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Maya Eclipses: Modern Data, the Triple Tritos and the Double Tzolkin

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University of Central Florida STARS Electronic Theses and Dissertations, 2004-2019 2007 Maya Eclipses: Modern Data, The Triple Tritos And The Double Tzolkin William Earl Beck University of Central Florida Part of the Anthropology Commons, and the The Sun and the Solar System Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Beck, William Earl, "Maya Eclipses: Modern Data, The Triple Tritos And The Double Tzolkin" (2007). Electronic Theses and Dissertations, 2004-2019. 3078. https://stars.library.ucf.edu/etd/3078 MAYA ECLIPSES: MODERN ASTRONOMICAL DATA, THE TRIPLE TRITOS AND THE DOUBLE-ZTOLKIN by WILLIAM E. BECK B.A. University of Central Florida, 2001 A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Arts in the Department of Liberal Studies in the College of Graduate Studies at the University of Central Florida Orlando, Florida Fall Term 2007 © William E. Beck ii ABSTRACT The Eclipse Table on pages 51-58 of the Dresden Codex has long fascinated Maya scholars. Researchers use the mean-value method of 173.3 days to determine nodal passage that is the place where eclipses can occur. These studies rely on Oppolzer’s Eclipse Canon and Schram’s Moon Phase Tables to verify eclipse occurrences. The newer canons of Jean Meeus and Bao-Lin Liu use decimal accuracy. What would be the effect of modern astronomical data on the previous studies and the Maya Eclipse Table? The study utilizes a general view of eclipses that includes eclipses not visible to the Maya. Lunar eclipses are also included. This inquiry differs from previous studies by calculating the Maya dates of eclipses instead of nodal passage. The eclipse dates are analyzed using the three eclipse seasons, of the 520 days, which is the Double Tzolkin or twice the Sacred Calendar of the Maya. A simulation of the Eclipse Table, using the 59-day calendar, is created to test modern data against the Dresden Table. The length of the Table is the Triple Tritos of 405 lunations. The use of the Tritos instead of the Saros suggests the Table is independent of Western Astronomy. Advanced Astronomy is not needed to produce this Table; a list of eclipses could produce this Table. The result of this inquiry will be to create a facsimile of the Eclipse Table, which can be compared to the Eclipse Table to test the structure, function and purpose of the Table. iii In the loving memory of my parents Harold and Virginia Beck iv ACKNOWLEDGMENTS I wish to thank my committee members, Drs. Arlen Chase, Diane Chase and Elayne Zorn, for their help and advice. I also wish thank the staff of the University of Central Florida Library for their tireless work in finding the resources for this project and the Office of Instructional Resources for their help with formatting the thesis and images in this study. v TABLE OF CONTENTS CHAPTER ONE: BACKGROUND............................................................................................... 1 Introduction................................................................................................................................. 1 Dresden Codex............................................................................................................................ 2 Science ...................................................................................................................................... 15 CHAPTER TWO: DISCUSSION................................................................................................. 26 Calendars and Maya Math ........................................................................................................ 26 Eclipse Data .............................................................................................................................. 31 Eclipse Periods.......................................................................................................................... 38 Simulation................................................................................................................................. 51 Chapter Three: Conclusion ........................................................................................................... 57 Appendix A Meeus Lunar Data .................................................................................................. 60 Appendix B Liu Lunar Data ....................................................................................................... 63 Appendix C Oppolzer Lunar Data .............................................................................................. 66 Appendix D Meeus Solar Data ................................................................................................... 69 Appendix E Oppolzer Solar Data ............................................................................................... 72 Appendix F Lunar-Solar Data..................................................................................................... 75 Appendix G Meeus Lunar Season Distribution.......................................................................... 79 Appendix H Meeus Solar Season Distribution ........................................................................... 81 Appendix I Teeple Season Distribution...................................................................................... 83 Appendix J Solar-Lunar Season Distribution ............................................................................. 85 Appendix K Table Simulation .................................................................................................... 87 Appendix L Glossary .................................................................................................................. 90 LIST OF REFERENCES.............................................................................................................. 95 vi LIST OF FIGURES Figure 1 Solar and Lunar Eclipse Glyphs Pages 53a and 58b of the Dresden Codex after Thompson (1972)............................................................................................................................ 6 Figure 2 “Bookend Gods” Page 68 of the Dresden Codex after Thompson (1972).................... 18 Figure 3 Serpent Images Pages 56b and 57b of the Dresden Codex after Thompson (1972) ..... 19 Figure 4 Ah Tzul Ahau Page 58b of the Dresden Codex after Thompson (1972) ...................... 21 Figure 5 Teeple Arc after Teeple (1930:89) ................................................................................. 34 Figure 6 Meeus Arc following Teeple (1930:89) ......................................................................... 37 vii LIST OF TABLES Table 1 Picture Intervals after Guthe (1978:11) ........................................................................... 13 Table 2 Lunar Semesters after Guthe (1932:275)......................................................................... 43 Table 3 Eclipse Periods after Table 4 Van Den Berg (1955:28) ................................................. 50 Table 4 Guthe's Semesters after Guthe (1932:275) ..................................................................... 53 Table 5 Tritos Simulation of Table 2............................................................................................ 54 viii CHAPTER ONE: BACKGROUND Introduction The purpose of this study is to compare modern astronomical data against the Dresden Eclipse Table on pages 51-58 of the Dresden Codex. The Dresden Codex is 405 lunations or 46 Tzolkins in length. A Tzolkin is the 260 day calendar used by the Maya. This duration of time is three times the Tritos eclipse period of 135 lunations or a Triple Tritos. The Dresden Codex is one of three surviving Maya texts that display charts believed to contain astronomical data. The Dresden Eclipse Table is one of the most studied and least understood pieces of Maya Iconography. Is it a lunar calendar; a solar warning table; a sysygy, (a list of actual eclipses) or just a list of potential eclipses? For this reason the chart on pages 51-58 will be referred to as the Eclipse Table in this thesis. This inquiry differs from earlier studies by computing the Maya Date of modern eclipses instead of nodal passage, the area where eclipses are most likely to occur. This method will allow for the elimination of the use of the mean-value method of 173.31 days, prominent in previous studies of Maya eclipses. Three times the mean-value is a close approximation to the 520-day period, the Double Tzolkin. This study will also investigate other eclipse periods and not just the Saros period used in the earlier studies. The Saros is very prominent in Western Astronomy but not in Maya astronomy. A secondary purpose is to compare modern astronomical data against the astronomical data used in the previous studies of the Eclipse Table. This data is Oppolzer’s Eclipse Canon (1887) and Schram’s Moon Phase Tables (1908). To test the validity of these texts, two newer eclipse 1 canons, one by Bao-Lin Liu (1992) and another by Jean Meeus (1966, 1979) will be compared to Oppolzer’s Canon. These newer canons are more accurate due to decimal approximations but the Maya did not use decimal numbers. Would
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