Durham E-Theses First visibility of the lunar crescent and other problems in historical astronomy.

266 Pages·2011·17.38 MB·English

Durham E-Theses
First visibility of the lunar crescent and other problems
in historical astronomy.
Fatoohi, Louay J.
How to cite:
Fatoohi, Louay J. (1998) First visibility of the lunar crescent and other problems in historical astronomy.,
Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/996/
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First Visibility
the Lunar Crescent
of
and
Other Problems in Historical
Astronomy
The copyright of this thesis rests
No
with the author. quotation
from it be
should published
the
of
without the written consent
information derived
author and
from it be
should acknowledged.
by
Louay J. Fatoohi
July 1998
A
thesis submitted to the University Durham for degree
of the Doctor Philosophy
of of
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For
My Sufi Master
and spiritual guide
Shaikh Muhammad
al-Casnazani al-Husseini
The Master Tariqa `Aliyyah Qadiriyyah Casnazaniyyah
of
A
Abstract
The first part of this dissertation investigates methods of predicting the first visibility of the
lunar that has the interest
crescent: an astronomical problem attracted of man since ancient
times. Many early nations used lunar calendars, the months of which began on the evening of
first lunar In
the sighting of the crescent after conjunction. modern times, the resolution of this
is importance both for historians determine
astronomical problem of special who need to
-
dates for Muslims is lunar. The
ancient exactly and around the world, whose religious calendar
interest in this matter over the centuries has resulted in the appearance of a number of solutions
by for first lunar The
a variety of authors predicting the visibility of the crescent. purpose of
the first part of this dissertation is to assess the accuracy of these prediction models using
data improvement. The
to
ancient, mediaeval and modern observational and explore possible
"zone be incorporated into lunar
study concludes that the concept of a of uncertainty" must any
it further
visibility criterion; applies this conclusion to the widely used modern criterion of true
lunar difference between the The data
altitude versus azimuthal sun and moon. observational
developing "zone in
show that a of uncertainty" this particular criterion yields the best results
of all.
The second part of the dissertation is an investigation of six problems in historical
These (i)
astronomy. are: assessing the accuracy of solar eclipse observations made by Jesuit
in China; (ii) the lunar by Jesuit
astronomers assessing accuracy of eclipse observations made
in China; (iii) dating the Thales; (iv) determining
astronomers solar eclipse of the modern
Babylonian (v) dating
equivalent of the angular units of measurement; the eclipses of
Thucydides; (vi) dating Plutarch. All have been
the
and solar eclipse of papers published or are
in
currently press.
-i-
Contents
i
Abstract
11
Contents
Part 1. The First Visibility the Lunar Crescent
of
1 Introduction 1
1.1 Overview 1
1.2 Literature Review 2
1.3 Abbreviations 3
1.4 Acknowledgement 4
2 The Observational Data 5
2.1 The Babylonian "Astronomical Diaries" 5
2.2 Conversion of Dates from the Babylonian to the Julian Calendar 9
2.3 The Babylonian Data
10
2.4 Determination of the Julian Dates of First Visibility of the Lunar Crescent for 12
Babylonian Observations
2.5 The Medieval Data 19
2.6 The Modern Data 24
3 The Computations 26
3.1 Computation Dates New Moons 26
the
of of
3.2 Computation Solar, Lunar Other Astronomical Parameters 28
of and
3.3 Computation Planetary Coordinates 30
of
3.4 Conversion Babylonian Dates into Julian Dates 31
the
of
3.5 Results Computations 33
of
-11-
4 The Babylonian Criterion First Visibility the Lunar Crescent 54
of of
5 The Islamic Calendar First Visibility the Lunar Crescent 61
and of
62
5.1 Characteristics Islamic Calendar
the
of
65
5.2 The Controversy Crescent Visibility in the Islamic World
of
69
5.3 Versions Islamic Calendar
the
of
6 The Criterion First Visibility Of the Lunar Crescent in the 79
of
Medieval Later Arab World
and
6.1 The (Xm, AX) Criterion 79
of al-Khawarizmi
6.2 The (Xm, AX) Criterion 82
of al-Qallas
6.3 The (Xm, AX) Criterion 84
of al-Lathiqi
6.4 The (Xs, AX, ß) Criterion Sanjufini 85
of al-
6.5 The (S, L, Vm) Criterion ibn Yunus 87
of
6.6 The (S, L) Criteria 90
6.7 Maimonides' (Xm, AX, S) Criterion 91
7 Modern Criteria First Visibility the Lunar Crescent 94
of of
7.1 The Danjon Visibility Limit
94
7.2 The Lunar Altitude-Azimuthal Difference Criterion
102
7.3 Bruin's Physical Criterion
107
7.4 Ilyas' Composite Criterion
111
7.5 The Lunar Age Criterion 114
7.6 The Moonset Lagtime Criterion 117
7.7 Schaefer's Criterion 120
7.8 Yallop's Empirical Criterion 121
8 Discussion Conclusion 127
and
Bibliography
137
-111-
Part 2. Problems in Historical Astronomy
1 Accuracy Solar Eclipse Observations by Jesuit
made
of
Astronomers in China. (published
paper)
2 Accuracy Lunar Eclipse Observations made by Jesuit
of
Astronomers in China. (published paper)
Solar Eclipse. (published
3 Thales's Prediction of a paper)
4 Angular Measurements in Babylonian Astronomy. (paper in
press)
5 The Eclipses Recorded by Thucydides. (paper in
press)
6 The Total Solar Eclipse Recorded by Plutarch. (paper in press)
Additional Published Studies Referenced in this Dissertation
1 Lunar Eclipse Times Recorded in Babylonian History.
Early Estimates Lunar Eclipse Magnitude.
2 Accuracy of
of
Unit Time.
3 The Babylonian of
-lv-
Part One
Lunar Crescent
The First Visibility the
of
1
Introduction
first lunar
The the visibility of the crescent attracted attention
problem of predicting
The
throughout history from many nations who used lunar calendars to regulate their activities.
oldest available records which reveal organised interest in this matter date back almost three
thousand years to the time of the Babylonians. Predicting the first visibility of the lunar
interest from medieval Muslim astronomers, largely because timings of
crescent received great
fasting Ramadhan
religious practices in Islam - such as the beginning and end of the month of -
determined by lunar
a calendar.
are
lunar has
In modern times, scientific interest in understanding the visibility of the crescent
dates historical
been by two factors: (i) the need to accurately convert of
motivated mainly
that the lunar calendar; (ii) the need of Muslims to ascertain when the
records of nations used
hence
lunar be for the first time after conjunction with the sun and to
crescent may visible -
it be The following how
look for it, and also to know when cannot seen. quotation expresses
first lunar
one of the contemporary investigators of the question of visibility of the crescent
described its present cultural and religious significance:
With roughly lx109 people of the Islamic faith following the Islamic calendar, this problem
is likely to be the one (non-trivial) problem in astronomy that has the greatest impact on our
(Schaefer, 1996: 759).
modern world
1.1 Overview
lunar is
Predicting the earliest visibility of the crescent after conjunction a matter of
human factors
It is
considerable complexity. a problem where astronomical, atmospheric and
(especially visual acuity) are all at work. The fact that even modern astronomers cannot agree
the best for determining the first visibility of the lunar crescent only attests to the
on criterion
this
complex nature of matter.
5
-i-