SEARCH FOR SOLUTION FOR A UNIQUE ISLAMIC CALENDAR ( Moedji Raharto ) di hotel sliwangi semarang 2012

SEARCH FOR SOLUTION FOR A UNIQUE ISLAMIC CALENDAR

Moedji Raharto

Astronomy Research Divisions, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung

Email: moedji@as.itb.ac.id or mraharto2009@gmail.com

Abstract

There are two kinds of motivations in constructing Islamic Lunar Calendar, first using tabulation, fix number of the days for each month and some rule of to keep a high global precision referred to synodic period of the moon and secondly using precise criteria of the first lunar crescent visibility after conjunction.  This paper will give some discussion for searching unique model of Islamic Lunar Calendar.

INTRODUCTION

Searching a unique model of Islamic Lunar Calendar is unsolved problem. The calendar itself has been using since early Islam, when the prophet Muhammad saw was alive. The basic reason to use lunar calendar, guided by verse of al Qur’an, [QS 2:189; QS 9:36 etc]. In early phase the model of Islamic calendar is just naked eye observation based on hilal (the first visibility of young lunar crescent after conjunction) especially for determining the beginning and the end of Ramadan as well as for the beginning of Dzulhijjah for determining the day for Hajji.

The length of each month in Islamic lunar calendar consists of 29 days or 30 days. The rule just hilal is visible or not visible, if hilal is visible after sunset then it is started the new month if not (due any reason, obscuration by dusty atmosphere or cloudy sky; or the brightness of crescent below the limit of minimum contrast or geometry based the moonset earlier than the sunset) then the new month will start on the next day. The name of month in Islamic lunar calendar came from the grandson of the prophet, it indicates that the early lunar calendar may exist in the region, may be a luni-solar model. For example the meaning of Ramadan corresponds to very hot seasons. Rabi’ul Awal corresponds to the first spring and Rabi’ul Akhir corresponds to the second spring etc. In this period the beginning of calendar was not determined yet, the name of each month have been determined, one year may consist of 12 month has been implemented. When is the beginning of Ramadan at 632 CE?

The Earth has the only one natural satellite which is known in English as Moon.  Almost all the people or community has their own name such as Bulan in Indonesian (with some variation name in ethic group such as Wulan in Javanese), as Qamar in Arabic, as Luna in Italian, Latin, and Spanish, as Lune in French, as Mond in German, as Selene in Greek etc.  The different names of the moon in each nation indicate that many independent thinking about her existence. The use of regular lunar phenomena such as phase of the moon for various calendar systems will be the consequence of the impressive appearance of the moon, clearly distinct between full moon phase, new moon phase, first quarter, last quarter.  In Indonesia 10 out of 13 national holidays are determined by the time of moon phase. Buddhist‘s new year and  Easter use the time of full moon between May 6 to June 6 for Buddhist new year and Sunday after the time of full moon on March 21, Hindu’s new year use the time of conjunction, Imlek or Chinese’s New Year use the time of conjunction.  Islamic New Year, the Idul Fitri, Idul Adha etc use the first crescent visibility after conjunction (is called hilal) or using some criteria that is  the altitude of the moon at sun set time, after conjunction. Then for common people should not make mistake with the distinct phenomena of moon phase.

 Unique case for Islamic calendar, based on a thin lunar crescent after conjunction, it is difficult compare to just calculation of the time of full moon, or conjunction or the first quarter. In order to know the crescent someone should make some observational plan, when and where the direction of the moon relative to the sun or relative to cardinal point in observing place. Observing technique for the lunar crescent visibility after conjunction has been developing, not only by naked eye or visual telescope, but also using information in near-infrared region of atmospheric window for day time observation of lunar crescent.  Finding the thin lunar crescent is in general easier and better precision; it will avoid mistakes in identification of the thin lunar crescent with other celestial or atmospherics objects. Prior 1980’s up to 1990’s, the thin lunar crescent were dominated by naked eye observation. After 1990’s observation with telescope and optical aid become popular.

The use of hilal to determine the beginning of new month in Islamic calendar confronted with some Islamic calendar just to calculate and apply some criteria for hilal’s visibility or using average value of the synodic period, or may be just to calculate and apply some criteria which may not consider the hilal’s visibility. Various ways to determine the beginning of new month in Islamic Calendar, it makes Islamic calendar works like a mosaic, there is same frame (verse of Qur’an, al Hadith and some agreement on the Islamic calendar structure) but inside the frame there are many pies of differences. The picture of implementation of Islamic calendar is very complex; there are the differences among countries, and also inside the country like in Indonesia. It is necessary to unify on Islamic calendar, to make complex situation become simpler and accepted by Muslim the entire world. 

What must be solved for unification?

We have to search for agreement criteria or rule for determining a new month in Islamic calendar for each country. We have to agree to a unique model of Islamic calendar which is used for Muslim the entire world.

THE NATURE CONSTRAINT OF CRESCENT OBSERVATION

In reality the continent distribute geographic position from the North Pole to the South Pole, majority population occupy within latitude 60⁰. Some example of several extreme south and extreme north of cities are Oslo Norway (59.9494° N, 10.7564° E), Melbourne (37°48′49″S 144°57′47″E / 37.81361°S 144.96306°E), Río Gallegos in Argentina. (51°38′S 69°13′W / 51.633°S 69.217°W) and Pretoria Capital of South Africa ( 25°44′46″S 28°11′17″E / 25.74611°S 28.18806°E ).

The true South and the true North refer to rotational axis of the earth, the orientation of the axis does not perpendicular to the earth orbit, and the axis makes inclination of about 23.5 degree to the normal of ecliptic plane. This condition will generate naturally geographic constraint on young lunar crescent visibility after conjunction (called Hilal). Hilal may not visible in the same day in area with the same longitude.  The different brightness of atmospheric condition between the South and the North part of celestial sphere also makes the different condition of hilal’s visibility. Table 1a and table 1b give example in June and December. Table 1a and 1b use longitude 106⁰ 33′ East, Polar 30S means latitude 30⁰ South, Polar 30N means latitude 30⁰ North, Polar 50S means latitude 50⁰ South Polar 50N means latitude 50⁰ North etc., “below” means below horizon, No SS means no sunset phenomena. All data in table 1a and 1b are obtained by using software at http://aa.usno.navy.mil/cgi-bin/aa_altazw.pl. 

Tabel 1a: Sunset and Moonset at different latitude
New Moon: June 19,  2012, at 22:03 (UT+7h)
Sunset and Moonset on June 20, 2012
	SS (UT+7h)	MS (UT+7h)
Pelabuhan -Ratu	17:47	18:25
Polar 30S	17:02	17:45
Polar 30N	18:58	19:27
Polar 50S	15:58	16:47
Polar 50N	20:07	20:22
Polar 55S	15:30	16:23
Polar 55N	20:37	20:45
Polar 60S	14:52	15:50
Polar 60N*	21:21	21:17
Polar 65S	13:43	14:55
Polar 65N*	22:57	22:06
Polar 70S	below	below
Polar 70N	No SS	24h03m
*moon set before sun set

Tabel 1b: Sunset and Moonset at different latitude
New Moon on December 13, 2012, at 15:43 (UT+7h)
Sunset and Moonset on December 14, 2012
	SS (UT+7h)	MS (UT+7h)
Pelabuhan -Ratu	18:04	19:07
Polar 30S	18:50	19:46
Polar 30N	16:56	18:07
Polar 50S	19:58	20:40
Polar 50N	15:52	20:22
Polar 55S	20:28	21:02
Polar 55N	15:25	16:47
Polar 60S	21:12	21:32
Polar 60N	14:47	16:15
Polar 65S*	22:43	22:18
Polar 65N*	15:23	13:40
Polar 70S	No SS	23:52
Polar 70N	below	below
*moon set before sun set

This constraint makes impossible to apply a single criteria and concluding that the beginning of new Islamic month in the same day (solar/Gregorian calendar). 

The first visibility (naked eye) thin crescent after conjunction occurred on June 20, 2012. Hilal should appear in Indonesia and south-east Asia, and determine the first Sya’ban 1433 H will be on June 21, 2012.  In region Polar 65N the sun was above horizon from sunrise at 00:49 (UT+7h) and sunset at 23:02 (UT+7h). The maximum altitude of the sun was 48⁰.4 at 11:38 up to 12:12. The moon rise at 02:27 and moonset at 22:01, then the moon set was happened before the time of sunset. The maximum altitude of the moon was about 45⁰ between 12:13 to 12:31. The crescent width achieved 1% at 14:17 when the altitude the moon was 41⁰.3 and the situation of the sky was very bright because the sun located above horizon, it is very difficult to watch the thin crescent by naked eye in the region Polar 65N compare to region in Pelabuhan Ratu (Indonesia) or equatorial region.

In the region Polar 65S, the sun rise at 10:04 and the sun set at 13:46, the maximum altitude of the sun was 1⁰.9 at 11:46. The moon rise at about 10:03 and the moon set at about 14:50. The maximum altitude of the moon is about 3⁰.7 at 12:11 up to 12:42. The crescent width achieved 1% at 14:17 or about 31 minutes after the time of sunset, but the altitude of the moon was 1⁰.4 or less than 2⁰ wich generally accepted as criteria in Taqwim Standard. The condition after sunset at 13:46, the altitude of the moon was 2⁰.5 (greater than 2⁰), but the width of lunar crescent was less than 1%.

In higher latitude the situation will be different, in Polar 70N the sun was always above the horizon at certain time with upper culmination or maximum altitude achieved by the sun was 43⁰.5 between 21:53 and 21:58. The lower culmination or minimum altitude of the sun was 3⁰.6 between 09:50 and 10:01.

The moon rise at 00:00 (UT+7h) and the moon set at 23:49, transition the width of crescent became 1% relative to the whole circle of the moon at 14:17 with altitude of the moon 37⁰.1 degree, maximum altitude 39⁰.9 was achieved between 12:04 to 12:40.  

Then it is not only to make agreement on criteria of the first lunar crescent visibility after conjunction, but it is also necessary to find an appropriate model of Islamic calendar.

In Polar 70S the sun was always below horizon as well as the moon was also always below horizon.

PROPOSED CRITERIA

The criteria of the first visibility of young moon crescent after conjunction should be calibrated with the atmospheric free parameter, such as elongation between the moon and the sun, it is hopefully can be used for observer in the entire world. I considered that the calibration arc of Vision could be obtained by comparing with observed data. Recently Sopwan and Raharto (2012) propose such criteria for the whole month of the year (see Figure 1 through Figure 4).   

Figure1. The distribution of Hilal data on ARCV – Elongation (ARCL) diagram. All data between the line of Odeh02 and Odeh03 are for naked eye observation. [Sopwan and Raharto, 2012]

Figure2. Upper part: The lower limit of hilal data on the elongation (elongasi) over the right ascension of the Sun for the naked eye observation.  Lower part: The lower limit of hilal data on the altitude difference (ARCV, Beda Tinggi) between the Sun and the Moon over the right ascension of the Sun for the naked eye observation. [Sopwan and Raharto, 2012]   

Figure 03. Distribution of Hilal data for Telescopic Observation on ARCV – Elongation diagram, between the line of Odeh01 and Odeh02. [Sopwan and Raharto, 2012]

Figure 4. Elongation (ARCL) and the azimuth difference between the Sun and the Moon over right ascension of the sun at the lower limit for telescopic observation. [Sopwan and Raharto, 2012]

TABULATION METHODS (HISAB URFI)

The earliest Islamic Calendar system or Hijriah Calendar using a tabulation methods developed during Khalifah Umar bin Khaththab (17 H or 639 CE) , called Hisab Urfi. Basically the calendar system adopts the mean value of the synodic period of the moon as basis to determine the rule. Usually the explanation to use the Islamic calendar system is the need for administration purposes to mark the exact date of official letter. The scientific reason behind the earliest Islamic Calendar system is the need to determine the first Ramadlan and Syawal , as well as  Hajj.  The Khalifah has a vision for the need universalism of Islamic Calendar.

In the beginning observation of hilal is an importance, but later we have to consider that not all hilal can be observed by the muslim in the northern part when the sun in the south (in December), and it tends older crescent will be observed by the people in south, due to the sun always above horizon when the crescent develop the width up to certain observable crescent.

In general Islamic calendar is a lunar calendar and the beginning of the calendar system 15 July 622 or 16 July 622, each month consists of 29 days or 30 days, each year consists 12 months. There are two types of Islamic Calendars, tabulation calendar and fixed number of days for each month and dynamic number of days, each month sometimes consists of 29 days or 30 days depend on the young moon crescent visibility in the beginning of month.  Some criteria for the first visibility of the young moon crescent after conjunction is still developed by Islamic scientist as well astronomers in several country in the world  for example Ilyas (1994); Odeh (2004); Sultan (2006, 2007), Yallop (1997)

URFI CALENDAR

The beginning of the calendar system is 16 July, 622 (Julian calendar era, CE).  One year consists of 12 months: (1) Muharram, (2) Shafar, (3) Rabi’ul Awal, (4) Rabi’ul Akhir, (5) Jumadal Ula, (6) Jumadal Akhirah, (7) Rajab, (8) Sya’ban, (9) Ramadlan, (10) Syawal, (11) Dzulqa’dah and (12) Dzulhijjah. The shortest month in hisab Urfi consists 29 days and the longest consists of 30 days. The shortest year, called basithah consist of 354 days composed by 6 months with 29 days and 6 months with 30 days ( 6 x 29 + 6 x 30 = 174 + 180  = 354) and the longest year, called kabisat composed by 5 months with 29 days and 7 months with 30 days ( 5 x 29 + 7 x 30 = 145 + 210  = 355). There are 6 months consist of 30 days for the shortest year, the first month (1) Muharram, the third month (3) Rabi’ul Awal, the fifth month (5) Jumadal Ula, the seventh month (7) Rajab, the ninth month (9) Ramadlan) and the eleventh month (11) Dzulqadah. For the longest year there is additional one of the longest month, the twelfth month (12) Dzulhijjah consist 30 days. The longest years of the Hijriah Calendar defined if m = 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 and 29; where  m = Frac (H / 30) x 30 and H = Islamic Year or Hijriah Year.  For example H = 1431 then m = Frac (1431 / 30) x 30 = 0.7 x 30 = 21 then 1431 H is the Kabisah year.  In the 30 years consist of 11 kabisah years and 19 basith years or average length of one month is (11 x 355 + 19 x 354) / (30 x 12) = 10631/360 = 29.53055556 days.  30 Islamic years equal to 29.1067133 tropical years.

The basic relationship between the mean value of synodic period of moon-phase, the mean solar time and mean tropical year of the sun

•       235 synodic months = 6939.688 mean solar day  or  19 year of Gregorian solar calendar = 6939.6075 days, 1 synodic month = 1 lunation = 29.5305869 days

•       (235 synodic months– 19 year of Gregorian solar calendar) = 6939.688 days – 6939.6075 days = 0.08 days

•       5700000 year of Gregorian solar calendar = 5700000 x 365.2425 days = 2081882250 days = 70499183 lunations = 70499183 x 29.5305869 days = 2081882250 days.

•       70499183 lunation = 5874931.917 year of Lunar calendar/or Hijriah year.

Improving the precision of Urfi Calendar by improving the rule may be found better solution, but will it able to match with the hisab hakiki or imkanurrukyat with great satisfactory?  

DISCUSSIONS

Several approaches have been done to implement Islamic calendar for entire Muslim in the world, from a simple model up to complicated model. Searching for optimize between practicality and syariah point of view should be found in near future with great satisfactory for entire Muslim in the world. 

References

http://aa.usno.navy.mil/cgi-bin/aa_altazw.pl

Affandi, Andi; 1976;  Kebesaran Islam dan Peralihan Tanggal (Jalan Masjid 20, Cicadas Bandung), Jawa Barat, Indonesia [in Indonesian]

Anonim; 1981; Almanak Hisab Rukyat; BHR Departemen Agama RI; (Proyek Pembinaan Badan Peradilan Agama Islam) [in Indonesian]

Ansari, ZA, Faruqi, ZZ, Mohammad Hanif, H.; 1987; Hijriah Calendar for the Indo Pakistan Sub-Continent Valid Between 1 – 1 – 1800 to 31 – 12 – 2049 Deduced from Times of Solar and Lunar Conjunction, Proceedings of the Second International Seminar on Qur’an and Science, Karachi  17 June 1987, Pakistan Association of Scientists and Scientific Professions 167 – 180

Ansari, ZA.; 1987; Prediction of Solar and Lunar Related Phenomena Using Computer; Proceedings of the Second International Seminar on Qur’an and Science, Karachi  17 June 1987, Pakistan Association of Scientists and Scientific Professions 73– 84

Aqil, Banadji (KH); 2008; Kalendar Urfi Tahun 0 s.d. 12000 M/0 s.d. 12400 H (sambutan Direktur Pembinaan DepAg RI) [in Indonesian]

Freeman –Grenville, GSP; 1963; the Muslim and Christian Calendars, Oxford University Press

Ilyas, M; 1994; QJRAS 35, 425

Khazin, Muhyiddin; 2007; 150 tahun (1925 – 2075) Kalendar Masehi – Hijriah ; Direktorat Urusan Agama Islam dan Pembinaan Syariah, Ditjen Bimas Islam Departemen Agama RI, www.bimasislam.net [in Indonesian]

Katsir, A. [Ustad A. Katsir , Hakim & Dosen; Malang – Jawa Timur – Indonesia ]; 1979; Matahari dan Bulan dengan Hisab; Bina Ilmu, Surabaya, Jawa Timur,  Indonesia [in Indonesian]

Kaleemur Rahman, Md; 1987; Perpentual Hijrah Calendar; Proceedings of the Second International Seminar on Qur’an and Science, Karachi  17 June 1987, Pakistan Association of Scientists and Scientific Professions 85 – 96 

Meeus, Jean; 1983; Astronomical Tables of the Sun, Moon, and Planets; Willmann – Bell, Inc, Richmond, Virginia, USA

Muhammad Wardan, 1957, Hisab Urfi dan Hakiki, Yogyakarta – Indonesia [in Indonesian]

Odeh, Mohammad SH; 2004; New Criterion for Lunar Crescent Visibility, Experimental Astronomy; 18, 39 – 64

Raharto, M., 2006, A Study of Metonic Cycle on Hilal Visibility, Proceedings of ICMNS 2006, p. 1240

Sopwan, N. and Raharto, M., 2012, Lower Limit of Hilal Visibility Criteria for the Naked Eye and Telescopic Observation, presented in ICMNS 2012 held on November 8-9, 2012 in Campus Institut Teknologi Bandung, Java, Indonesia

Sultan, AH; 2006, “Best Time” For the First Visibility of the Lunar Crescent, The Observatory, 126, 115 – 118

Sultan, AH; 2007; First Visibility of The Lunar Crescent beyond Danjon’s Limit, The Observatory 127, February 2007, 53 – 59

 Yallop, BD; 1997; A Method for predicting the first sighting of the new Crescent Moon, RGO NAO Tech. Note 69 (pp 1 – 15)

 

Polar 70 degree on June, 20, 2012 Latitude 70 N (newer sunset phenomena)

Maximum altitude of the sun 43.5 degree (upper culmination)

21:52       43.4       178.9

21:53       43.5       179.2

21:54       43.5       179.5

21:55       43.5       179.8

21:56       43.5       180.1

21:57       43.5       180.4

21:58       43.5       180.8

21:59       43.4       181.1

Minimum altitude of the sun (lower culmination) is 3.6 09:50 – 10:01

09:49        3.7       358.5

09:50        3.6       358.7

09:51        3.6       359.0

09:52        3.6       359.2

09:53        3.6       359.4

09:54        3.6       359.7

09:55        3.6       359.9

09:56        3.6         0.1

09:57        3.6         0.3

09:58        3.6         0.6

09:59        3.6         0.8

10:00        3.6         1.0

10:01        3.6         1.3

10:02        3.7         1.5

The moon set at 09:49 wib

09:45        0.1       345.5       0.01

09:46        0.1       345.7       0.01

09:47        0.0       345.9       0.01

09:48        0.0       346.2       0.01

09:49        0.0       346.4       0.01

09:50       -0.0       346.6       0.01

09:51       -0.0       346.8       0.01

09:52       -0.0       347.1       0.01

09:53       -0.1       347.3       0.01

The moon rise at 11:57 wib [ about 3 hours the moon below horizon)

11:53       -0.1        14.6       0.01

11:54       -0.0        14.8       0.01

11:55       -0.0        15.0       0.01

11:56       -0.0        15.3       0.01

11:57        0.0        15.5       0.01

11:58        0.0        15.7       0.01

11:59        0.0        15.9       0.01

12:00        0.1        16.2       0.01

12:01        0.1        16.4       0.01

12:02        0.1        16.6       0.01

12:03        0.1        16.8       0.01

h  m         o           o                                                  

00:00       37.9       208.1       0.00

00:01       37.8       208.4       0.00

00:02       37.8       208.7       0.00

00:03       37.8       209.0       0.00

00:04       37.7       209.3       0.00

00:05       37.7       209.5       0.00

00:06       37.6       209.8       0.00

00:07       37.6       210.1       0.00

Change the width 3% in one day moon set and moon rise 22:49 – 23:30

22:49       37.7       172.8       0.03

22:50       37.8       173.1       0.03

22:51       37.8       173.4       0.03

22:52       37.8       173.7       0.03

22:53       37.8       174.0       0.03

22:54       37.8       174.3       0.03

22:55       37.8       174.6       0.03

22:56       37.8       174.9       0.03

22:57       37.8       175.2       0.03

22:58       37.8       175.4       0.03

22:59       37.8       175.7       0.03

23:00       37.8       176.0       0.03

23:01       37.8       176.3       0.03

23:02       37.8       176.6       0.03

23:03       37.8       176.9       0.03

23:04       37.8       177.2       0.03

23:05       37.8       177.5       0.03

23:06       37.8       177.8       0.03

23:07       37.8       178.1       0.03

23:08       37.8       178.4       0.03

23:09       37.8       178.7       0.03

23:10       37.8       179.0       0.03

23:11       37.8       179.3       0.03

23:12       37.8       179.6       0.03

23:13       37.8       179.8       0.03

23:14       37.8       180.1       0.03

23:15       37.8       180.4       0.03

23:16       37.8       180.7       0.03

23:17       37.8       181.0       0.03

23:18       37.8       181.3       0.03

23:19       37.8       181.6       0.03

23:20       37.8       181.9       0.03

23:21       37.8       182.2       0.03

23:22       37.8       182.5       0.03

23:23       37.8       182.8       0.03

23:24       37.8       183.1       0.03

23:25       37.8       183.4       0.03

23:26       37.8       183.7       0.03

23:27       37.8       183.9       0.03

23:28       37.8       184.2       0.03

23:29       37.8       184.5       0.03

23:30       37.7       184.8       0.03

Sun rise

00:46       -1.0        11.6

00:47       -1.0        11.8

00:48       -1.0        12.1

00:49       -1.0        12.3

Until sunset

23:02       -1.0       347.7

23:03       -1.0       348.0

23:04       -1.0       348.2

23:05       -1.0       348.4

With maximum altitude of the sun achieved 48.4 degree.

11:37       48.3       173.6

11:38       48.4       174.0

11:39       48.4       174.3

11:40       48.4       174.7

11:41       48.4       175.0

11:42       48.4       175.4

11:43       48.4       175.7

11:44       48.4       176.1

11:45       48.4       176.4

11:46       48.4       176.8

11:47       48.4       177.1

11:48       48.4       177.4

11:49       48.4       177.8

11:50       48.4       178.1

11:51       48.4       178.5

11:52       48.4       178.8

11:53       48.4       179.2

11:54       48.4       179.5

11:55       48.4       179.9

11:56       48.4       180.2

11:57       48.4       180.6

11:58       48.4       180.9

11:59       48.4       181.2

12:00       48.4       181.6

12:01       48.4       181.9

12:02       48.4       182.3

12:03       48.4       182.6

12:04       48.4       183.0

12:05       48.4       183.3

12:06       48.4       183.7

12:07       48.4       184.0

12:08       48.4       184.4

12:09       48.4       184.7

12:10       48.4       185.0

12:11       48.4       185.4

12:12       48.4       185.7

12:13       48.3       186.1

The moon crescent

The moon rise at about 02:28

02:24       -0.1        32.3       0.00

02:25       -0.1        32.5       0.00

02:26       -0.0        32.8       0.00

02:27        0.0        33.0       0.00

02:28        0.1        33.2       0.00

02:29        0.1        33.4       0.00

02:30        0.2        33.6       0.00

02:31        0.2        33.8       0.00

02:32        0.3        34.1       0.00

02:33        0.3        34.3       0.00

The moon set at

21:58        0.2       321.6       0.01

21:59        0.2       321.9       0.01

22:00        0.1       322.1       0.01

22:01        0.0       322.3       0.01

22:02       -0.0       322.5       0.01

22:03       -0.1       322.7       0.01

22:04       -0.1       322.9       0.01

The moon set is before the time of sunset

The crescent width achieved 1% at 14:17 when the sun above horizon, it is very difficult to watch by naked eye

14:14       41.5       214.4       0.00

14:15       41.4       214.7       0.00

14:16       41.4       215.0       0.00

14:17       41.3       215.3       0.01

14:18       41.3       215.6       0.01

14:19       41.2       215.9       0.01

14:20       41.1       216.2       0.01

With maximum altitude of the moon achieved about 45 degree, 12:13 to 12:31

12:12       44.9       176.1       0.00

12:13       45.0       176.4       0.00

12:14       45.0       176.7       0.00

12:15       45.0       177.0       0.00

12:16       45.0       177.4       0.00

12:17       45.0       177.7       0.00

12:18       45.0       178.0       0.00

12:19       45.0       178.3       0.00

12:20       45.0       178.7       0.00

12:21       45.0       179.0       0.00

12:22       45.0       179.3       0.00

12:23       45.0       179.6       0.00

12:24       45.0       180.0       0.00

12:25       45.0       180.3       0.00

12:26       45.0       180.6       0.00

12:27       45.0       180.9       0.00

12:28       45.0       181.2       0.00

12:29       45.0       181.6       0.00

12:30       45.0       181.9       0.00

12:31       45.0       182.2       0.00

12:32       44.9       182.5       0.00

12:33       44.9       182.9       0.00

 In the south situation is different

The moon rise at about 10:03

10:00       -0.1        32.3       0.00

10:01       -0.1        32.1       0.00

10:02       -0.0        31.8       0.00

10:03        0.0        31.6       0.00

10:04        0.1        31.4       0.00

10:05        0.1        31.2       0.00

10:06        0.2        31.0       0.00

10:07        0.2        30.8       0.00

10:08        0.2        30.5       0.00

The moon set at about 14:50

14:47        0.2       327.9       0.01

14:48        0.1       327.7       0.01

14:49        0.1       327.5       0.01

14:50        0.0       327.3       0.01

14:51       -0.0       327.0       0.01

14:52       -0.0       326.8       0.01

14:53       -0.1       326.6       0.01

The maximum is about 3.7

12:09        3.6         3.4       0.00

12:10        3.6         3.2       0.00

12:11        3.7         3.0       0.00

12:12        3.7         2.8       0.00

12:13        3.7         2.5       0.00

12:14        3.7         2.3       0.00

12:15        3.7         2.1       0.00

12:16        3.7         1.8       0.00

12:17        3.7         1.6       0.00

12:18        3.7         1.4       0.00

12:19        3.7         1.2       0.00

12:20        3.7         0.9       0.00

12:21        3.7         0.7       0.00

12:22        3.7         0.5       0.00

12:23        3.7         0.3       0.00

12:24        3.7         0.0       0.00

12:25        3.7       359.8       0.00

12:26        3.7       359.6       0.00

12:27        3.7       359.4       0.00

12:28        3.7       359.1       0.00

12:29        3.7       358.9       0.00

12:30        3.7       358.7       0.00

12:31        3.7       358.4       0.00

12:32        3.7       358.2       0.00

12:33        3.7       358.0       0.00

12:34        3.7       357.8       0.00

12:35        3.7       357.5       0.00

12:36        3.7       357.3       0.00

12:37        3.7       357.1       0.00

12:38        3.7       356.9       0.00

12:39        3.7       356.6       0.00

12:40        3.7       356.4       0.00

12:41        3.7       356.2       0.00

12:42        3.7       355.9       0.00

12:43        3.6       355.7       0.00

12:44        3.6       355.5       0.00

The crescent width achieve 1% at (after sunset at 13:46, the altitude of the moon greater than 2 degree, but the width of crescent less than 1%, the width of crescent achieved 1%, at 14:17 or about 31 minutes after sunset,  the altitude was 1.4 degree.

13:42        2.6       342.4       0.00

13:43        2.6       342.2       0.00

13:44        2.6       341.9       0.00

13:45        2.5       341.7       0.00

13:46        2.5       341.5       0.00

13:47        2.5       341.3       0.00

13:48        2.4       341.0       0.00

13:49        2.4       340.8       0.00

13:50        2.4       340.6       0.00

14:14        1.6       335.2       0.00

14:15        1.5       335.0       0.00

14:16        1.5       334.8       0.00

14:17        1.4       334.6       0.01

14:18        1.4       334.3       0.01

14:19        1.4       334.1       0.01

14:20        1.3       333.9       0.01

14:21        1.3       333.7       0.01

The sunrise at 10:04 and the sunset 13:46, maximum altitude 1.9 degree at 11:46

10:02       -1.1        25.8

10:03       -1.1        25.6

10:04       -1.0        25.4

10:05       -1.0        25.2

10:06       -0.9        24.9

10:07       -0.9        24.7

The altitude of the sun achieved maximum at

11:42        1.8         3.1

11:43        1.9         2.8

11:44        1.9         2.6

11:45        1.9         2.4

11:46        1.9         2.2

11:47        1.9         1.9

11:48        1.9         1.7

11:49        1.9         1.5

11:50        1.9         1.2

11:51        1.9         1.0

11:52        1.9         0.8

11:53        1.9         0.5

11:54        1.9         0.3

11:55        1.9         0.1

11:56        1.9       359.9

11:57        1.9       359.6

11:58        1.9       359.4

11:59        1.9       359.2

12:00        1.9       358.9

12:01        1.9       358.7

12:02        1.9       358.5

12:03        1.9       358.3

12:04        1.9       358.0

12:05        1.9       357.8

12:06        1.9       357.6

12:07        1.9       357.3

12:08        1.9       357.1

12:09        1.8       356.9

12:10        1.8       356.6

The sunset at

13:44       -0.9       335.2

13:45       -0.9       335.0

13:46       -1.0       334.8

13:47       -1.0       334.6

13:48       -1.1       334.3

13:49       -1.1       334.1