New Moon's Visibility and International Islamic Calendar for the American Region 1407H - 1421H By Mohammad Ilyas. Penang, Malaysia: The International Islamic Calendar Programme, n.d.

Abstract

The International Islamic Calendar Programme relies on calculations
of the new moon's expected visibility. The term "new moon's visibility"
gives a wrong connotation, because the astronomical term "new moon"
refers to a moon that is completely dark and invisible. Therefore, from
here on the term "crescent moon" or simply "crescent" will be used for a
moon that could be visible after the new moon phase.
The problem of predicting the crescent moon's visibility has been of
interest to astronomers in general for a friendly competition of sighting
a young crescent moon and to Muslims for their needs associated with
the Islamic calendar. The earliest astronomical criterion for visibility
appeared in the Babylonian era: the moon's age after conjunction must
be more than 24 hours, an arc of separation as must be more than 12° or
the moon sets 48 minutes after sunset. Hindus (500-700 C.E.) developed
a more elaborate system of calculations with the same as >= 12° criterion.
In the eighth to tenth centuries C.E., Muslim astronomers, notably
Ya'qub ibn Tariq, Habash, al Khwarizmi, al Farghani, and al Battani
excelled in mathematical astronomy and developed rules for predicting
the crescent's visibility based on the importance of the crescent's width.
A century later, al Biruni recommended al Battani's procedures. In the
fifth century, al Sufi and al Kashani still quoted the early Babylonian criterion
of as >=12° .
In the late part of the nineteenth century, Schmidt recorded observations
in Athens, Greece, throughout a period of twenty years. Fotheringham
(1910) and Maunder (1911), who used Schmidt's data and then
added some more observational data, made the first significant developments
in criterion for visibility since the time of al Battani. Bruin (1977)
developed an independent physics-based criterion involving such variables
as the sky's brightness, contrast, the crescent's intensity, and so on.
However, his criterion was only theoretical and its validity needed to be
proven by actual observations. Ilyas (1981) modified Bruin's criterion in
order to remove the discrepancy in his method and the actual observational
criterion of Maunder. All of these suggested criteria for calculating
expected visibility have been summarized in a tabular form on page
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