Literature on Computing and Observing the First Visibility of the Lunar Crescent

• I. Traditional Techniques for Computing the Visibility of the Lunar Crescent
• II. Modern Techniques for Computing the Visibility of the Lunar Crescent and Observations of Young Lunar Crescent
• III. Relevant Entries in The Encyclopaedia of Islam: New Edition (Leiden: E.J. Brill)
• IV. Websites on the Prediction of the Visibility of the Lunar Crescent

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].
• 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 Yaʿqub 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.
• Asaad, A.S. & Mikhail, J.S., “The Empirical Visibility Limits of New Moon Derived by Ancient Arabs in Comparison with the Values Detected Photoelectrically”, Helwan Observatory Bulletins, nr. 105 (1974).
• Neugebauer, Otto E., A History of Ancient Mathematical Astronomy (Berlin [etc.]: Springer-Verlag, 1975 [= Studies in the History of Mathematics and Physical Sciences, nr. 1]), Part One, pp. 533-540.
• 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 Yaʿqub 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].
• Gautschy, Rita, “On the Babylonian Sighting-Criterion for the Lunar Crescent and its Implications for Egyptian Lunar Data”, Journal for the History of Astronomy, 45 (2014), 79-90 [ADS link].
• Thomann, Johannes, ““Few things more perfect”: Ḥabash al-Ḥāsib's Criterion for the Visibility of the Lunar Crescent and the Dustūr al-munajjimīn”, in: E. Orthman & P.G. Schmidl (eds.), Science in the City of Fortune: The Dustūr al-munajjimīn and its World (Berlin: EB-Verlag, 2017 [= Bonner Islamstudien, Band 39]), pp. 137-172.
• Gautschy, Rita & Thomann, Johannes, “Dating Historical Arabic Observations”, in: M.T. Lago (ed.), Astronomy in Focus XXX: As Presented at the IAU XXX General Assembly, Vienna, Austria, 2018 (Cambridge: Cambridge University Press, 2020), pp. 163-166 [ADS link].

II. Modern Techniques for Computing the Visibility of the Lunar Crescent and Observations of Young Lunar Crescent

• 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: A Review of Astronomy, 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.
• 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.
• Denning, William F., “Visibility of the New Moon and the Pleiades”, The Journal of the British Astronomical Association, 19 (1909), 242-243.
• Watson, H., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19 (1909), 253-254.
• Whitmell, C.T., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19 (1909), 254-255.
• Henderson, Alexander C., “Early Visibility of the Crescent Moon, &c.”, The Journal of the British Astronomical Association, 19 (1909), 255-256.
• Johnson, E.W., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19 (1909), 256.
• Gheury, M.E.J., “Early Visibility of the Crescent Moon”, The Journal of the British Astronomical Association, 19 (1909), 310.
• 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 [see also ibid., 343-344].
• Bougon, J., “La visibilité de la lune”, The Journal of the British Astronomical Association, 22 (1911), 48-49.
• Cave, Charles J.P., “Early Visibility of the New Moon”, The Observatory: A Review of Astronomy, 34 (1911), 121 [ADS link].
• Horner, D.W., “Early Visibility of the New Moon”, The Observatory: A Review of Astronomy, 34 (1911), 162-163 [ADS link].
• Whitmell, C.T., “Early Visibility of the New Moon”, The  Observatory: A Review of Astronomy, 34 (1911), 203 [ADS link].
• Whitmell, C.T., “Early Visibility of the New Moon”, The  Observatory: A Review of Astronomy, 34 (1911), 305-306 [ADS link].
• Horner, D.W., “Early Visibility of the New Moon”, The  Observatory: A Review of Astronomy, 34 (1911), 344-345 [ADS link].
• Whitmell, C.T., “Early Visibility of the New Moon”, The  Observatory: A Review of Astronomy, 34 (1911), 374-375 [ADS link].
• Horner, D.W., “Early Visibility of the New Moon”, The  Observatory: A Review of Astronomy, 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: A Review of Astronomy, 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.
• Asaad, A.S. & Mikhail, J.S., “The Moon’s Brightness Near 20 Degree Elongation”, Helwan Observatory Bulletins, nr. 69 (1967).
• 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 [ADS link] – reprinted in L.J. Robinson (ed.), 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 [ADS link] – reprinted in L.J. Robinson (ed.), Joseph Ashbrook: The Astronomical Scrapbook. Skywatchers, Pioneers, and Seekers in Astronomy (Cambridge [Mass.]/Cambridge: Sky Publishing Corporation/Cambridge University Press, 1984), pp. 200-209.
• 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]).
• Asaad, A.S., Mikhail, J.S. & Nawar A. al-Shaheed, S., “The First Visibility of New Moon at Helwan and Daraw”, Helwan Observatory Bulletins, nr. 138 (1976).
• 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: A Review of Astronomy, 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].
• Dizer, Muammer, A Calculation Method for the Visibility Curve of the New Moon (Istanbul: Bosphorus University/Kandilli Observatory, 1984) [local pdf link].
• Ilyas, Mohammad, A Modern Guide to Astronomical Calculations of Islamic Calendar, Times & Qibla (Kuala Lumpur: Berita 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).
• 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.
• 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.
• 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.
• 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].
• Lyle, Emily, “Beat the Babylonians”, Sky & Telescope, 82 (1991), 454 [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.
• 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].
• 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].
• Victor, Robert C., “Thin Crescents”, Sky & Telescope, 91 (1996), nr. 1, 73.
• 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].
• Ilyas, Mohammad, Astronomy of Islamic Calendar (Kuala Lumpur: A.S. Noordeen Publishers, 1997).
• 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: A Review of Astronomy, 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].
• Seronik, Gary, “Opposing Crescent Moon Record”, Sky & Telescope, 98 (1999), nr. 3, 128 [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: A Review of Astronomy, 123 (2003), 49-50 [ADS link].
• Kordi, Ayman S., “The Psychological Effect on Sightings of the New Moon”, The  Observatory: A Review of Astronomy, 123 (2003), 219-222 [ADS link].
• Sinnott, Roger W., “Seeking Thin Crescent Moons”, Sky & Telescope, 107 (2004), nr. 2, 102-106.
• Odeh, Mohammad Sh., “New Criterion for Lunar Crescent Visibility”, Experimental Astronomy, 18 (2004), 39-64 [ADS link].
• 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: A Review of Astronomy, 125 (2005), 25-30 [ADS link].
• Hoffman, Roy E., “Rational Design of Lunar-Visibility Criteria”, The  Observatory: A Review of Astronomy, 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: A Review of Astronomy, 125 (2005), 227-231 [ADS link].
• Sinnott, Roger W., “Crescent Moons in 2006”, Sky & Telescope, 111 (2006), nr. 2, 60-61.
• Sultan, Abdul Haq, “‘Best Time’ for the Visibility of the Lunar Crescent”, The  Observatory: A Review of Astronomy, 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.
• Guessoum, Nidhal & Odeh, Mohammad Sh. (eds.), Applications of Astronomical Calculations to Islamic Issues: Proceedings of the First Emirates Astronomical Conference, Held at the Center for Documentation and Research, Abu-Dhabi, United Arab Emirates, 22-23 Thul Keadah 1427 AH, 13-14 December 2006 CE (Abu-Dhabi: ICOP, 2007) [ICOP link] – papers in English and in Arabic (with an English abstract), including:
• Yallop, Bernard, “Single Parameter First Visibility Criteria”, pp. 9-17.
• Odeh, Mohammad Sh., “New Criterion for Lunar Crescent Visibility”, pp. 19-28.
• Fernini, Ilias M., “Astronomical Crescent Visibility Criteria”, pp. 29-36.
• Riazi, Nematollah, “On Lunar Crescent Visibility Criteria”, pp. 37-42.
• bin Yahya, Firdaus, “An Analytical Study of Beginning and End of Ramadan During Prophet Muhammad’s Time”, pp. 43-55.
• Shaikh, Salman, “Hilal Sighting & Islamic Dates: Issues & Solution, Insha’Allah”, pp. 57-68.
• Schulte in den Bäumen, Joachim, Schulte in den Bäumen, Jens-Peter, Kroll, Peter, Müller, Bernd & Berthold, Thomas, “Professional Lunar Crescent Observation Telescope: Necessary Standards and First Sightings of the Waxing Moon in Broad Daylight”, pp. 69-76.
• Guessoum, Nidhal, “Progress in Solving the Problem of the Crescent-Based Islamic Calendar”, pp. 77-86.
• Hayman Z. M., “Islamic Moon Observation Satellite”, pp. 87-92.
• Sultan, Abdul Haq, “First Visibility of the Lunar Crescent: Beyond Danjon’s Limit”, The  Observatory: A Review of Astronomy, 127 (2007), 53-59 [ADS link].
• Sinnott, Roger W., “Catching Crescent Moons in 2008”, Sky & Telescope, 115 (2008), nr. 2, 72-73.
• Hoffman, Roy E., “Back-to-Back Crescent Moons”, The Observatory: A Review of Astronomy, 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].
• Guessoum, Nidhal & Odeh, Mohammad Sh. (eds.), Astronomy for the Islamic Society: Proceedings of the Second Emirates Astronomical Conference, Held at the National Center for Documentation and Research, Abu-Dhabi, United Arab Emirates, 16-18 Jumadal ’Akherah 1431 AH, 30 May – 01 June 2010 CE (Abu-Dhabi: ICOP, 2010) [ICOP link] – papers in English and in Arabic (with an English abstract), including:
• Shaukat, Syed Khalid, “A Suggested Global Islamic Calendar”, pp. 23-30.
• Nayyeri, AliAkbar, “Age of the Crescent: Topocentric or Geocentric?”, pp. 31-36.
• Rostami, Seyyed Ghasem, “The Modeling Error in Crescent Visibility Criteria”, pp. 37-44.
• Zainuddin, Mohd Zambri; Nawawi, Mohd Saiful Anwar & Ahmad, Nazhatulshima, “Sky Illumination for Lunar Crescent Visibility at Telok Kemang, Malaysia”, pp. 45-51.
• Stamm, Jim, “Techniques and Problems Associated With Telescopic Observations of Thin Lunar Crescents”, pp. 53-58.
• Elsässer, Martin, “Observing the Lunar Crescent Through Electronic Cameras”, pp. 59-65.
• Uddin, Qamar, “The Use of Technology to Live Webcast Crescent Moon Observations”, pp. 67-75.
• Qamardeen, Muhammad Yasin, “A Telecommunications Instrument for Data Collection and Dissemination of Hilal Sighting Information”, pp. 77-79.
• Durrani, Mohibullah N., “Challenges and Research Issues in Crescent Sighting and Related Moon Matters”, pp. 81-89.
• 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.
• Caldwell, John A.R., “Moonset Lag with Arc of Light Predicts Crescent Visibility”, Monthly Notes of the Astronomical Society of Southern Africa, 70 (2011), 220-235 [errata in ibid., 71 (2012), 6] [ADS link].
• Nawawi, Mohd Saiful Anwar Mohd; Zainuddin, Mohd Zambri; Ahmad, Nazhatulshima; Niri, Mohammaddin Abdul; Man, Saadan; Wahab, Raihana Abdul; Ismail, Khadijah & Zaki, Nurul Huda Ahmad, “Application of Scientific Approach to Determine Lunar Crescent’s Visibility”, Middle-East Journal of Scientific Research, 12 (2012), 96-100 [IDOSI link].
• Galal, A.A. & Rashed, M.G., “Helaical [sic] Rising of the New Moon as a Precursor of the Beginning of Hegri Lunar Month”, NRIAG Journal of Astronomy and Geophysics, 1 (2012), 156-158 [ADS link].
• Hasanzadeh, Amir, “Study of Danjon Limit in Moon Crescent Sighting”, Astrophysics and Space Science, 339 (2012), 211-221 [ADS link].
• Krauss, Rolf, “Babylonian Crescent Observation and Ptolemaic-Roman Lunar Dates”, PalArch’s Journal of Archaeology of Egypt/Egyptology, 9 (2012), nr. 5, 1-95 [PalArch link] – the introductory part gives a detailed history and analysis of modern lunar crescent visibility algorithms.
• Hafez, Yaser A.; Trojan, Lorenzo; Albaqami, Fahad H.; Almutairi, Abdulmajeed Z.; Davies, Rodney D.; Dickinson, Clive & Piccirillo, Lucio, “A Radio Determination of the Time of the New Moon”, Monthly Notices of the Royal Astronomical Society, 439 (2014), 2271-2280 [ADS link].
• Ahmed, Ahmed Kamil & Aziz, Abdul Halim Abdul, “Young Moon Visibility Criterion Based on Crescent Illumination and Sky Brightness Contrast Model”, Middle-East Journal of Scientific Research, 21 (2014), 1641-1644 [IDOSI link].
• Aziz, Abdul Halim Abdul & Ahmed, Ahmed Kamil, “A Unified Islamic Calendar Proposal for the World”, Middle-East Journal of Scientific Research, 22 (2014), 115-120 [IDOSI link].
• Fakhar, Mostafa; Moalem, Peyman & Badri, Mohamad Ali, “Lunar Crescent Detection Based on Image Processing Algorithms”, Earth, Moon, and Planets, 114 (2014), 17-34 [ADS link].
• Meziane, Karim & Hamza, Abdelhaq M., “Crescent-Visibility and Hijri-Calendar: The Limitations of Mediocre Erudition”, in: The Muslim 500: The World’s 500 Most Influential Muslims – 2017 Edition (Amman: The Royal Islamic Strategic Studies Centre, 2017), pp. 205-212 [The Muslim 500 link].
• Shariff, Nur Nafhatun Md.; Hamidi, Zety Sharizat & Faid, Muhamad Syazwan, “The Impact of Light Pollution on Islamic New Moon (Hilal) Observation”, International Journal of Sustainable Lighting, 19 (2017), 10-14 [IJSL link].
• Alrefay, T.; Alsaab, S.; Alshehri, F.; Alghamdi, A.; Hadadi, A.; Alotaibi, M.; Almutari, K. & Mubarki, Y., “Analysis of Observations of Earliest Visibility of the Lunar Crescent”, The Observatory: A Review of Astronomy, 138 (2018), 267-291 [ADS link / pdf link].
• Mahasena, P.; Yusuf, M.; Irfan, M.; Akbar, E.I.; Jatmiko, A.T.P.; Mandey, D.; Setiawan, A.; Sulaeman, M.; Hidayat, T.; Herdiwijaya, D.; Raharto, M. & Dermawan, B., “CCD Observation of Daylight Crescent Moon at Bosscha Observatory”, Journal of Physics: Conference Series, 1127 (2019), A012049 [ADS link].
• Raharto, M.; Sopwan, N.; Hakim, M. I. & Sugianto, Y., “New Approach on Study of New Young Crescent (Hilal) Visibility and New Month of Hijri Calendar”, Journal of Physics: Conference Series, 1170 (2019), A012080 [ADS link].
• Utama, Judhistira Aria; Simatupang, Ferry Mukharradi & Amsor, “The New Hilaal Visibility Criterion for Tropical Region”, Journal of Physics: Conference Series, 1280 (2019), A022073 [ADS link].
• Ahmed, Tafseer, “Predicting the Visibility of the First Crescent”, KIET Journal of Computing and Information Sciences, 3 (2020), Issue 2, 53-62 [doi link].
• Faid, Muhamad Syazwan; Nawawi, Mohd Saiful Anwar Mohd; Nahwandi, Muhammad Syaoqi; Shariff, Nur Nafhatun Md & Hamidi, Zety Sharizat, “Hilal-Obs: Authentication A[l]gorithm for New Moon Visibility Report”, Astrophysics Source Code Library, record ascl:2104.003 (2021) [ADS link].
• Muztaba, Robiatul; Malasan, Hakim L. & Djamal, Mitra, “Development of an Automated Moon Observation System using the ALTS-07 Robotic Telescope: 2. Progress Report on Standard Contrast Enhancement of Moon Crescent Image with OpenCV”, Journal of Physics: Conference Series, 2214 (2022), art. 012004 [ADS link].
• Sabiq, Fairuz, “The Geometry of the Position of the Sun and the Moon when Rukyatul Hilal”, AIP Conference Proceedings, 2566 (2022), art. 060001 [ADS link / online link].
• Al-Rajab, Murad; Loucif, Samia & Al Risheh, Yazan, “Predicting New Crescent Moon Visibility applying Machine Learning Algorithms”, Scientific Reports, 13 (2023), art. 6674 [doi link].
• Utama, Judhistira Aria; Zuhudi, A.R.; Prasetyo, Y.; Rachman, A.; Sugeng Riadi, A.R.; Nandi & Riza, L.S., “Young Lunar Crescent Detection based on Video Data with Computer Vision Techniques”, Astronomy and Computing, 44 (2023), art. 100731 [ADS link].
• Faid, Muhamad Syazwa; Mohd Nawawi, Mohd Saiful Anwar & Mohd Saadon, Mohd Hafiz, “HilalPy: Analysis Tool for Lunar Crescent Visibility Criterion”, Astrophysics Source Code Library, record ascl:2307.031 (2023) [ADS link].
• Faid, Muhamad Syazwan; Mohd Nawawi, Mohd Saiful Anwar & Mohd Saadon, Mohd Hafiz, “Analysis Tool for Lunar Crescent Visibility Criterion based on Integrated Lunar Crescent Database”, Astronomy and Computing, 45 (2023), art. 100752 [ADS link].
• Muztaba, Robiatul; Malasan, Hakim L. & Djamal, Mitra, “Deep Learning for Crescent Detection and Recognition: Implementation of Mask R-CNN to the Observational Lunar Dataset collected with the Robotic Lunar Telescope System”, Astronomy and Computing, 45 (2023), art. 100757 [ADS link].
• Faid, Muhamad Syazwan; Nawawi, Mohd Saiful Anwar Mohd; Saadon, Mohd Hafiz Mohd; Nahwandi, Muhammad Syaoqi; Shariff, Nur Nafhatun Md; Hamidi, Zety Sharizat; Wahab, Raihana Abdul; Norman, Mohd Paidi & Ahmad, Nazhatulshima, “Confirmation Methodology for a Lunar Crescent Sighting Report”, New Astronomy, 103 (2023), art. 102063 [ADS link].
• Faid, Muhamad Syazwan; Nawawi, Mohd Saiful Anwar Mohd; Saadon, Mohd Hafiz Mohd; Wahab, Raihana Abdul; Ahmad, Nazhatulshima; Nahwandi, Muhamad Syauqi; Ahmed, Ikramullah & Mohamed, Ibrahim, “Assessment and Review of Modern Lunar Crescent Visibility Criterion”, Icarus, 412 (2024), art. 115970 [ADS link].

III. 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].
• “Ruʾyat al-Hilāl”, vol. 8 (1994), pp. 649-650 [King, David A.].

IV. Websites on the Prediction of the Visibility of the Lunar Crescent

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 visibility criterion.
• Mondsichtung: Die Jagd nach der jüngsten Mondsichel – German-language website with predictions and reports of sighting. The predictions are based on the Yallop visibility 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.
• HilalMap: Crescent Moon Visibility Map – website hosted by Alhabib Islamic Web Service which generates maps of the visibility of the lunar crescent based on the lunar visibility criterion of Mohammad Odeh.
• Moonsighting – website hosted by Khalid Shaukat with predictions and reports of sightings. The predictions are based on the lunar visibility criterion of Khalid Shaukat, which is more optimistic than the Yallop criterion.
• Lettre d’information de l’IMCCE – The newsletter of the L’Institut de Mécanique céleste et de calcul des éphémérides (IMCCE) annually provides astronomical predictions of the visibility of the lunar crescent at the begin and the end of the Islamic month of Ramaḍān.
• MoonCalc 6.0 – MS-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 visual appearance of the lunar crescent from any terrestrial location.

I am grateful to Qamar Uddin (York, UK) for suggesting several improvements to the lunar crescent visibility maps. The world maps are based on the ETOPO1 Global Relief Model.