Predicting the first visibility of the young lunar crescent
for a given location is a problem that has challenged astronomers and
mathematicians for more than four millennia. Already in the second half of the
first millennium BCE Babylonian priest-astronomers developed sophisticated
numerical algorithms for predicting the motion of the moon and the times of its
synodic phases and the first visibility of the lunar crescent above the western
horizon just after sunset.
In the past the dates of first lunar visibility were crucial
parameters in regulating the religious and administrative calendars of many
cultures. In the present time more than a billion Muslims around the world still
eagerly await each year the first sighting of the lunar crescent which announces
the begin and the end of Ramadān, the Islamic month of fasting and abstinence,
or the lunar crescent which announces the begin of Dhū ’l-Hijja, the Islamic
month of pilgrimage.
Progress in astronomy and in computing techniques has now made
it possible to calculate the geocentric positions of the sun and the moon at any
time with stunning precision but predicting when the thin sliver of the lunar
crescent can first be seen in the sky from a given location after its
conjunction with the sun still remains a difficult problem.
The main cause for this problem is the fact that the faint and
narrow lunar crescent has to be detected shortly after sunset, when the moon is
still close to the western horizon in the twilight sky. It is obvious that
weather and the local transparency of the atmosphere are important factors for
successfully detecting the lunar crescent, as well as the experience of the
observer.
Numerous computational methods and algorithms for predicting
the visibility of the lunar crescent have been proposed in the past (a
comprehensive bibliography is given at the bottom of this webpage)
but the method now most favoured by astronomers is based on the
Yallop algorithm, proposed in 1997 by Bernard D. Yallop of the computing
section of HM Nautical Almanac
Office.
Yallop’s algorithm computes a lunar visibility test parameter
q that is based on the geocentric difference in altitude (i.e.
uncorrected for atmospheric refraction and parallax) between the centre of the
sun and the centre of the moon at the ‘best time’ for a given observer and the
topocentric width of the lunar crescent. From an analysis of nearly 300
observations (successful or not) of the lunar crescent, Yallop determined the
following visibility criteria for the lunar crescent:
A
q > +0.216
easily visible to the naked eye
B
–0.014 < q < +0.216
visible to the naked eye under perfect
atmospheric conditions
C
–0.160 < q < –0.014
may need optical aid to find the crescent
before it can be seen with the naked eye
D
–0.232 < q < –0.160
can only be seen with binoculars or a
(small) conventional telescope
E
–0.293 < q < –0.232
below the normal limit of detection with a
(small) conventional telescope
F
q < –0.293
not visible with a (large) conventional
telescope, below the Danjon limit (8°)
The ‘best time’ is here defined as the time of sunset
increased by 4/9ths of the time interval between sunset and moonset. For
instance, if the local times of sunset and moonset are at 18:00 and 19:30, then
the ‘best time’ to search for the lunar crescent is around 18:40.
The global lunar crescent visibility maps on this webpage were
generated from Yallop’s algorithm and indicate the local visibility of the lunar
crescent at the begin of each lunar month from 2010 to 2019 (lunation numbers
1100 to 1207). For each month three world maps (in Mercator projection) are
given indicating the visibility of the lunar crescent on the day of luni-solar
conjunction (or astronomical new moon) and for the two following days.
As these world maps will also be useful for Muslims who wish
to determine the astronomical begin of the months in the Islamic calendar, the
visibility maps are grouped in yearly batches starting with the first month
(Muharram) and ending with the last month (Dhū ’l-Hijja) of the Islamic lunar
calendar.
Yearly batches of lunar crescent visibility diagrams for the
Islamic years 1432 AH to 1440 AH (2010 CE to 2019 CE) can be downloaded as pdf
files from the following table:
The following world maps indicate the visibility of the young
lunar crescent for the months Ramadān, Shawwāl and Dhū ’l-Hijja of the Islamic
year 1433, which determine the begin and end of the annual period of fasting and
the begin of the month of pilgrimage.
Global lunar crescent
visibility maps for Ramadān 1433 AH
Day of conjunction
[19 July 2012]
Day after conjunction
[20 July 2012]
Second day after conjunction
[21 July 2012]
Global lunar crescent
visibility maps for Shawwāl 1433 AH
Day of conjunction
[17 August 2012]
Day after conjunction
[18 August 2012]
Second day after conjunction
[19 August 2012]
Global lunar crescent
visibility maps for Dhū ’l-Hijja 1433 AH
Visibility diagrams for the years when the prophet Muhammad
resided in Medina can be obtained from the following table. These may be of use
to historians and theologians who wish to study the chronology of early Islam.
AH
Islamic
Lunation
Numbers
Muharram
New Moon
Dhū ’l-Hijja
New Moon
Download
0
–11 - 0
24 Jul 621
14 Jun 622
1
1 - 12
14 Jul 622
3 Jun 623
2
13 - 24
3 Jul 623
22 May 624
3
25 - 36
21 Jun 624
12 May 625
4
37 - 48
10 Jun 625
1 May 626
5
49 - 60
31 May 626
21 Apr 627
6
61 - 72
20 May 627
10 Apr 628
7
73 - 84
9 May 628
30 Mar 629
8
85 - 96
29 Apr 629
19 Mar 630
9
97 - 108
18 Apr 630
8 Mar 631
10
109 - 120
7 Apr 631
25 Feb 632
11
121 - 132
26 Mar 632
14 Feb 633
The months and years in these diagrams are denoted in the
‘proleptic’ Islamic lunar calendar, which assumes (as in the present-day Islamic
calendar) that no intercalary months were inserted during the first decade of
the Islamic calendar. However, before the ‘Farewell Pilgrimage’ (Dhū ’l-Hijja,
10 AH) when the intercalation of extra months in the Arabian calendar was
abolished (Qur’ān,
sūra 9:36-37), it was customary to add an extra month to the
year every two or three years in order to keep the lunar calendar in step with
the seasons.
As the intercalation scheme of the Arabian calendar is
uncertain, all proposed reconstructions of the Islamic calendar before 10 AH can
only be regarded as hypothetical. For this reason, Western calendar dates
commonly cited for key events in early Islam such as the
hijra,
the
Battle of
Badr, the
Battle of
Uhud and the
Battle of the Trench, should be viewed with caution as they can be in error
by one, two or even three lunar months.
Similar diagrams predicting the visibility of the young lunar
crescent can also be obtained from the following websites:
Moon Watch – Website of HM
Nautical Almanac Office which provides global maps for the first visibility of
the young lunar crescent. The predictions of previous new moon crescents are compared
with sightings reported by various observers around the world. The predictions
are based on the Yallop criterion.
Islamic Crescents’
Observation Project (ICOP) – Website which collects observations of
young lunar crescent sightings and gives monthly predictions for the
visibility of the lunar crescent. These predictions are based on the lunar
visibility criterion of Mohammad Odeh, which is slightly more optimistic
than the Yallop criterion.
MoonCalc 6.0 – DOS
program developed by Monzur Ahmed for calculating the visibility of the lunar
crescent according to various modern and historical visibility criteria with many
other useful options.
Useful websites for determining the actual location of the
moon (and other celestial objects) in the sky at any time from any terrestrial
location:
Sky View Café
– Online astronomy applet for determining the times of sunset, moonset and
the appearance of the lunar crescent from any terrestrial location.
I. Traditional Techniques for Computing the
Visibility of the Lunar Crescent
von Littrow, Carl Ludwig, “Zur Kenntniss der kleinsten sichtbaren Mondphasen”, Sitzungsberichte der Kaiserlichen
Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Classe, Abteilung II, 66
(1872), 459-480.
Hildesheimer, Israel, Die astronomischen Kapitel in Maimonidis Abhandlung über die Neumondsheiligung (Berlin:
Driesner, 1881 [= Jahres-Bericht der Rabbiner-Seminars zu Berlin für 1880]).
Mahler, Eduard, Maimonides’ Kiddusch Hachodesch (Vienna: Verag von Adolf Fanto, 1889)
[Internet Archive link].
Baneth, Eduard, Maimuni’s Neumondsberechnung (Berlin: Itzkowski, 1898/1903 [= Bericht über die Lehranstalt
für die Wissenschaft des Judenthums in Berlin, nrs. 16, 17, 20 & 21]) [CM link / pdf link].
Nallino, Carlo Alfonso, Al-Battānī sive Albatenii Opus Astronomicum (Milan: Ulrico Hoepli, 1899-1907
[= Pubblicazioni del Reale Osservatorio di Brera in Milano, 40]), vol. I, pp. 85-92 & 265-272.
Cohn, Berthold, “Zur Frage der Sichtbarkeit der neuen Mondsichel”, Astronomische Nachrichten, 171 (1906), 35-38
[nr. 4083] [ADS link].
Cohn, Berthold, Der Almanach perpetuum des Abraham Zacuto: Ein Beitrag zur Geschichte der Astronomie im Mittelalter
(Strassburg: Karl J. Trübner, 1918 [= Schriften der Wissenschaftlichen Gesellschaft in Straßburg, Heft 32]),
22-26 & 29 [Internet Archive link].
Neugebauer, Otto E., Astronomical Cuneiform Texts: Babylonian Ephemerides of the Seleucid Period for the Motion
of the Sun, the Moon, and the Planets (Princeton/London: Institute for Advanced Study/Lund Humphries, 1955), vol. I,
pp. 43, 66-68 & 83-85.
Gandz, Solomon (ed.), The Code of Maimonides: Book 3, Treatise 8. Sanctification of the New Moon (New Haven
[Conn]: Yale University Press, 1956 [= Yale Judaica Series, nr. 11]) – with a supplement and an introduction by
J. Obermann and an astronomical commentary by O.E. Neugebauer.
Kennedy, Edward Stewart, “The Crescent Visibility Theory of Thâbit ibn Qurra”, Proceedings of the Mathematical and Physical
Society of the United Arab Republic, 24 (1960), 71-74 – reprinted in: Studies in the Islamic Exact Sciences
(Beirut: American University of Beirut, 1983), pp. 140-143.
Wacholder, Ben Zion & Weisberg, David B., “Visibility of the New Moon in Cuneiform and Rabbinic Sources”,
Hebrew Union College Annual, 42 (1971), 227-242.
Kennedy, Edward Stewart & Janjanian, Mardiros, “The Crescent Visibility Table in Al-Khwarizmi’s Zij”, Centaurus:
International Magazine of the History of Science and Medicine, 11 (1965), 73-78 – reprinted in: Studies in the
Islamic Exact Sciences (Beirut: American University of Beirut, 1983), pp. 151-156.
Kennedy, Edward Stewart, “The Lunar Visibility Theory of Ya‘qub ibn Tariq”, Journal of Near Eastern Studies, 27
(1968), 126-132 [JSTOR link] – reprinted in: Studies in
the Islamic Exact Sciences (Beirut: American University of Beirut, 1983), pp. 157-163.
Bruin, Frans, “The First Visibility of the Lunar Crescent”, Vistas in Astronomy, 21 (1977), 331-358
[ADS link /
ScienceDirect link].
Rizvi, Saiyid Samad Husain, “Al-Bīrūnī’s Method of Visibility of Moon and its Modern Version”, Journal of Central
Asia: Journal of International Association for the Study of the Cultures of Central Asia, 3/4 (1980),
61-84.
Ilyas, Mohammad, “The Ancients’ Criterion of Earliest Visibility of the Lunar Crescent: How Good is It?”, in: G. Swarup,
A.K. Bag & K.S. Shukla (eds.), History of Oriental Astronomy: IAU Colloquium 91 (Cambridge:
Cambridge University Press, 1987), pp. 147-152 [ADS link].
King, David A., “Some Early Islamic Tables for Determining Lunar Crescent Visibility”, in: D.A. King & G. Saliba (eds.):
From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of
E.S. Kennedy (New York: New York Academy of Sciences, 1987), pp. 185-225 [ADS link / Wiley link] – reprinted in:
King (1993), nr. II.
Morelon, Régis, Thābit ibn Qurra: Œuvres d’astronomie (Paris: Société d’édition “Les Belles Lettres”, 1987),
pp. xciii-cxviii & 93-116.
Hogendijk, Jan Pieter, “New Light on the Lunar Visibility Table of Ya‘qub ibn Tariq”, Journal of Near Eastern Studies,
47 (1988), 95-104 [JSTOR link].
Hogendijk, Jan Pieter, “Three Islamic Lunar Crescent Visibility Tables”, Journal for the History of Astronomy, 19
(1988), 29-44 [ADS link].
King, David A., “Ibn Yūnus on Lunar Crescent Visibility”, Journal for
the History of Astronomy, 19 (1988), 155-168 [ADS
link] – reprinted in: King (1993), nr. III.
Kennedy, Edward Stewart & Hogendijk, Jan Pieter, “Two Tables from an Arabic Astronomical Handbook for the Mongol Viceroy of
Tibet”, in: E. Leichty, M. de J. Ellis & P. Gerardi (eds.), A Scientific Humanist: Studies in Memory of
Abraham Sachs (Philadelphia: The University Museum, 1988 [= Occasional Publications of the Samuel Noah Kramer Fund,
nr. 9]), pp. 233-242.
King, David A., “Lunar Crescent Visibility Predictions in Medieval Islamic Ephemerides”, in: S.M. Seikaly, R. Baalbaki
& P. Dodd (eds.), Quest for Understanding: Arabic and Islamic Studies in Memory of Malcolm H. Kerr (Beirut:
American University of Beirut, 1991), pp. 233-251 – reprinted in: King (1993),
nr. IV.
Rizvi, Saiyid Samad Husain, “Al-Bīrūnī’s Criterion for the Visibility of the Lunar Crescent”, Hamdard Islamicus: Quarterly
Journal of Studies and Research in Islam, 14 (1991), nr. 1, 43-52.
King, David A., Astronomy in the Service of Islam (Aldershot: Variorum, 1993).
McPartlan, M.A., “Astronomical Calculations of New Crescent Visibility 579-583 AH”, Quarterly Journal of the
Royal Astronomical Society, 37 (1996), 837-842 [ADS link].
Moosa, Ebrahim, “Shaykh Ahmad Shākir and the Adoption of a Scientifically-Based Lunar Calendar”, Islamic Law and
Society, 5 (1998), 57-89 [JSTOR link].
Fatoohi, Louay J., Stephenson, F. Richard & Al-Dargazelli, Shetha S., “The Babylonian First Visibility of the Lunar
Crescent: Data and Criterion”, Journal for the History of Astronomy, 30 (1999), 51-72
[ADS link].
Giahi Yazdi, Hamid-Reza, “Nasīr al-Dīn al-Tūsī on Lunar Crescent Visibility and an Analysis with Modern Altitude-Azimuth
Criteria”, Suhayl: Journal for the History of the Exact and Natural Sciences in Islamic Civilisation, 3 (2002/03),
231-243 [Suhayl link].
Stern, Sacha, “The Babylonian Month and the New Moon: Sighting and Prediction”, Journal for the History of Astronomy,
39 (2008), 19-42 [ADS link].
Giahi Yazdi, Hamid-Reza, “Al-Khāzinī’s Complex Tables for Determining Lunar Crescent Visibility”, Suhayl: Journal for the
History of the Exact and Natural Sciences in Islamic Civilisation, 9 (2009/10), 149-184
[Suhayl link].
II. Modern Techniques for Computing the Visibility of the Lunar Crescent and Observations of Young Lunar Crescents
Schmidt, Johann Friedrich Julius, “Ueber die früheste Sichtbarkeit der Mondsichel am Abendhimmel”, Astronomische Nachrichten,
71 (1868), 201-208 [nr. 1693] [ADS link].
Denning, William F., “Early Visibility of New Moon – Apparent Brilliancy of Planets”, The Astronomical Register: A Medium
of Communication for Amateur Observers, and all Others Interested in the Science of Astronomy, 19 (1881), 119
[ADS link].
Hopkins, B.J., “Abnormal Appearance of the Lunar Crescent”, The Observatory, 6 (1883), 247-248
[ADS link].
Mommsen, August, Chronologie: Untersuchungen über das Kalenderwesen der Griechen, insonderheit der Athener (Leipzig:
Teubner Verlag, 1883), pp. 69-80.
Johnson, S.J., “Early Visibility of New Moon”, The Journal of the British Astronomical Association, 11
(1901), 277-278 [ADS link].
Schrader, Otto, “Die Sichtbarkeit der schmalen Mondsichel bald nach Neumond”, Astronomische Nachrichten, 168
(1905), 319-322 [nr. 4028] [ADS link].
Günther, Ludwig, “Zur Frage der Sichtbarkeit der Mondsichel vor und nach Neumond”, Astronomische Nachrichten, 169
(1905), 269-272 [nr. 4049] [ADS link].
Gheury, M.E.J., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19
(1909), 219 [ADS link].
Denning, William F., “Visibility of the New Moon and the Pleiades”, The Journal of the British Astronomical Association,
19 (1909), 242-243 [ADS link].
Watson, H., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19
(1909), 253-254 [ADS link].
Whitmell, C.T., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19
(1909), 254-255 [ADS link].
Henderson, Alexander C., “Early Visibility of the Crescent Moon, &c.”, The Journal of the British Astronomical Association,
19 (1909), 255-256 [ADS link].
Johnson, E.W., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association,
19 (1909), 256 [ADS link].
Gheury, M.E.J., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association,
19 (1909), 310 [ADS link].
Fotheringham, John Knight, “On the Smallest Visible Phase of the Moon”, Monthly Notices of the Royal Astronomical
Society, 70 (1910), 527-531 [ADS
link].
Maunder, E. Walter, “On the Smallest Visible Phase of the Moon”, The Journal of the British Astronomical Association,
21 (1911), 355-362 [ADS
link] [see also ibid., 343-344].
Bougon, J., “La visibilité de la lune”, The Journal of the British Astronomical Association,
22 (1911), 48-49 [ADS link].
Cave, Charles J.P., “Early Visibility of the New Moon”, The Observatory, 34 (1911), 121
[ADS link].
Horner, D.W., “Early Visibility of the New Moon”, The Observatory, 34 (1911), 162-163
[ADS link].
Whitmell, C.T., “Early Visibility of the New Moon”, The Observatory, 34 (1911), 203
[ADS link].
Whitmell, C.T., “Early Visibility of the New Moon”, The Observatory, 34 (1911), 305-306
[ADS link].
Horner, D.W., “Early Visibility of the New Moon”, The Observatory, 34 (1911), 344-345
[ADS link].
Whitmell, C.T., “Early Visibility of the New Moon”, The Observatory, 34 (1911), 374-375
[ADS link].
Horner, D.W., “Early Visibility of the New Moon”, The Observatory, 37 (1914), 291-292
[ADS link].
Ginzel, Friedrich Karl, “Das Neulicht”, Himmel und Erde: ???,
27 (1916), 147-156.
Fotheringham, John Knight, “Astronomical Comments on Dr. Holmes’s Note on the Julian Calendar”, The Classical Quarterly,
14 (1920), 97-99 [JSTOR
link].
Holmes, T. Rice, “The Earliest Visible Phase of the Moon”, The Classical Quarterly, 14 (1920), 172
[JSTOR link].
Schoch, Carl, “The Earliest Visible Phase of the Moon”, The Classical Quarterly, 15 (1921), 194
[JSTOR link].
Fotheringham, John Knight, “The Visibility of the Lunar Crescent”, The Observatory, 44 (1921), 308-311
[ADS link].
Neugebauer, Paul Victor, Hilfstafeln zur Berechnung von Himmels-Erscheinungen: Zum Gebrauch für Historiker,
Philologen und Astronomen (Leipzig: J.C. Hinrichs’sche Buchhandlung, 1925 [= Tafeln zur astronomische
Chronologie, vol. III]), 2nd ed., pp. xxviii-xxxi & 44 [Tafel 14].
Schoch, Carl, Planeten-Tafeln für Jedermann zur Berechnung der geozentrischen Örter der großen Planeten (und des
Mondes) für den Zeitraum von 3400 v.Chr. bis 2600 n.Chr. ohne Anwendung der Logarithmen und trigonometrischen
Funktionen bis auf ein Zehntel Grad unter besonderer Berücksichtigung der Babylonischen Astronomie (Berlin-Pankow:
Linser-Verlag G.M.B.H., 1927), col. xxxvii-xxxviii & p. 14 [Tafel K].
Fotheringham, John Knight, “The Visibility of the Lunar Crescent”, in: S. Langdon & J.K. Fotheringham,
The Venus Tablets of Ammizaduga: A Solution of Babylonian Chronology by Means of the Venus Observations of the
First Dynasty (Oxford: Oxford University Press, 1928), pp. 45-48.
Neugebauer, Paul Victor, Astronomische Chronologie (Berlin/Leipzig: Walter de Gruyter & Co., 1929),
vol. I, pp. 79-85, & vol. II, p. 23 (Tafel E21).
Neugebauer, Paul Victor, “Berichtigungen und Zusätze zu Schochs Planetentafeln für Jedermann: Tafel für Neulicht”,
Astronomische Abhandlungen: Ergänzungshefte zu den Astronomischen Nachrichten, 8, nr. 2 (1930), B17
[“Tafel für Neulicht”].
[Franz], “Wahrnehmung der Mondsichel 24 Stunden nach Neumond”, Die Sterne: Monatsschrift über alle Gebiete
der Himmelskunde, 10 (1930), 124.
[Sackay, D.], “Frühe Sichtung des zunehmenden Mondes”, Die Sterne: Monatsschrift über alle Gebiete der Himmelskunde,
10 (1930), 271.
Danjon, André-Louis, “Jeunes et vieilles lunes”, l’Astronomie: Bulletin de la Société Astronomique de France,
46 (1932), 57-66 [pdf link].
Chant, Clarence Augustus, “Notes and Queries: How Young a Moon can be Seen?”, The Journal of the Royal Astronomical
Society of Canada, 27 (1933), 257 [ADS
link].
Danjon, André-Louis, “Le croissant lunaire”, l’Astronomie: Bulletin de la Société Astronomique de France,
50 (1936), 57-65 [pdf link].
Reynolds, J.H., “The Mohammedan Calendar and the First Visibility of the New Moon in Egypt”, Occasional Notes of the
Royal Astronomical Society, nr. 7 (1939), 100-101.
Bruin, Frans, “The First Visibility of the Lunar Crescent”, Al-Bīrūnī Newsletter, nr. 18 (1969).
Ashbrook, Joseph, “Some Very Thin Lunar Crescents”, Sky and Telescope, 42 (1971), 78-79
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Joseph Ashbrook: The Astronomical Scrapbook. Skywatchers, Pioneers, and Seekers in Astronomy (Cambridge [Mass.]/Cambridge:
Sky Publishing Corporation/Cambridge University Press, 1984), pp. 200-209.
Ashbrook, Joseph, “More About the Visibility of the Lunar Crescent”, Sky and Telescope, 43 (1972), 95-96
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Yallop, Bernard D. & Hohenkerk, Catherine Y., A Note on the Prediction of the Dates of First Visibility of the New
Crescent Moon (Greenwich/Cambridge: Nautical Almanac Office, 1974, reprinted 1996 [= NAO Astronomical Information Sheets,
nr. 6]).
Ilyas, Mohammad, “New Moon’s Visibility and Monthly Lunar Date Lines: Calculations for Important dates in 1979”, Islamic
Culture: ???, 53 (1979), 133-136.
Ilyas, Mohammad, “Lowest Limit of w in the New Moon’s First Visibility Criterion of Bruin and its Comparison with the
Maunder Criterion”, Quarterly Journal of the Royal Astronomical Society, 22 (1981), 154-160
[ADS link].
Ilyas, Mohammad, “New Moon’s First Visibility [1]: Review of Astronomy and Current Islamic Calendrical Practices”, Islamic Culture:
???, 56 (1982), 43-63.
Ilyas, Mohammad, “Earliest Global Visibility of the New Moon 1981-85”, The Journal of the Royal Astronomical Society of Canada,
76 (1982), 371-381 [ADS link].
Ilyas, Mohammad, “Age as a Criterion of Moon’s Earliest Visibility”, The Observatory, 103 (1983), 26-28
[ADS link].
Ilyas, Mohammad, “The Danjon Limit of Lunar Visibility: A Re-Examination”, The Journal of the Royal Astronomical Society of Canada,
77 (1983), 214-219 [ADS link].
Ilyas, Mohammad, “New Moon’s First Visibility 2: Lunar Date Line (LDL) Calculations, Sighting and Calendar”, Islamic Culture:
???, 57 (1983), 87-112.
McNally, D., “The Length of the Lunar Crescent”, Quarterly Journal of the Royal Astronomical Society, 24 (1983), 417-429
[ADS link].
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Publishing, 1984).
Ilyas, Mohammad, “Limb Shortening and the Limiting Elongation for the Lunar Crescent’s Visibility”, Quarterly Journal of the Royal
Astronomical Society, 25 (1984), 421-422 [ADS
link].
Gavin, Maurice, “The Young Crescent Moon at Apogee; 30.9 Hours Old”, The Journal of the British Astronomical Association,
94 (1984), 187 [ADS link].
Ilyas, Mohammad, “Visibility of the Young Crescent Moon”, The Journal of the British Astronomical Association,
95 (1985), 183-184 [ADS link].
Vincent, F., “Earliest Visibility of Crescent Moon”, The Journal of the British Astronomical Association, 95 (1985), 272
[ADS link].
Ilyas, Mohammad, “A Shifting Date Line: An Interesting Feature of the Solar Calendar”, The Journal of the Royal Astronomical Society
of Canada, 80 (1986), 134-141 [ADS
link].
Ilyas, Mohammad, “Lunar Calendars: The Missing Date-Lines”, The Journal of the Royal Astronomical Society of Canada, 80
(1986), 328-335 [ADS link].
Schaefer, Bradley E., “An Algorithm for Predicting the Visibility of the Lunar Crescent”, Bulletin of the American Astronomical
Society, 19 (1987), 1042-1043 [ADS
link].
Ilyas, Mohammad, “Limiting Altitude Separation in the New Moon’s First Visibility Criterion”, Astronomy & Astrophysics,
206 (1988), 133-135 [ADS link].
Schaefer, Bradley E., “An Algorithm for Predicting the Visibility of the Lunar Crescent”, in: Imad-ad-Dean Ahmad (ed.), Proceedings
of IIIT Lunar Calendar Conference held at the International Institute of Islamic Thought, Herndon, VA, 9-10 Shawwal, 1407 A.H.,
6-7 June, 1987 A.C. (Herndon [VA]: International Institute of Islamic Thought, 1988),
pp. ???-???.
Doggett, Leroy E., Seidelmann, P. Kenneth & Schaefer, Bradley E., “Moonwatch – July 14, 1988”, Sky & Telescope,
76 (1988), 34-35 [ADS link].
Doggett, Leroy E. & Schaefer, Bradley E., “Moonwatch 88: An Observational Study of Lunar Calendars”, Bulletin of the American
Astronomical Society, 20 (1988), 991 [ADS link].
Schaefer, Bradley E., “Visibility of the Lunar Crescent”, Quarterly Journal of the Royal Astronomical Society, 29
(1988), 511-523 [ADS link] – cf. also the addenda by
Y. Loewinger, ibid., 36 (1995), 449-452 [ADS link].
Schaefer, Bradley E., “Astronomy and the Limits of Vision”, Archaeoastronomy: The Journal of the Center for Archaeoastronomy,
11 (1989/93), 78-90 [ADS link].
Durrani, Mohibullah N., “New World Record for Youngest Naked-Eye Crescent Moon Sighting”, The Journal of the Royal Astronomical
Society of Canada, 83 (1989), L34-L36 [ADS link]
– summary in: “A Still Younger Moon”, Sky & Telescope, 79 (1990), 582 [ADS
link].
Ilyas, Mohammad, “Crescent Wrench”, Sky & Telescope, 77 (1989), 349
[ADS link] – with a comment by Bradley E. Schaefer.
Doggett, Leroy E. & Schaefer, Bradley E., “Results of the July Moonwatch”, Sky & Telescope, 77 (1989), 373-375
[ADS link].
di Cicco, Dennis, “Breaking the New-Moon Record”, Sky & Telescope, 78 (1989), 322-323
[ADS link].
Bortle, John E., “April’s Old and Young Moon”, Sky & Telescope, 80 (1990), 215
[ADS link].
Laing, Drummond, “More on Record Moons”, Sky & Telescope, 81 (1991), 573
[ADS link].
Schaefer, Bradley E., “Length of the Lunar Crescent”, Quarterly Journal of the Royal Astronomical Society,
32 (1991), 265-277 [ADS link].
Ilyas, Mohammad, “Hijrah Day Number, Islamic Day Number and Islamic Lunar
Number: New Parameters for Exacting the Islamic Calendar”, The Journal of the British Astronomical Association, 101
(1991), 175-176 [ADS link].
Schaefer, Bradley E., “Astronomy and the Limits of Vision”, Vistas in Astronomy, 36 (1993), 311-361
[ADS link /
ScienceDirect link].
Schaefer, Bradley E., Ahmad, Imad A. & Doggett, Leroy E., “Records for Young Moon Sightings”, Quarterly Journal of the
Royal Astronomical Society, 34 (1993), 53-56 [ADS link].
Doggett, Leroy E. & Schaefer, Bradley E., “Lunar Crescent Visibility”, Icarus, 107 (1994), 388-403
[ADS link /
ScienceDirect link] – summary in: “Sighting the Crescent
Moon”, Sky & Telescope, 88 (1994), nr. 1, 14 [ADS
link].
Ilyas, Mohammad, “Lunar Crescent Visibility Criterion and Islamic Calendar”, Quarterly Journal of the Royal Astronomical
Society, 35 (1994), 425-461 [ADS
link].
Mikhail, J.S., Asaad, A.S., Nawar, S. & Hassanin, N.Y., “Visibility of the New Moon at Two Sites. I: Maryland situated at
Northern Geographical Latitude. II: Sacramento Peak situated at High Altitude above Sea Level”, Earth, Moon and Planets,
70 (1995), 93-108 [ADS link /
SpringerLink].
Mikhail, J.S., Asaad, A.S., Nawar, S. & Hassanin, N.Y., “Improving the Crescent Visibility Limits due to Factors causing
Decrease in the Sky Twilight Brightness”, Earth, Moon and Planets, 70 (1995), 109-121
[ADS link /
SpringerLink].
Victor, Robert C., “Thin Crescents”, Sky & Telescope, 91 (1996), nr. 1, 73
[ADS link].
Pepin, M. Barlow, “In Quest of the Youngest Moon”, Sky & Telescope, 92 (1996), nr. 6, 104-106
[ADS link].
Schaefer, Bradley E., “Lunar Crescent Visibility”, Quarterly Journal of the Royal Astronomical Society, 37 (1996), 759-768
[ADS link].
Schaefer, Bradley E., “Crescent Wars”, Bulletin of the American Astronomical Society, 29 (1997), 1206
[ADS link].
Yallop, Bernard D., A Method for Predicting the First Sighting of the New Crescent Moon (Cambridge: Nautical
Almanac Office, 1997, revised 1998 [= NAO Technical Notes, nr. 69]) [pdf link].
Fatoohi, Louay J., Stephenson, Francis Richard & Al-Dargazelli, Shetha S., “The Danjon Limit of First Visibility of
the Lunar Crescent”, The Observatory, 118 (1998), 65-72 [ADS link].
Schaefer, Bradley E., “Celestial Visibility for Astronomy History”, Bulletin of the American Astronomical Society,
30 (1998), 1283-1284 [ADS link].
Schaefer, Bradley E., “To the Visual Limits”, Sky & Telescope, 95 (1998), nr. 5, 57-60
[ADS link].
Sayyad, Mohammad-Reza, Taromi, Hasan & Bagheri, Mohammad, Ro'yat-e helāl-e māh teyye sāl-hāye 1415-1418
Hejri qamari [“Lunar Crescent Visibility during the Years 1415-1418 A.H.”] (Qum: Belagh Publication
Office, 1999).
Caldwell, John A.R. & Laney, C. David, “First Visibility of the Lunar Crescent”, Monthly Notes of the Astronomical
Society of Southern Africa, 58 (1999), 150-163 [ADS link] – reprinted in African Skies/Cieux Africains, 5 (2000), 15-23
[ADS link].
Djamaluddin, Thomas, “Visibilitas Hilal di Indonesia [Re-evaluation of Hilal Visibility in Indonesia]”, Warta LAPAN, 2
(2000), 137-??? [ADS link / pdf link].
Schaefer, Bradley E., “New Methods and Techniques for Historical Astronomy and Archaeoastronomy”, Archaeoastronomy: The
Journal of the Center for Archaeoastronomy, 15 (2000), 121-135 [ADS link].
Guessoum, Nidal & Meziane, K., “Visibility of the Thin Lunar Crescent: The Sociology of an Astronomical Problem (A Case Study)”,
Journal of Astronomical History & Heritage, 4 (2001), 1-14 [ADS link].
Hoffman, Roy E., “Observing the New Moon”, Monthly Notices of the Royal Astronomical Society, 340 (2003), 1039-1051
[ADS link].
Al-Mostafa, Zaki A. & Kordi, Moataz N., “A New Local Observation Record for a Young Moon from Saudi Arabia”, The
Observatory, 123 (2003), 49-50 [ADS
link].
Kordi, Ayman S., “The Psychological Effect on Sightings of the New Moon”, The Observatory, 123 (2003), 219-222
[ADS link].
Sinnott, Roger W., “Seeking Thin Crescent Moons”, Sky & Telescope, 107 (2004), nr. 2, 102-106
[ADS link].
Odeh, Mohammad Sh., “New Criterion for Lunar Crescent Visibility”, Experimental Astronomy, 18 (2004), 39-64
[ADS link /
SpringerLink].
MacRobert, Alan M. & Sinnott, Roger W., “Young-Moon Hunting in 2005”, Sky & Telescope,
109 (2005), nr. 2, 75-76 [ADS
link].
Al-Mostafa, Zaki A., “Lunar Calendars: The New Saudi Arabian Criterion”, The Observatory, 125 (2005), 25-30
[ADS link].
Hoffman, Roy E., “Rational Design of Lunar-Visibility Criteria”, The Observatory, 125 (2005), 156-168
[ADS link].
Odeh, Mohammad, “Jordanian Astronomical Society Glimpses a Challenging Crescent”, The Journal of the Royal Astronomical
Society of Canada, 99 (2005), 33-34 [ADS link].
Sinnott, Roger W., “Q&A: Youngest Visible Moon”, Sky & Telescope, 110 (2005), nr. 3, 116
[ADS link].
Sultan, Abdul Haq, “Explaining and Calculating the Length of the New Crescent Moon”, The Observatory, 125
(2005), 227-231 [ADS link].
Sinnott, Roger W., “Crescent Moons in 2006”, Sky & Telescope, 111 (2006), nr. 2, 60-61
[ADS link].
Sultan, Abdul Haq, “‛Best Time’ for the Visibility of the Lunar Crescent”, The Observatory, 126
(2006), 115-118 [ADS
link].
Qureshi, Muhammad Shahid & Khan, Nasiruddin, “A Comparative Study of Arithmetic, Observational and Predicted Lunar
Calendar for Pakistan for Years 2000-2004”, Journal of Basic & Applied Sciences, 2 (2006), 91-103
[web link].
Qureshi, Muhammad Shahid & Khan, Nasiruddin, “Methods of Calculating Crescent Length”, Journal of Basic &
Applied Sciences, 3 (2007), 65-72
[web link].
Sinnott, Roger W., “Crescent Moons in 2007”, Sky & Telescope, 113 (2007), nr. 2, 65-66
[ADS link].
Sultan, Abdul Haq, “First Visibility of the Lunar Crescent: Beyond Danjon’s Limit”, The Observatory,
127 (2007), 53-59 [ADS
link].
Sinnott, Roger W., “Catching Crescent Moons in 2008”, Sky & Telescope, 115 (2008), nr. 2,
72-73 [ADS link].
Hoffman, Roy E., “Back-to-Back Crescent Moons”, The Observatory, 129 (2009), 1-5
[ADS link].
Raharto, Moedji, Arumaningtyas, E.P. & Sopwan, Novi, “ Theoritical Contrast for Hilal Visibility Prediction
at Pelabuhan Ratu”, in: Khairurrijal et al. (eds.), The 4th Asian Physics Symposium: An International
Event, Bandung, West Java, Indonesia, 12–13 October 2010 (Melville: American Institute of Physics, 2010 [= AIP
Conference Proceedings, nr. 1325]), pp. 105-108 [ADS link].
Arumaningtyas, E.P. & Raharto, Moedji, “Contrast Threshold of Lunar Crescents Visibility for Ramadan and Syawal
1431 H at Bosscha Observatory”, in: Khairurrijal et al. (eds.), The 4th Asian Physics Symposium: An
International Event, Bandung, West Java, Indonesia, 12–13 October 2010 (Melville: American Institute of Physics,
2010 [= AIP Conference Proceedings, nr. 1325]), pp. 117-120
[ADS link].
Fouka, M., “Visibility of the Thin Lunar Crescent”, African Skies/Cieux Africains, 14 (2010), 54-57
[ADS link].
Qureshi, Muhammad Shahid, “A New Criterion for Earliest Visibility of New Lunar Crescent”, Sindh University
Research Journal (Sci. Ser.), 42 (2010), 1-16 [web link].
Bentchikou, Abdelhamid, Rasiwala, Moiz & Patel, Amit, “On the Visibility of the Earliest Crescent Moon: An
Islamic Calendar for Makkah”, Selenology Today, 21 (2011), 39-58
[Selenology link].
Relevant Entries in The Encyclopaedia of Islam: New Edition (Leiden: E.J. Brill)
“Hilāl: i. In Religious Law”, vol. 3 (1966), pp. 379-381 [Schacht, Joseph].
“Ru’yat al-Hilāl”, vol. 8 (1994), pp. 649-650 [King, David A.].
