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Five Millennium Canon of Lunar Eclipses: –1999 to +3000 (2000 BCE to 3000 CE)

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NASA/TP–2009–214172 Five Millennium Canon of Lunar Eclipses: –1999 to +3000 (2000 BCE to 3000 CE) Fred Espenak and Jean Meeus January 2009 COVER CAPTION: Basic lunar eclipse geometry is illustrated in this figure from “New Astronomy” by David Todd (1906). The NASA STI Program Offi ce … in Profi le Since its founding, NASA has been ded i cated to the • CONFERENCE PUBLICATION. Collected ad vancement of aeronautics and space science. The pa pers from scientifi c and technical conferences, NASA Sci en tifi c and Technical Information (STI) symposia, sem i nars, or other meetings spon sored Pro gram Offi ce plays a key part in helping NASA or co spon sored by NASA. maintain this impor tant role. • SPECIAL PUBLICATION. Scientifi c, techni cal, The NASA STI Program Offi ce is operated by or historical information from NASA pro grams, Langley Research Center, the lead center for projects, and mission, often concerned with sub- NASA’s scientifi c and technical infor ma tion. The jects having substan tial public interest. NASA STI Program Offi ce pro vides ac cess to the NASA STI Database, the largest collec tion of • TECHNICAL TRANSLATION. En glish-language aero nau ti cal and space science STI in the world. trans la tions of foreign scien tifi c and techni cal ma- The Pro gram Offi ce is also NASA’s in sti tu tion al terial pertinent to NASA’s mis sion. mecha nism for dis sem i nat ing the results of its research and devel op ment activ i ties. These results Specialized services that complement the STI Pro- are published by NASA in the NASA STI Report gram Offi ce’s diverse offerings include creat ing Series, which includes the following report types: custom thesau ri, building customized data bas es, organizing and publish ing research results . even • TECHNICAL PUBLICATION. Reports of pro vid ing videos. com pleted research or a major signifi cant phase of research that present the results of NASA pro- For more information about the NASA STI Pro gram grams and include exten sive data or theo ret i cal Offi ce, see the following: analysis. Includes compi la tions of sig nifi cant • Access the NASA STI Program Home Page at scientifi c and technical data and infor ma tion http://www.sti.nasa.gov/STI-homepage.html deemed to be of continu ing ref er ence value. NASA’s counterpart of peer-re viewed formal • E-mail your question via the Internet to pro fes sion al papers but has less stringent limi ta - [email protected] tions on manuscript length and extent of graphic pre sen ta tions. • Fax your question to the NASA Access Help Desk at (301) 621-0134 • TECHNICAL MEMORANDUM. Scientifi c and techni cal fi ndings that are prelim i nary or of • Telephone the NASA Access Help Desk at (301) spe cialized interest, e.g., quick release reports, 621-0390 working papers, and bib li og ra phies that contain • Write to: minimal annotation. Does not contain extensive NASA Access Help Desk analysis. NASA Center for AeroSpace In for ma tion • CONTRACTOR REPORT. Scientifi c and techni- 7115 Standard Drive cal fi ndings by NASA-sponsored con tractors and Hanover, MD 21076 grantees. NASA/TP–2009–214172 Five Millennium Canon of Lunar Eclipses: –1999 to +3000 (2000 BCE to 3000 CE) Fred Espenak NASA Goddard Space Flight Center, Greenbelt, Maryland Jean Meeus (Retired) Kortenberg, Belgium National Aeronautics and Space Administration Goddard Space Flight Center Greenbelt, Maryland 20771 January 2009 Available from: NASA Center for AeroSpace Information National Technical Information Service 7115 Standard Drive 5285 Port Royal Road Hanover, MD 21076-1320 Springfield, VA 22161 TABLE OF CONTENTS TABLE OF CONTENTS Preface . v Section 1: Figures and Predictions. 1 Section 2: Time . 17 Section 3: Lunar Eclipse Statistics. 25 Section 4: Eclipses and the Moon’s Orbit . 45 Section 5: Lunar Eclipse Periodicity . 57 Acronyms and Units . 73 References . 74 Appendix . A-1 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) iii PREFACE PREFACE PREFACE Theodor von Oppolzer’s 1887 Canon der Finsternisse (Canon of Eclipses) stands as one of the greatest accomplishments in computational astronomy of the nineteenth century. It contains the elements of all 8000 solar eclipses and 5200 lunar eclipses occurring between the years –1207 and +2161, together with maps showing the approximate positions of the central lines of total, annular and hybrid solar eclipses. To make this remarkable achievement possible, a number of approximations were used in the calculations and maps. Fur- thermore, the 19th century ephemerides for the Sun and Moon, which are critical to eclipse predictions, cannot compare to the accuracy and precision of modern ephemerides. Finally, the 1887 canon did not take into account the shifts in latitude and timing of ancient eclipses due to Earth’s variable rotation rate and the secular acceleration of the Moon. Nevertheless, von Oppolzer’s canon remained the seminal reference on predictions of eclipses until well into the 20th century. With the arrival of the electronic computer, the time was ripe to produce updated solara and lunar eclipse can- ons. In 1979, Meeus and Mucke published Canon of Lunar Eclipses: –2002 to +2526 containing the Besselian elements of 10,936 lunar eclipses. It was intended mainly for historical research and served as the modern day successor of von Oppolzer’s great canon. The Meeus-Mucke work also contains data on penumbral eclipses that are not included in von Oppolzer’s canon. Neither of these publications offers diagrams or maps to illustrate the geometry or visibility of each eclipse. Espenak’s Fifty Year Canon of Lunar Eclipses (1989) includes individual Moon-shadow geometry diagrams and eclipse visibility maps of all lunar eclipses, but it covers a relatively short period from +1986 to +2035. Both of these recent lunar eclipse canons are based on Newcomb’s Tables of the Sun (1895) and Brown’s lunar theory (1905), subject to later modifications in the Improved Lunar Ephemeris (1954). These were the best ephemerides of their day but they have since been superseded. The Canon of Lunar Eclipses 1500 B.C.–A.D. 3000 (Liu and Fiala, 1992) uses modern theories of the Sun and the Moon prepared by the Bureau des Longitudes of Paris. However, it does not contain individual eclipse geometry diagrams or maps. Instead, it offers a series of map templates to approximate the geographic regions of eclipse visibility, and an op- tional computer program do generate these figures for any eclipse in the Canon. The present publication is the first to offer eclipse geometry diagrams and visibility maps for every lunar eclipse (12,064 eclipses) over a period covering five thousand years from –1999 to +3000. The following points highlight the features and characteristics of this work. • based on modern theories of the Sun and the Moon constructed at the Bureau des Longitudes of Paris rather than the older Newcomb and Brown ephemerides • ephemerides and eclipse predictions performed in Terrestrial Dynamical Time • covers historical period of eclipses as well as one millennium into the future • diagrams for each eclipse depict the Moon’s path through Earth’s penumbral and umbral shadows a. Several new solar eclipse canons were published in the second half of the 20th century. Meeus, Grosjean, and Vanderleen published Canon of Solar Eclipses (1966) containing the Besselian elements of all solar eclipses from +1898 to +2510, together with central line tables and maps. The aim of this work was principally to provide data on future eclipses. The Mucke and Meeus work Canon of Solar Eclipses: –2003 to +2526 (1983) was intended mainly for historical research and served as a modern day successor of von Oppolzer’s great canon. Espenak’s Fifty Year Canon of Solar Eclipses (1987) includes individual detailed maps and central path data for all solar eclipses from +1986 to +2035. Finally, the Espenak and Meeus work Five Millennium Canon of Solar Eclipses: –1999 to +3000 (2006) contains individual maps of every solar eclipse and uses modern ephemerides of the Sun and Moon. FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) v PREFACE • world maps identify geographic regions of visibility for each phase of every eclipse • visibility maps are based of the most current determination of the historical values of ∆T • estimates of eclipse visibility map accuracy based on the uncertainty in the value of ∆T (i.e., standard error in ∆T) A primary goal of this work is to assist historians and archeologists in the identification and dating of eclipses found in references and records from antiquity. For example, an ancient mechanical calculator known as the Antikythera mechanism was apparently designed to calculate eclipses and other astronomical phenomena (Freeth, et. al., 2008). The decoding of this device was possible in part by comparing its combination of wheel positions with the dates of lunar eclipses. Correlating historical records with specific eclipses is no easy task since there are usually several possible candidates. Ac- curate visibility maps using the best available values of ∆T coupled with estimates in the standard error of ∆T are critical in discriminating among potential eclipses candidates. Ultimately, historical eclipse identification can lead to improved chronologies in the time line of a particular culture. The maps can also be used to quickly estimate the approximate circumstances for any geographic location during each eclipse without any calculations. The position of the moonrise and moonset curves for each eclipse contact show which eclipse phases can be seen from any location. The Canon will also be of value to educators, planetariums, and anyone interested in knowing when and where past and future eclipses occur.
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