Astro Lunar

Download Astro Lunar

Post on 21-Sep-2015

14 views

Category:

Documents

8 download

Embed Size (px)

DESCRIPTION

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

TRANSCRIPT

<ul><li><p>Five Millennium Canon of Lunar Eclipses:1999 to +3000 (2000 BCE to 3000 CE)</p><p>NASA/TP2009214172</p><p>January 2009</p><p>Fred Espenak and Jean Meeus</p></li><li><p>COVER CAPTION:</p><p>Basic lunar eclipse geometry is illustrated in this figure from New Astronomy by David Todd (1906).</p><p>.</p><p>The NASA STI Program Offi ce in Profi le</p><p>Since its founding, NASA has been ded i cat ed to the ad vance ment of aeronautics and space science. The NASA Sci en tifi c and Technical Information (STI) Pro gram Offi ce plays a key part in helping NASA maintain this im por tant role.The NASA STI Program Offi ce is operated by Langley Re search Center, the lead center for NASAs scientifi c and technical in for ma tion. The NASA STI Program Offi ce pro vides ac cess to the NASA STI Database, the largest col lec tion of aero nau ti cal and space science STI in the world. The Pro gram Offi ce is also NASAs in sti tu tion al mech a nism for dis sem i nat ing the results of its research and de vel op ment ac tiv i ties. These results are published by NASA in the NASA STI Report Series, which includes the following report types: TECHNICAL PUBLICATION. Reports of </p><p>com plet ed research or a major signifi cant phase of research that present the results of NASA pro-grams and include ex ten sive data or the o ret i cal analysis. Includes com pi la tions of sig nifi cant scientifi c and technical data and in for ma tion deemed to be of con tinu ing ref er ence value. NASAs counterpart of peer-re viewed formal pro fes sion al papers but has less stringent lim i ta -tions on manuscript length and ex tent of graphic pre sen ta tions.</p><p> TECHNICAL MEMORANDUM. Scientifi c and tech ni cal fi ndings that are pre lim i nary or of spe cial ized interest, e.g., quick re lease reports, working papers, and bib li og ra phies that contain minimal annotation. Does not contain extensive analysis.</p><p> CONTRACTOR REPORT. Scientifi c and techni-cal fi ndings by NASA-sponsored con trac tors and grantees.</p><p> CONFERENCE PUBLICATION. Collected pa pers from scientifi c and technical conferences, symposia, sem i nars, or other meet ings spon sored or co spon sored by NASA.</p><p> SPECIAL PUBLICATION. Scientifi c, tech ni cal, or historical information from NASA pro grams, projects, and mission, often con cerned with sub-jects having sub stan tial public interest.</p><p> TECHNICAL TRANSLATION. En glish-language trans la tions of foreign sci en tifi c and tech ni cal ma-terial pertinent to NASAs mis sion.</p><p>Specialized services that complement the STI Pro-gram Offi ces diverse offerings include cre at ing custom the sau ri, building customized da ta bas es, organizing and pub lish ing research results . . . even pro vid ing videos.</p><p>For more information about the NASA STI Pro gram Offi ce, see the following:</p><p> Access the NASA STI Program Home Page at http://www.sti.nasa.gov/STI-homepage.html</p><p> E-mail your question via the Internet to help@sti.nasa.gov</p><p> Fax your question to the NASA Access Help Desk at (301) 621-0134</p><p> Telephone the NASA Access Help Desk at (301) 621-0390</p><p> Write to: NASA Access Help Desk NASA Center for AeroSpace In for ma tion 7115 Standard Drive Hanover, MD 21076</p></li><li><p>NASA/TP2009214172</p><p>Five Millennium Canon of Lunar Eclipses:1999 to +3000 (2000 BCE to 3000 CE)</p><p>January 2009</p><p>Fred EspenakNASA Goddard Space Flight Center, Greenbelt, Maryland</p><p>Jean Meeus (Retired)Kortenberg, Belgium</p><p>National Aeronautics and Space Administration</p><p>Goddard Space Flight CenterGreenbelt, Maryland 20771</p></li><li><p>Available from:</p><p>NASA Center for AeroSpace Information National Technical Information Service7115 Standard Drive 5285 Port Royal RoadHanover, MD 21076-1320 Springfield, VA 22161</p></li><li><p>TABLE OF CONTENTS</p><p>Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v</p><p>Section 1: Figures and Predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1</p><p>Section 2: Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17</p><p>Section 3: Lunar Eclipse Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25</p><p>Section 4: Eclipses and the Moons Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45</p><p>Section 5: Lunar Eclipse Periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57</p><p>Acronyms and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73</p><p>References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74</p><p>Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1</p><p>FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: 1999 TO +3000 (2000 BCE TO 3000 CE) iii</p><p>TABLE OF CONTENTS</p></li><li><p>PREFACE</p><p>PREFACE</p><p>Theodor von Oppolzers 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. </p><p>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 Earths variable rotation rate and the secular acceleration of the Moon.</p><p>Nevertheless, von Oppolzers 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 Oppolzers great canon.</p><p>The Meeus-Mucke work also contains data on penumbral eclipses that are not included in von Oppolzers canon. Neither of these publications offers diagrams or maps to illustrate the geometry or visibility of each eclipse. Espenaks 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. </p><p>Both of these recent lunar eclipse canons are based on Newcombs Tables of the Sun (1895) and Browns 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.</p><p>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.</p><p>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.</p><p> 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</p><p> 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 Moons path through Earths penumbral and umbral shadows </p><p>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 Oppolzers great canon. Espenaks 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.</p><p>FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: 1999 TO +3000 (2000 BCE TO 3000 CE) v</p><p>PREFACE </p></li><li><p> 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</p><p> estimates of eclipse visibility map accuracy based on the uncertainty in the value of T (i.e., standard error in T)</p><p>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.</p><p>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.</p><p>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.</p><p>The Canon will also be of value to educators, planetariums, and anyone interested in knowing when and where past and future eclipses occur. The general public is fascinated by eclipseswith each major eclipse, the question always arises as to when a particular location experienced its last and next eclipses. The maps presented here are ideally suited to ad-dressing such queries.</p><p>Fred Espenak and Jean Meeus2009 January</p><p> vi FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: 1999 TO +3000 (2000 BCE TO 3000 CE)</p><p>PREFACE</p></li><li><p>SECTION 1: FIGURES AND PREDICTIONS</p><p>1.1 Introduction</p><p>Earth will experience 12,064 eclipses of the Moon during the 5000-year period from 1999 to +3000 (2000 BCE to 3000 CEa ). An individual diagram and visibility map for every lunar eclipse over the five-millennium interval is presented in the Appendix. The Moons path through Earths penumbral and umbral shadows illustrates the eclipse geometry, and the accompanying equidistant cylindrical projectionb map shows the geographic region of visibility during every phase of each eclipse.</p><p>1.2 Explanation of Lunar Eclipse Figures</p><p>The figure for each eclipse consists of two diagrams. The top one depicts the Moons path through Earths penumbral and umbral shadows with Celestial North directed up. The Moons orbital motion is from west to east (right to left)c with re-spect to the shadows. Each phase of the eclipse is defined by the instant when the Moons limb is externally or internally tangent to the penumbra or umbra as follows. </p><p>Penumbral lunar eclipses have two primary contacts. Neither of these events is observable.</p><p>P1Instant of first exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Begins)</p><p>P4Instant of last exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Ends)</p><p>Partial lunar eclipses have two additional contacts as the Moons limb enters and exits the umbral shadow (U1 and U4, respectively). At these two instants, the partial phase of the eclipse begins and ends.</p><p>P1Instant of first exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Begins)</p><p>U1Instant of first exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Begins)</p><p>U4Instant of last exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Ends)</p><p>P4Instant of last exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Ends)</p><p>Total lunar eclipses have two additional umbral contacts at the instants when the Moons entire disk is first and last internally tangent to the umbra (U2 and U3, respectively). These are the times when the total phase of the eclipse begins and ends.</p><p>P1Instant of first exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Begins)</p><p>U1 Instant of first exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Begins)</p><p>U2Instant of first interior tangency of the Moon with the Umbra. (Total Umbral Eclipse Begins)U3Instant of last interior tangency of the Moon with the Umbra. (Total Umbral Eclipse Ends)U4Instant of last exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Ends)</p><p>P4 Instant of last exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Ends)</p><p>The instant when the Moon passes closest to the shadow axis is known as the instant of greatest eclipse. This corresponds to the maximum phase of the eclipse, and the Moons position at this instant is also shown in the eclipse path diagrams.</p><p>a. The terms BCE and CE are abbreviations for Before the Common Era and Common Era, respectively. They are the secular equivalents to the BC and AD dating conventions. A major advantage of the BCE/CE convention is that both terms are suffixes, whereas BC and AD are used as a suffix and prefix, respectively. </p><p>b. The equidistant cylindrical projection (also known as the equirectangular projection) is a simple x-y Cartesian map projection where lines of latitude and longitude are represented by straight, equally spaced horizontal and vertical lines.</p><p>c. By convention, maps are plotted north up, west to the left, and e...</p></li></ul>