8   90.3  +6 19:29*17:22 -10:  1  +8 -7  +5 IMPOSSIBLE@
.AGRA--India  27.2   77.9  +6 17:56 18:12 -11:  4  +8 -7  +5 IMPOSSIBLE@
.PESHAWR-Pks  33.6   71.4  +5 18:43*17:32  -9: 47  +8 -6  +5 IMPOSSIBLE@
.KABUL-Afghn  34.5   69.2  +5 18: 2*17:40  -9: 58  +8 -5  +5 IMPOSSIBLE@
.TEHRAN-Iran  35.7   51.4  +3 18: 9*16:53  -8: 21  +7 -5  +5 IMPOSSIBLE@
 
=============================================================================
EXAMPLE 3A1:
        
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1416 SHAWWAL   [ 9th Islamic Month]
    Astronomical New Moon Date    1996 Feb 18d 23h 30m (UT) (Sun) [INVISIBLE]
    Sighting Date, Evening of     1996 Feb 19 (Mon) evening 
    Sighting Date Increase           1 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 18:22 18:58  15: 52  +9 +8  +3 VERY DFCLT$
%ISTNBUL-Trk  41.0   28.9  +2 17:44 18:34  16: 14  +9 +9  -0 DIFFICULT $
.CAIRO-Egypt  30.1   31.3  +2 17:46 18:29  16: 16  +9 +9  +2 DIFFICULT $
.CPETOWN-SAf -33.8   18.6  +2 19:35 19:47  18:  5 +11 +2 +10 IMPOSSIBLE
.ALGIERS-Alg  36.8    3.0  +0 17:32 18:24  18:  2 +10+10  +0  PROBABLE $
%GRENWCH-Eng  51.5    0.0  +0 17:21 18:26  17: 51 +10 +9  -3 DIFFICULT $
.DAKAR-Sengl  14.7  -17.5  +0 19:15 19:57  19: 45 +11+10  +4  PROBABLE $
 
%RIOJNRO-Brz -22.9  -43.2  -3 18:29 18:56  21: 59 +12<+6 +11 IMPOSSIBLE$
.SnTIGO-Chle -33.2  -71.0  -4 19:32 19:54  24:  2 +14 +5 +13 IMPOSSIBLE
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:41 19:23  24: 11 +13+10  +9  PROBABLE
%MIAMI---USA  25.8  -80.2  -5 18:16 19:16  23: 46 +13+13  +2  VISIBLE
%SnDIEGO-USA  32.7 -117.1  -8 17:37 18:48  26:  7 +14+14  -0  VISIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 18: 3 20: 4  26: 33 +15+12  -9 MOST PROBL
%ANCHORG-Als  61.1 -150.0  -9 17:57 19:53  27: 27 +15+12  -9  VISIBLE
.HONOLU--Hwi  21.3 -157.5 -10 18:29 19:39  28: 59 +16+15  +3  VISIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 17:22*17:10   5: 52  +5 -3  +5 IMPOSSIBLE
.TOKYO-Japan  35.7  139.7  +9 17:27 17:53   8: 57  +5 +5  +2 IMPOSSIBLE
.PERTH-Austr -31.8  116.2  +8 19: 2 19: 3  11: 32  +7 +0  +7 IMPOSSIBLE
.JAKARTA-Ind  -6.3  106.9  +7 18:16 18:31  11: 46  +7 +3  +6 IMPOSSIBLE
 
.KULALMP-Myl   3.1  101.7  +8 19:29 19:48  11: 59  +7 +4  +5 IMPOSSIBLE
.DHAKA-BngDs  23.8   90.3  +6 17:57 18:26  12: 27  +7 +6  +3 IMPOSSIBLE$
.AGRA--India  27.2   77.9  +6 18:44 19:17  13: 44  +8 +7  +3 VERY DFCLT$
.PESHAWR-Pks  33.6   71.4  +5 18: 3 18:40  13: 33  +7 +7  +1 VERY DFCLT$
.KABUL-Afghn  34.5   69.2  +5 18:10 18:48  14: 10  +8<+8  +1 VERY DFCLT$
.TEHRAN-Iran  35.7   51.4  +3 17:20 18: 2  14: 50  +8 +8  +1 VERY DFCLT$
 
=============================================================================
EXAMPLE 3B:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1412 RABI-2    [ 4th Islamic Month]
    Astronomical New Moon Date    1991 Oct 07d 21h 39m (UT) (Mon) [INVISIBLE]
    Sighting Date, Evening of     1991 Oct 07 (Mon) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 18: 5*17:34  -6: 34  +7 -7  -1 IMPOSSIBLE@
%ISTNBUL-Trk  41.0   28.9  +2 17:39*17: 2  -6:  0  +7 -7  +1 IMPOSSIBLE@
.CAIRO-Egypt  30.1   31.3  +2 17:34*17: 1  -6:  5  +7 -7  -0 IMPOSSIBLE@
.CPETOWN-SAf -33.8   18.6  +2 18:53*18:40  -4: 46  +6 -2  -5 IMPOSSIBLE@
.ALGIERS-Alg  36.8    3.0  +0 17:24*16:51  -4: 15  +6 -6  -1 IMPOSSIBLE@
%GRENWCH-Eng  51.5    0.0  +0 17:26*16:44  -4: 13  +6 -6  +1 IMPOSSIBLE@
.DAKAR-Sengl  14.7  -17.5  +0 18:55*18:33  -2: 44  +6 -5  -3 IMPOSSIBLE@
 
%RIOJNRO-Brz -22.9  -43.2  -3 17:53*17:47   0:-46  +5 -1  -5 IMPOSSIBLE@
.SnTIGO-Chle -33.2  -71.0  -4 18:50 18:53   1: 11  +5 +1  -5 IMPOSSIBLE
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:13*18: 5   1: 34  +5 -2  -5 IMPOSSIBLE@
%MIAMI---USA  25.8  -80.2  -5 18: 1*17:42   1: 22  +6 -4  -4 IMPOSSIBLE@
%SnDIEGO-USA  32.7 -117.1  -8 17:26*17: 6   3: 47  +6 -4  -4 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 18:26*17:29   4: 47  +6 -6  -3 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 18:14*17:24   5: 35  +7 -6  -3 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 18:12*18: 3   6: 33  +6 -2  -6 IMPOSSIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 16:33*15:54 -17:  6 +11 -8  -8 IMPOSSIBLE@
.TOKYO-Japan  35.7  139.7  +9 17:19*16:34 -13: 20  +9 -9  +3 IMPOSSIBLE@
.PERTH-Austr -31.8  116.2  +8 18:21*17:50 -11: 18  +8 -6  -6 IMPOSSIBLE@
.JAKARTA-Ind  -6.3  106.9  +7 17:48*17:14 -10: 51  +8 -8  -3 IMPOSSIBLE@
 
.KULALMP-Myl   3.1  101.7  +8 19: 4*18:30 -10: 35  +8 -8  -2 IMPOSSIBLE@
.DHAKA-BngDs  23.8   90.3  +6 17:41*17: 5  -9: 58  +8 -8  +0 IMPOSSIBLE@
.AGRA--India  27.2   77.9  +6 17:41 17:54  -9: 28  +8 -8  +0 IMPOSSIBLE@
.PESHAWR-Pks  33.6   71.4  +5 18: 5*17:15  -8: 34  +8 -8  +1 IMPOSSIBLE@
.KABUL-Afghn  34.5   69.2  +5 17:39*17:23  -8: 30  +7 -7  +1 IMPOSSIBLE@
.TEHRAN-Iran  35.7   51.4  +3 17:34*16:35  -7:  5  +7 -7  +1 IMPOSSIBLE@

=============================================================================
EXAMPLE 3B1:
        
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1412 RABI-2    [ 4th Islamic Month]
    Astronomical New Moon Date    1991 Oct 07d 21h 39m (UT) (Mon) [INVISIBLE]
    Sighting Date, Evening of     1991 Oct 08 (Tue) evening 
    Sighting Date Increase           1 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 18: 4 18:14  17: 25 +10 +2 -10 IMPOSSIBLE
%ISTNBUL-Trk  41.0   28.9  +2 17:37*17:30  17: 58 +11 -1 -11 IMPOSSIBLE
.CAIRO-Egypt  30.1   31.3  +2 17:33 17:37  17: 54 +10 +1 -10 IMPOSSIBLE
.CPETOWN-SAf -33.8   18.6  +2 18:54 19:44  19: 15 +10+10  -3  PROBABLE $
.ALGIERS-Alg  36.8    3.0  +0 17:22 17:22  19: 43 +11 +0 -11 IMPOSSIBLE
%GRENWCH-Eng  51.5    0.0  +0 17:23*17: 3  19: 44 +12 -3 -11 IMPOSSIBLE
.DAKAR-Sengl  14.7  -17.5  +0 18:54 19:16  21: 15 +12 +5 -11 IMPOSSIBLE
 
%RIOJNRO-Brz -22.9  -43.2  -3 17:54 18:45  23: 15 +12+11  -5 MOST PROBL
.SnTIGO-Chle -33.2  -71.0  -4 18:51 19:57  25: 12 +13+13  -2  VISIBLE
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:13 18:56  25: 34 +13+10  -9  PROBABLE
%MIAMI---USA  25.8  -80.2  -5 18: 0 18:20  25: 21 +14 +4 -13 IMPOSSIBLE
%SnDIEGO-USA  32.7 -117.1  -8 17:24 17:41  27: 45 +15 +3 -15 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 18:22*17:27  28: 43 +16 -5 -15 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 18:10*17:30  29: 31 +16 -4 -16 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 18:11 18:44  30: 32 +16 +7 -15 VERY DFCLT$
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 16:34 17: 3   6: 55  +6 +4  -4 IMPOSSIBLE
.TOKYO-Japan  35.7  139.7  +9 17:18*17: 6  10: 39  +8 -2  -7 IMPOSSIBLE
.PERTH-Austr -31.8  116.2  +8 18:21 18:53  12: 42  +7 +6  -4 IMPOSSIBLE$
.JAKARTA-Ind  -6.3  106.9  +7 17:47 18: 5  13:  8  +8 +4  -7 IMPOSSIBLE
 
.KULALMP-Myl   3.1  101.7  +8 19: 4 19:18  13: 25  +8 +3  -8 IMPOSSIBLE
.DHAKA-BngDs  23.8   90.3  +6 17:41 17:43  14:  2  +9 +1  -9 IMPOSSIBLE
.AGRA--India  27.2   77.9  +6 18:29 18:30  15: 20  +9 +1 -10 IMPOSSIBLE
.PESHAWR-Pks  33.6   71.4  +5 17:51*17:48  15: 12  +9 -1  -9 IMPOSSIBLE
.KABUL-Afghn  34.5   69.2  +5 17:59*17:55  15: 50 +10 -0 -10 IMPOSSIBLE
.TEHRAN-Iran  35.7   51.4  +3 17:10*17: 7  16: 31 +10 -1 -10 IMPOSSIBLE
 
=============================================================================
=============================================================================
EXAMPLE 4A:  [Same as Example 1A, 1418 Shaban, 1997 Nov 30
 
=============================================================================
EXAMPLE 4B:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1418 Ramdan [9th Islamic Month]
    Astronomical New Moon Date    1997 Dec 29d 16h 56m (UT) (Mon) [INVISIBLE]
    Sighting Date, Evening of     1997 Dec 29 (Mon) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 17:50*17:48  -2:  6  +5 -0  +5 IMPOSSIBLE
%ISTNBUL-Trk  41.0   28.9  +2 16:46 16:53  -2: 10  +4 +1  +4 IMPOSSIBLE
.CAIRO-Egypt  30.1   31.3  +2 17: 4 17: 6  -1: 52  +5 +0  +5 IMPOSSIBLE
.CPETOWN-SAf -33.8   18.6  +2 19:59*19:40   1:  3  +5 -4  +4 IMPOSSIBLE@
.ALGIERS-Alg  36.8    3.0  +0 16:41 16:50   0:-15  +4 +2  +4 IMPOSSIBLE
%GRENWCH-Eng  51.5    0.0  +0 16: 0 16:19   0:-56  +4 +2  +3 IMPOSSIBLE
.DAKAR-Sengl  14.7  -17.5  +0 18:50 18:54   1: 54  +4 +1  +4 IMPOSSIBLE
 
%RIOJNRO-Brz -22.9  -43.2  -3 18:40*18:35   4: 44  +5 -1  +5 IMPOSSIBLE
.SnTIGO-Chle -33.2  -71.0  -4 19:56*19:50   7:  0  +6 -1  +6 IMPOSSIBLE
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:33 18:41   6: 37  +5 +2  +5 IMPOSSIBLE
%MIAMI---USA  25.8  -80.2  -5 17:40 17:58   5: 44  +5 +4  +3 IMPOSSIBLE
%SnDIEGO-USA  32.7 -117.1  -8 16:52 17:18   7: 56  +5 +5  +2 IMPOSSIBLE
.DWSONyk-Cnd  64.1 -139.4  -8 15:29 16:40   6: 33  +5 +4  -2 IMPOSSIBLE
%ANCHORG-Als  61.1 -150.0  -9 15:51 16:51   7: 55  +5 +5  -2 IMPOSSIBLE
.HONOLU--Hwi  21.3 -157.5 -10 17:57 18:26  11:  1  +6<+6  +2 IMPOSSIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 17:57*17: 9 -10: 59  +8 -8  -0 IMPOSSIBLE@
.TOKYO-Japan  35.7  139.7  +9 16:38*16:26  -9: 18  +7 -2  +7 IMPOSSIBLE@
.PERTH-Austr -31.8  116.2  +8 19:23*18:50  -5: 33  +6 -6  +2 IMPOSSIBLE@
.JAKARTA-Ind  -6.3  106.9  +7 18:10*17:49  -5: 46  +6 -5  +4 IMPOSSIBLE@
 
.KULALMP-Myl   3.1  101.7  +8 19:15*18:57  -5: 41  +6 -4  +5 IMPOSSIBLE@
.DHAKA-BngDs  23.8   90.3  +6 17:22*17:13  -5: 34  +6 -2  +5 IMPOSSIBLE@
.AGRA--India  27.2   77.9  +6 18: 5*17:59  -4: 21  +5 -1  +5 IMPOSSIBLE@
.PESHAWR-Pks  33.6   71.4  +5 17:16*17:13  -4: 40  +5 -0  +5 IMPOSSIBLE
.KABUL-Afghn  34.5   69.2  +5 17:22*17:20  -4:  4  +5 -0  +5 IMPOSSIBLE
.TEHRAN-Iran  35.7   51.4  +3 16:31 16:32  -3: 25  +5 +0  +5 IMPOSSIBLE
 
=============================================================================
EXAMPLE 4C:
 
        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1418 Shawwal [10th Islamic Month]
    Astronomical New Moon Date    1998 Jan 28d 06h 01m (UT) (Wed) [INVISIBLE]
    Sighting Date, Evening of     1998 Jan 28 (Wed) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 18:10 18:30   9:  9  +5 +4  +2 IMPOSSIBLE
%ISTNBUL-Trk  41.0   28.9  +2 17:17 17:46   9: 16  +5 +5  -0 IMPOSSIBLE
.CAIRO-Egypt  30.1   31.3  +2 17:29 17:53   9: 28  +5 +5  +1 IMPOSSIBLE
.CPETOWN-SAf -33.8   18.6  +2 19:54 20: 1  11: 53  +7 +1  +7 IMPOSSIBLE
.ALGIERS-Alg  36.8    3.0  +0 17: 9 17:41  11:  8  +6<+6  -0 IMPOSSIBLE
%GRENWCH-Eng  51.5    0.0  +0 16:43 17:21  10: 42  +5 +5  -2 IMPOSSIBLE
.DAKAR-Sengl  14.7  -17.5  +0 19: 7 19:35  13:  6  +7 +6  +2 IMPOSSIBLE$
 
%RIOJNRO-Brz -22.9  -43.2  -3 18:40 19: 1  15: 39  +8 +4  +7 IMPOSSIBLE
.SnTIGO-Chle -33.2  -71.0  -4 19:50 20:10  17: 49 +10 +4  +9 IMPOSSIBLE
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:42 19:15  17: 41  +9<+8  +5 VERY DFCLT$
%MIAMI---USA  25.8  -80.2  -5 18: 2 18:44  17:  1  +9 +9  +0 DIFFICULT $
%SnDIEGO-USA  32.7 -117.1  -8 17:18 18:10  19: 17 +10+10  -2  PROBABLE $
.DWSONyk-Cnd  64.1 -139.4  -8 16:53 18:18  18: 52 +10<+7  -8 VERY DFCLT$
%ANCHORG-Als  61.1 -150.0  -9 16:58 18:20  19: 57 +11 +7  -8 VERY DFCLT$
.HONOLU--Hwi  21.3 -157.5 -10 18:17 19:11  22: 16 +12+12  +0 MOST PROBL
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 17:47*17:30   0:-14  +4 -3  +2 IMPOSSIBLE@
.TOKYO-Japan  35.7  139.7  +9 17: 6 17:12   2:  5  +2 +1  +2 IMPOSSIBLE
.PERTH-Austr -31.8  116.2  +8 19:19*19:14   5: 18  +4 -1  +4 IMPOSSIBLE
.JAKARTA-Ind  -6.3  106.9  +7 18:18 18:22   5: 17  +4 +1  +3 IMPOSSIBLE
 
.KULALMP-Myl   3.1  101.7  +8 19:27 19:33   5: 26  +3 +1  +3 IMPOSSIBLE
.DHAKA-BngDs  23.8   90.3  +6 17:43 17:56   5: 42  +3 +3  +2 IMPOSSIBLE
.AGRA--India  27.2   77.9  +6 18:28 18:43   6: 57  +4 +4  +2 IMPOSSIBLE
.PESHAWR-Pks  33.6   71.4  +5 17:42 18: 0   6: 41  +4 +3  +1 IMPOSSIBLE
.KABUL-Afghn  34.5   69.2  +5 17:49 18: 8   7: 18  +4 +4  +1 IMPOSSIBLE
.TEHRAN-Iran  35.7   51.4  +3 16:58 17:21   7: 57  +4 +4  +1 IMPOSSIBLE
 
=============================================================================
EXAMPLE 4D:

        SUBJECT: CRESCENT MOON: FIRST VISIBILITY (every lunar month)
       **************************************************************
    ISLAMIC  Year and Month       1418 Zul-Hijja [12th Islamic Month]
    Astronomical New Moon Date    1998 Mar 28d 03h 14m (UT) (Sat) [INVISIBLE]
    Sighting Date, Evening of     1998 Mar 28 (Sat) evening 
    Sighting Date Increase           0 [day(s) from Astro New Moon Date]
 
 Event times are approximate       Civil  --   Clock  Standard   Time
(nearest)  (+N,-S) (+E)  Zone SUN   MOON   AGEat  MOON-SUN   Unaided-Eye
 CITY          LAT   LONG -UT SET   SET    Sunset ElgAlt Azm SIGHTING
 ***********   deg    deg  hr Hr:Mn Hr:Mn  Hr:Min DegDeg Deg **********

.MAKKAH-SArb  21.4   39.8  +3 18:36 19: 4  12: 22  +7 +6  -3 IMPOSSIBLE$
%ISTNBUL-Trk  41.0   28.9  +2 18:26 18:57  13: 12  +8<+6  -5 IMPOSSIBLE
.CAIRO-Egypt  30.1   31.3  +2 18:11 18:42  12: 57  +7 +6  -4 IMPOSSIBLE$
.CPETOWN-SAf -33.8   18.6  +2 18:47 19:17  13: 33  +8<+6  +5 IMPOSSIBLE
.ALGIERS-Alg  36.8    3.0  +0 18: 6 18:42  14: 52  +9<+7  -5 VERY DFCLT$
%GRENWCH-Eng  51.5    0.0  +0 18:26 19: 3  15: 12  +9 +5  -7 IMPOSSIBLE
.DAKAR-Sengl  14.7  -17.5  +0 19:21 19:59  16:  7  +9 +9  -2 DIFFICULT $
 
%RIOJNRO-Brz -22.9  -43.2  -3 17:56 18:35  17: 42 +10 +9  +5 DIFFICULT $
.SnTIGO-Chle -33.2  -71.0  -4 18:45 19:25  19: 31 +11 +8  +8 VERY DFCLT$
.GUYQIL-Ecdr  -4.5  -80.0  -5 18:27 19:14  20: 13 +11+11  +3 MOST PROBL
%MIAMI---USA  25.8  -80.2  -5 18:35 19:26  20: 21 +12+11  -4 MOST PROBL
%SnDIEGO-USA  32.7 -117.1  -8 18: 5 19: 4  22: 51 +13+12  -6 MOST PROBL
.DWSONyk-Cnd  64.1 -139.4  -8 19:57 21:12  24: 43 +15<+8 -12 VERY DFCLT$
%ANCHORG-Als  61.1 -150.0  -9 19:36 20:51  25: 22 +15 +9 -12 DIFFICULT $
.HONOLU--Hwi  21.3 -157.5 -10 18:43 19:47  25: 29 +15+14  -3  VISIBLE
 
              (INCREASE   date one day, if crossing   EAST TO WEST)
  #####################    INTERNATIONAL DATE LINE    ###################### 
              (DECREASE   date one day, if crossing   WEST TO EAST)
 
.WLNGTN-NwZd -41.3  174.8 +12 16:21 16:33   1:  7  +2 +2  -0 IMPOSSIBLE
.TOKYO-Japan  35.7  139.7  +9 18: 0 18: 9   5: 46  +4 +2  -3 IMPOSSIBLE
.PERTH-Austr -31.8  116.2  +8 18:17 18:35   7:  3  +4 +4  +2 IMPOSSIBLE
.JAKARTA-Ind  -6.3  106.9  +7 18: 1 18:19   7: 47  +4 +4  -0 IMPOSSIBLE
 
.KULALMP-Myl   3.1  101.7  +8 19:23 19:42   8:  9  +5 +4  -1 IMPOSSIBLE
.DHAKA-BngDs  23.8   90.3  +6 18:13 18:33   8: 59  +5 +4  -3 IMPOSSIBLE
.AGRA--India  27.2   77.9  +6 19: 5 19:27  10: 21  +6 +5  -4 IMPOSSIBLE
.PESHAWR-Pks  33.6   71.4  +5 18:32 18:55  10: 18  +6 +4  -4 IMPOSSIBLE
.KABUL-Afghn  34.5   69.2  +5 18:41 19: 4  10: 57  +7 +5  -4 IMPOSSIBLE
.TEHRAN-Iran  35.7   51.4  +3 17:53 18:19  11: 39  +7 +5  -4 IMPOSSIBLE
 
=============================================================================
=============================================================================