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/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk me91 In the name of Allah, the Gracious, the Merciful >° 9 43'' 0' eji e' e e> igo4 U61 J CO J: lic 6..ý v Lo ý , ý.,, "ý J ýs ýºý. ur ý,r11 Lýi is' ý9r ZU LZJE rju No disaster can befall on the earth or in your souls but it is in a book before We bring it into being; that is easy for Allah. In order that you may not grieve for what has escaped you, nor be exultant at what He has given you; and Allah does not love any prideful boaster. (The Holy Qur'an, 057: 022-023) Io 1, ýtý ; äýLm}I1ý I19 Li. Jea J1 ; ýý'=pLu9 dýýsa§ dýl doý419 stq ..4ný1 #a" t; aM May Allah send blessings on our Master whose quality, revelation, message, and wisdom are praised [Muhammad], and on his lineage and companions, and salute him with a perfect salutation First Visibility of the Lunar Crescent and Other Problems in Historical Astronomy The copyright of this thesis rests with the author. No quotation from it should be published without the written consent of the author and information derived from it should be acknowledged. by Louay J. Fatoohi July 1998 A thesis University submitted to the of Durham for the degree of Doctor of Philosophy ýý 11 x., res c5- JJ c5`. ccJ ýjJ JI tl oJJ ýI11wig .;, ýI j ii .s, ý. v _11 ý,:,Iýý511 ý, Ix11d. 9. ý11 ýLý. ýý1.9]Iý, ý, ýý For My Sufi Master and spiritual guide Shaikh Muhammad al-Casnazani al-Husseini The Master of Tariqa `Aliyyah Qadiriyyah Casnazaniyyah A Abstract The first part of this dissertation investigates methods of predicting the first visibility of the lunar crescent: an astronomical problem that has attracted the interest of man since ancient times. Many early nations used lunar calendars, the months of which began on the evening of the first sighting of the lunar crescent after conjunction. In modern times, the resolution of this is astronomical problem of special importance - both for historians who need to determine ancient dates exactly and for Muslims around the world, whose religious calendar is lunar. The interest in this matter over the centuries has resulted in the appearance of a number of solutions by a variety of authors for predicting the first visibility of the lunar crescent. The purpose of the first part of this dissertation is to assess the accuracy of these prediction models using ancient, mediaeval and modern observational data and to explore possible improvement. The study concludes that the concept of a "zone of uncertainty" must be incorporated into any lunar visibility criterion; it further applies this conclusion to the widely used modern criterion of true lunar altitude versus azimuthal difference between the sun and moon. The observational data show that developing a "zone of uncertainty" in this particular criterion yields the best results of all. The second part of the dissertation is an investigation of six problems in historical astronomy. These are: (i) assessing the accuracy of solar eclipse observations made by Jesuit astronomers in China; (ii) assessing the accuracy of lunar eclipse observations made by Jesuit astronomers in China; (iii) dating the solar eclipse of Thales; (iv) determining the modern equivalent of the Babylonian angular units of measurement; (v) dating the eclipses of Thucydides; and (vi) dating the solar eclipse of Plutarch. All papers have been published or are currently in press. -i- Contents Abstract i Contents 11 Part 1. The First Visibility of the Lunar Crescent 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 of the Dates of New Moons 26 3.2 Computation of Solar, Lunar and Other Astronomical Parameters 28 3.3 Computation of Planetary Coordinates 30 3.4 Conversion of the Babylonian Dates into Julian Dates 31 3.5 Results of Computations 33 -11- 4 The Babylonian Criterion of First Visibility of the Lunar Crescent 54 5 The Islamic Calendar and First Visibility of the Lunar Crescent 61 62 5.1 Characteristics of the Islamic Calendar 65 5.2 The Controversy of Crescent Visibility in the Islamic World 69 5.3 Versions of the Islamic Calendar 6 The Criterion of First Visibility Of the Lunar Crescent in the 79 Medieval and Later Arab World 6.1 The (Xm, AX) Criterion of al-Khawarizmi 79 6.2 The (Xm, AX) Criterion of al-Qallas 82 6.3 The (Xm, AX) Criterion of al-Lathiqi 84 6.4 The (Xs, AX, ß) Criterion of al- Sanjufini 85 6.5 The (S, L, Vm) Criterion of ibn Yunus 87 6.6 The (S, L) Criteria 90 6.7 Maimonides' (Xm, AX, S) Criterion 91 7 Modern Criteria of First Visibility of the Lunar Crescent 94 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' CompositeCriterion 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 and Conclusion 127 Bibliography 137 -111- Part 2. Problems in Historical Astronomy 1 Accuracy of Solar Eclipse Observations made by Jesuit Astronomers in China. (published paper) 2 Accuracy of Lunar Eclipse Observations made by Jesuit Astronomers in China. (published paper) 3 Thales's Prediction of a Solar Eclipse. (published 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. 2 Accuracy of Early Estimates of Lunar Eclipse Magnitude. 3 The Babylonian Unit of Time. -lv- Part One The First Visibility of the Lunar Crescent 1 Introduction The problem of predicting the first visibility of the lunar crescent attracted attention throughout history from many nations who used lunar calendars to regulate their activities. The in date back oldest available records which reveal organised interest this matter almost three first lunar thousand years to the time of the Babylonians. Predicting the visibility of the largely because crescent received great interest from medieval Muslim astronomers, timings of beginning fasting Ramadhan religious practices in Islam - such as the and end of the month of - are determined by a lunar calendar. has In modern times, scientific interest in understanding the visibility of the lunar crescent dates historical been motivated mainly by two factors: (i) the need to accurately convert of records of nations that used the lunar calendar; (ii) the need of Muslims to ascertain when the hence lunar crescent may be visible for the first time after conjunction with the sun - and to following how look for it, and also to know when it cannot be seen. The 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 modern world (Schaefer, 1996: 759). 1.1 Overview Predicting the earliest visibility of the lunar crescent after conjunction is a matter of factors considerable complexity. It is a problem where astronomical, atmospheric and human (especially visual acuity) are all at work. The fact that even modern astronomers cannot agree on the best criterion for determining the first visibility of the lunar crescent only attests to the complex nature of this matter. 5 -i- Throughout history, each attempt to put forward a criterion has followed either an empirical or theoretical approach. The empirical approach, which is more frequently employed, is based on analysing a collection of observational data and then formulating a criterion that best fits the observations. On the other hand, the theoretical approach is embodied in attempts to resolve the problem through considering the various factors affecting crescent visibility and designing a descriptive mathematical model. While the Babylonian criterion was empirical, the Arab astronomers took mostly a theoretical approach.