The Crescent Visibility Table in Al‐Khwārizmīs Zīj *

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... This knowledge passed on to the medieval Muslim astronomers. A matter that has been investigated by several researchers, which have shown that Muslim astronomers used the Indian criterion (Fatoohi 1998;Hogendijk 1988;Kennedy and Janjanian 1965). ...
... Al-Qallas lunar visibility criterion The name of al-Qallas (10th century) is associated with other criterion of visibility (Suter 1914;Newgebauer 1962;Kennedy and Janjanian 1965;King 1987;Hogendijk 1988). Table 3 shows King's computation,calculated by (17) at the time of the moonset. ...
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We show that the criteria of lunar crescent visibility of al-Khwarizmi (9th century) and al-Qallas (10th century) is not the Indian criterion, according to which the Moon will be visible if between the moonset and sunset there are more than 48 minutes. Therefore, we distinguished two new visibility criteria: al-Khwarizmi and al-Qallas, which we analyze and generalize.
... This approach was used by Muslim astronomers during the classical era to make visibility predictions. The most simple of these visibility curves is that proposed by Al-Khawarizmi[3] (#_ftn3), and which relies on a single variable. Ever since Fotheringham[4] (#_ftn4) published his pioneering study in 1910 on lunar crescent visibility, the standard was set for the generation and production of visibility curves. ...
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The question of time reckoning has always played a central role in human history in general, and has ever since the advent of Islam preoccupied the best minds among Muslim astronomers for its relevance to religious practice. While the timings of the five daily canonical prayers are determined by the relative position of the Sun with respect to a local horizon, the determination of the new Lunar Hijri month relies on the visibility of the first thin lunar crescent following a Luni-Solar conjunction. To date, the scientific prediction of the visibility of the first crescent remains difficult and challenging for various technical reasons. To be able to predict its visibility, scientists have to first resolve the celestial mechanics problems: a daunting task that can be performed using high performance computing. The next challenge is not as trivial as the first one for it involves the reflection of light off the Moon and its transmission through the Earth’s atmosphere, a highly variable and turbulent medium that affects the propagation and absorption of light. The final limitation is directly connected to human physiology since one requires naked-eye observation. If the dynamics of the Moon-Earth system is now known and understood with a remarkable precision, predicting the physical state of the atmospheric medium over any given time of interest is obviously a complex and difficult task for anyone familiar with the field of fluid dynamics and atmospheric physics. This in turn leads to the logical conlcusion that a crescent visibility-based calendar is unfeasible since it requires real time observations. By combining celestial mechanics computations with atmospheric radiative transfer conditions and naked-eye observations, one can clearly get a feel for the amount of uncertainty involved in predicting first crescent visibility.
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A Festschrift for E. S. "Ted" Kennedy, the leading scholar of the history of Islamic astronomy in the 2nd half of the 20th century, edited by two of his former students. The volume contains some 35 articles on astronomy and mathematics in the ancient and medieval Near East by distinguished scholars of divers nationalities. It well reflects the respect that all of these colleagues held for Ted Kennedy.
This article deals with an unstudied criterion for determining lunar crescent visibility, which appears in the Mufrad Z\(\bar{\iota }\)j, (compiled by Ḥāsib al-Ṭabar\(\bar{\upiota }\), 5thc.A.H./11th c.A.D.). Al-Ṭabar\(\bar{\upiota }\) attributes this circular criterion to Al-B\(\bar{\upiota }\)rūn\(\bar{\upiota }\). Initially, Prof. David King shed light on this criterion in 1987 and explained it briefly. We will examine this criterion by re-computing the underlying numerical values to reconstruct it, in order to demonstrate that it originates from Ḥabash’s simple criterion.
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The Code of Maimonides
  • S Gandz
  • J Obermann
  • Neugebauer
Gandz, S., Obermann. J., and Neugebauer, 0.. The Code of Maimonides, Book 3. Treatise 8. Sanctification of the New Moon, New Haven. 1956.
Place Names of Medieval Islam
  • F I Haddad
  • E S Kennedy
Haddad, F. I., and Kennedy, E. S., Place Names of Medieval Islam, Geographical Review, 54 (1964), pp. 439-440.
The Astronomical Tables of al-KhwilrizmI
  • Neugebauer
Neugebauer, 0. (transl.), The Astronomical Tables of al-KhwilrizmI, Hist. Filos. Skr. Dan. Vid. Selsk. 4, no.