The Copan Baseline: K&#39;atun 9.11.0.0.0 and the Three Hearthstones in Orion

Michael Grofe

The acropolis in the Classic Maya city of Copan occupies a central position in the Copan Valley. On either side of the valley, Stela 10 and Stela 12 form a 6.5-km baseline that appears to have served an astronomical purpose. Taking into account the hieroglyphic texts on both Stela 10 and Stela 12, this article provides a new interpretation of the purpose of the Copan baseline as a commemoration of astronomical observations on the eastern horizon, involving the sunrise on the K'atun ending 9.11.0.0.0 at the identical azimuth as the rising of Na'ir al Saif, the brightest star in Orion's Sword, a nebulous region recognized by the K'iche' Maya as the smoke from the hearth fire in an asterism known as the Three Hearthstones of Alnitak, Saiph, and Rigel. In the text from Stela 12, the ruler K'ahk' Uti' Witz' K'awiil is said to have witnessed the First Three Hearthstones at the "edge of the sky," a phrase commonly referenced in widely shared texts dealing with the mythical start of the Long Count in 3114 BC. However, this is the only known text with a specific historical reference to an observation of the Three Hearthstones. Evoking the cosmological rebirth of the Sun, the Copan baseline and its associated inscription appear to commemorate K'atun 9.11.0.0.0, when the Sun rose at the same azimuth as that of the central fire in the Three Hearthstones. The evidence from this article specifically both supports the 584285 GMT calendar correlation and provides additional evidence to support the hypothesis that the asterism of the Three Hearthstones from Classic period Maya texts is directly ancestral to the K'iche' asterism with the same name.

The Copan Baseline: K'atun 9.11.0.0.0 and the Three Hearthstones in Orion MICHAEL J. GROFE Abstract The acropolis in the Classic Maya city of Copan occupies a central position in the Copan Valley. On either side of the valley, Stela 10 and Stela 12 form a 6.5-km baseline that appears to have served an astronomical purpose. Taking into account the hieroglyphic texts on both Stela 10 and Stela 12, this article provides a new interpretation of the purpose of the Copan baseline as a commem-• oration of astronomical observations on the eastern horizon, involving the sunrise on the K'atun ending 9.11.0.0.0 at the identical azimuth as the rising of Na'ir al Saif, the brightest star in Orion's Sword, a nebulous region recognized by the K'iche' Maya as the smoke from the hearth fire in an asterism known as the Three Hearthstones of Alnitak, Saiph, and Rigel. In the text from Stela 12, the ruler K'ahk' Uti' Witz' K'awiil is said to have witnessed the First Three Hearthstones at the "edge of the sky," a phrase commonly referenced in widely shared texts dealing with the mythical start of the Long Count in 3114 BC. However, this is the only known text with a specific historical reference to an observation of the Three Hearthstones. Evoking the cosmological rebirth of the Sun, the Copan baseline and its associated inscription appear to commemorate K'atun 9.11.0.0.0, when the Sun rose at the same azimuth as that of the central fire in the Three Hearthstones. The evidence from this article specifically both supports the 584285 GMT calendar correlation and provides additional evidence to support the hypothesis that the asterism of the Three Hearthstones from Classic period Maya texts is directly ancestral to the K'iche' asterism with the same name. Resumen La acropolis de Ia ciudad maya clasico de Copan ocupa una posicion central en el valle de Copan. A cada !ado del valle, la Estela 10 y Ia Estela 12 forman una linea de base de 6.5 km que parece haber servido a un proposito astronomico. Teniendo en cuenta los textos jeroglificos tanto en la Estela 10 y Ia Estela 12, este articulo ofrece una nueva interpretacion del proposito de la linea de base de Copan como una conmemoracion de las observaciones astronomicas en el horizonte oriental, que implica la salida del sol en el final de K'atun 9.11.0.0 0,0 en el acimut identica como la salida de Na'ir al Saif, la estrella mas brillante de la espada de Orion, una region nebulosa reconocido por el K'iche' Maya como el humo del fuego del hogar en un asterismo conocido como las tres piedras de hogar de Alnitak, Saiph, y Rigel. En el texto de la Estela 12, el gobernante K'ahk' Uti' Witz' K'awiil se dice que ha sido testigo de las tres primeras pie- Michael J. Grote, a specialist in Maya hieroglyphic writing, archaeoastronomy, comparative mythology, and cacao, is particularly interested in the analysis of Maya deep-time intervals and the confluence of mythological narratives and astronomical science in Mesoamerica . In his doctoral research at the University of California at Davis, he explored a new astronomical interpretation of the Serpent Series within the Dresden Codex that incorporates precise measurements of the sidereal year, and he is currently expanding this research to systematically explore the theoretical astronomy found throughout the inscriptions. He leads multiple field courses with the Maya Exploration Center and currently teaches cultural anthropology, archaeology, physical anthropology, and linguistics at American River College and Sacramento City College in California . © 2012-2013 by the University of Texas Press dras de hagar en el "borde del cielo," una frase comunmente se hace referencia en los textos ampliamente compartidos que se ocupan de la mftica inicio de la Cuenta Larga en 3114 aC. Sin embargo, esto es el unico texto conocido con una referencia hist6rica especffica a una observaci6n de las tres piedras de hagar. Evocando el renacimiento cosmo16gico del Sol, la linea de base de Copan y su inscripci6n asociada parecen conmemorar K'atun 9.11.0.0.0, cuando el Sol se levant6 en el mismo azimut que la del fuego central en las tres piedras de hagar. La evidencia de este articulo especfficamente tanto apoya el 584285 GMT correlaci6n calendario, y proporciona evidencia adicional para apoyar la hip6tesis de que el asterismo de las tres piedras de hagar, dentro de los textos mayas del epoca Clasica, es directamente ancestral a asterismo K'iche' con el mismo nombre. The acropolis in the Classic Maya city of Copan occupies a central position in the Copan Valley. On ei- FIGURE 1. ther side of the valley, Stela 10 and Stela 12 form a 6.5-km baseline that aligns with the southern side of the central acropolis, and it appears to have served an astronomical purpose (Figure 1). These two stelae were erected by Ruler 12 of Copan, whose full name reads K'ahk' Uti' Witz' K'awiil (Stuart 2007). Nicknamed "Smoke Imix" (Grube and Martin 2000:201), Ruler 12 dedicated Stela 10 and Stela 12 as part of a larger sculpture program of seven monuments with dates leading up to and commemorating the K'atun ending on the Long Count date 9.11.0.0.0. 1 Several authors have suggested that Stela 10 and Stela 12 intend to mark positions of the Sun on the western horizon, thus demarcating two specific days in the tropical year. However, using either of the widely accepted Goodman-Martinez-Thompson (GMT) correlations between the Maya and Christian chronologies, neither of the Initial Series dates on either stela appears to corroborate the proposed solar alignments suggested by the baseline. All previous analyses of the Copan baseline have assumed that it is intended to indicate a solar Map of Copan, showing Copan baseline: (left) Stela 10; (right) Stela 12 (after Morley 1920). VOLUME XXV 2012-2013 55 alignment on the western horizon or that the Initial Series dates on Stela 10 and Stela 12 should necessarily correspond to one of the two days on which the Sun appears at this western azimuth position. Taking into account the hieroglyphic texts on both Stela 10 and Stela 12 and the associated monuments dedicated by K'ahk' Uti' Witz' K'awiil, this article provides a new interpretation of the purpose of the Copan baseline as a commemoration of both solar and stellar observations on the eastern horizon that specifically target the sunrise on 9.11.0.0.0 and the asterism of the Three Hearthstones in Orion, referenced in the text from Stela 12 and known among the contemporary K'iche'. Previous Analyses of the Copan Baseline Following his explorations of Copan, Colonel !uan Galindo (1835) first mentioned Stela 10 and Stela 12, but it was Herbert Spinden (1913:164) who first suggested that these two stelae form an intentional eastwest sight line. Under the auspices of the Carnegie Institution, Arthur Carpenter obtained a magnetic compass bearing of Stela 10 from Stela 12, as well as of the sunset azimuth on March 8, 1916 (Morley 1926). Using this data, Robert Wheeler Willson calculated that the Sun would set 8°13' north of west directly behind Stela 10 when seen from the position of Stela 12 (Figure 2), 20.3 days after the vernal equinox on April 9, and 20.6 days prior to the autumnal equinox on September 2 (Morley 1920:132136). Citing Willson, who calculated the bearing as N 81°47' W (an azimuth of 278°13'), Morley (1920: 133) mistakenly restates the second of these days as September 10. Considering an earlier magnetic bearing of N 86°46' W together with the magnetic declination of 6° obtained from George B. Gordon (1896), Willson recalculated another bearing of N 80°46' W (azimuth 279°14'), which shifted the dates by three days forward from April 9 and three days backward from the September 2 date. Morley (1920:134) records these dates as April 12 and incorrectly as September 7, based on his prior error. Accompanying Morley in 1926, John Lindsay from the Carnegie Department of Terrestrial Magnetism confirmed an actual sighting of sunset behind the baseline on 56 ARCHAEOASTRONOMY April 12 at a bearing of N 81°9' W (an azimuth of 278°51'), noting that the reciprocal sunset would occur on August 30 (Morley 1926:277-282). Nevertheless, several authors (Aldana 2002; Aveni 1977, 1980, 2001; Baudez 1987) have continued to state that the dates for the sunset behind the baseline are April 12 and September 1, but this latter date is again incorrect and impossible, and apparently based on an attempt to correct Morley's original error without accounting for the subsequent three-day subtraction confirmed by Lindsay's measurement. Spinden (1930:101) notes that the two dates should be April 12 and its reciprocal date, August 30. In his unpublished notes from the Peabody Museum, Gordon calculated that Stela 10 stands at the crest of a hill 4.5 km west of the central acropolis at an elevation 228 m above the Great Plaza, while Stela 12 stands on a hillside 2.5 km east of the central acropolis and 188.6 m above it (Morley 1920:133). Providing a revision of these measurements, Lindsay and Morley give the distance between the two ste- c Stela 12 East FIGURE 2. View of sunset behind Stela 10, as viewed from Stela 12 (from Morley et a!. 1983:564). lae as 6,625.5 m (21 ,734 ft), with Stela 10 at an elevation of 847 m (2,779 ft) and Stela 12 at an elevation of 778.1 m (2,553 ft) above sea level. Finally, they estimate the geographic coordinates of the two monuments, with Stela 10 at 14°51' N, 89°8.1' W; and Stela 12 at 14°50.4' N, 89°4.5' W (Morley 1926). Given the multiple errors as well as the significant differences in results obtained by several researchers, I resolved to gather additional data using methods unavailable to previous investigators. Based on measurements taken on-site using a handheld, digital GPS unit, I obtained the coordinates of Stela 10 as 14°50'31.2" Nand 89°11'3.5" W at an elevation of 827 m, slightly lower than either Morley's or Gordon's estimate. Stela 12 appeared at 14°49'58.56" N and 89°7'26.7" W at an elevation of 758 m, showing the same 20-m difference from Morley's calculation, which may result from fluctuating atmospheric pressure at the same time of day. However, the measurements I obtained nicely preserve the same relative elevation difference Lindsay calculated between the two stelae. The coordinates I obtained provide an azimuth bearing of 278°51'37" and a distance of 6,551 m using a spherical Earth model, or a bearing of278°48'20" and a true distance of 6,559 m using Thaddeus Vincenty's model for an ellipsoidal Earth. 2 These measurements closely conform to Lindsay's measurement of 278°51' (Morley 1926). Even within a large margin of error of ±5 m for each of the GPS coordinates obtained, the azimuth bearing still generally holds within 278°25' to 279°8', which remains relatively consistent as a solar alignment, given that the apparent width of the solar disk is approximately half a degree, or 30'. As Lindsay notes, Stela 10 would have to shift by 41.2 m (135 ft) north or south in order to change the date of the alignment by one day (Morley 1926). Stela 10 appears at an altitude of .6°, or 36' above the true horizon from the point of observation at Stela 12. However, from this perspective Stela 10 is not exactly against the sky, as there is a 940-m hill 1.6 km behind it just to the southwest of Cerro Gavil<in, bringing the skyline to an altitude of about 1o above the true horizon, or about half a degree above Stela 10. Because of this discrepancy, Claude Baudez (1987) criticized the proposals that Stela 10 would have been used as a sight line for solar observations. In response, Anthony Aveni and colleagues (1993:88) note that Stela 10 indeed "lies V2°, or one sun disk, below the skyline," but they contend that such a placement does not disqualify it as an effective solar measuring device. Furthermore, they contend that Baudez's assumptions to the contrary demonstrate a decidedly "ethnocentric posture." An azimuth of 278°48'20" to 278°51'37" confirms Lindsay's measurement of 278°51', thereby repeating the dates of Lindsay's observations. Combined with the altitude of 1°, the current dates for the observation of the Sun behind Stela 10 from the perspective of Stela 12 correspond with Aprilll-12 and August 29-30, depending on the time relative to the insertion of the intercalary leap year. Due to slight changes in the Earth's elliptical orbit and the resulting changes in the Earth's differential velocity, these dates would have been slightly shifted on April 12 and August 30-31 in AD 652, at the proposed time of the dedication of the baseline monuments, using either of the two widely accepted GMT correlation constants. 3 As a result of Willson's and Lindsay's calculations, Morley concluded that the two stelae were used to time the yearly burning of the milpas to prepare them for planting in early April. Prior to the general acceptance of the GMT correlation of the Long Count with the Gregorian calendar, Morley predicted that the dates inscribed on Stela 10 and Stela 12 would enable an exact correlation with the above dates on which the Sun sets behind the baseline (Morley 1920:134). Following Morley, Aveni (1977:9-14, 1980:240244, 2001:251-255) proposed that the solar alignment of the Copan baseline represents a system with which the Maya were observing a division of the tropical year into 20-day segments, given that the Sun sets on the baseline approximately 20 days after the vernal equinox and 20 days prior to the first solar zenith at Copan. Likewise, Aveni suggested that this repeats for the second solar zenith, approximately 20 days prior to when the sunset again would appear on the baseline, some 20 days prior to the autumnal equinox. However, the confirmed baseline date of April 12 is actually 22-23 days after the vernal VOLUME XXV 2012-2013 57 equinox and 18-19 days prior to the first zenith, while August 30 (though Aveni gives September 1 in error) is 19-20 days after the second zenith and 2122 days prior to the autumnal equinox. Moreover, Aveni's proposal did not directly take into account the inscribed dates of Stela 10 and Stela 12 and their associated texts. Despite the general acceptance of the two GMT correlations, neither of the dates on either Stela 10 or Stela 12 reveals any correspondence with either April 12 or August 30. This led Gerardo Aldana (2002) to propose that the eroded Initial Series Long Count date on Stela 12 had been misread and that both of the GMT correlations may be incorrect. However, Aldana based this, in part, on an interpretation of Morley's drawing of Stela 12 that did not include the top portion of the monument, which missing at the time Morley recorded the inscriptions. The missing fragment has since been identified and reattached to Stela 12 (Schele 1992:1), revealing the Wind Deity as the Haab patron for the month of Mak (Figure 3). Therefore, it appears that Morley's original reading of the date on Stela 12 is correct as 9.10.15.0.0, 6 Ajaw 13 Mak. This reading is further supported by the presence of the expected lunar data in the Supplementary Series, as Linda -- ,)) Stela 12 Haab Patron of Mak, Wind Deity (drawing by author after B. Fash, in Schele 1992). FIGURE 3. 58 ARCHAEOASTRONOMY Schele (1992:1-2) has demonstrated. As we shall see, there is also a reference in the text on Stela 12 to the 9.10.15.0.0 Hotun completion of its Initial Series date, five Tuns prior to the K'atun ending on 9.11.0.0.0. The Three Hearthstones and the Orion Nebula An analysis of the full text on Stela 12 reveals critical information that leads to an alternative interpretation of the function of the Copan baseline, combining hieroglyphic text, historical dates, astronomical references, and the architectural alignment found within the baseline itself. On the north side of Stela 12 (Figure 4), we find the inscription concluding with a series of events that begins with the accession date of K'ahk' Uti' Witz' K'awiil, then a reference to the Initial Series date of Stela 12 as the completion of the fifteenth Tun-the Hotun, five Tuns prior to the K'atun ending. The ubiquitous mentioning of the K'atun commemoration on 9.11.0.0.0, 12 Ajaw 8 Keej, follows: 12 Ajaw 8 Keej, It was completed, the 11th K'atun. Was witnessed his supervising (of it), [at the] edge of the sky, First/New Three Hearthstone Place The text continues with the subject on the east side, where it contains the glyph for 'cave/wellspring,' CH'EN-ni, which seems to be a metaphor for the heart of a city, and the title 3-WINIKHAAB ch'a-ho-ma, 'Three K'atun Incense Offerer,' followed by the name of Ruler 12. An almost exact parallel text concerning Ruler 12's observance of the same K'atun completion appears on Copan Stela 2 with the same reading order, though it curiously omits the reference to the Three Hearthstones that we find on Stela 12. A known Maya asterism, the Three Hearthstones were first identified by Barbara Ted lock (1982:181-182) and Dennis Tedlock (1996:73) in ethnographic accounts from the K'iche' community of Momostenango in the highlands of Guatemala. Recognized by contemporary K'iche' astronomers as the oxib xc'ub, the Three Hearthstones form a triangular 1 WINIKHAAB 1 K'atun FIGURE 4. chu-[mu-wa]-ni-ya since he was seated ti AJAW-wa? as Ajaw 6 CHAN 6 Chikchan 16 K'AN-a-[si]-ya 16 K'ayab i-IL-ya and was witnessed ?? ?? ti WI' at the lacking of 5-TUN-ni 5 Tuns ?? ?? K'ALTUN-ni Tun completion 12 AJAW 12 Ajaw 8 KEEJ 8 Keej TZUTZ-ja was completed 11 WINIKHAAB 11 K'atuns i-IL-ya and he witnessed it u-KAB-ji-ya he supervised it TI'-CHAN-na [at the] edge of sky YAX-YOKEHT?-NAL First/New ThreeHearthstone Place Stela 12, north side (drawing by author from original monument on-site, and after Stuart, in Schele 1989:85). asterism composed of three stars in Orion-Alnitak, Saiph, and Rigel-representing the triangular configuration of the large stones that compose a common Maya hearth. Furthermore, the K'iche' identify the diffuse region of the Orion Nebula in the center of this asterism as the smoke from this fire (Figure 5a). Barbara Tedlock (1982:182) notes that even though it has a current apparent magnitude of 4, the relatively bright Orion Nebula curiously was not mentioned in any European texts earlier than 1610, and some astronomers suggest that this may be the result of a variable magnitude over time (Herczeg 1998). The VOLUME XXV 2012-2013 59 The K'iche' Three Hearthstones asterism, composed of Alnitak, Saiph, and Rigel, with the Orion Nebula as the central smoke from the hearth fire. Na'ir al Saif appears beneath the Orion Nebula as the "bright star of the word." Note the distinction between the asterism of the sword of Orion, which resembles three vertically aligned stars, and the more horizontally oriented three belt stars above it. Among the three belt stars, only Alnitak is considered by the K'iche' to be one of the Three Hearthstones (image made using Starry Night Pro 6.4.3 © Simulation Curriculum Corp.). FIGURE SA. Orion Nebula (M42) occupies the central position in what at first appears to be another three-star asterism known as Orion's Sword-actually a collection of nebulas and open clusters of stars, the brightest of which is the southernmost Na'ir al Saif, meaning "the bright star of the sword" in Arabic. In all likelihood, the nebulosity of Orion's Sword and its central location within the Three Hearthstone asterism led Maya observers to see this entire collection as puffs of smoke "rising" from a celestial hearth fire. Linda Schele and Matthew Looper subsequently identified repeated textual references to the Three Hearthstones in Late Classic mythological accounts from Palenque and Quirigua (Figure 5b) associated with the mythological events that were said to have taken place at the very beginning of the current era, at the time of the completion of a previous 13 Bak'tun cycle in the Long Count on 4 Ajaw 8 Kurnk'u (Freidel et al. 1993:79-82). As in Stela 12, 60 ARCHA EOASTRO N OMY these text references depict the Three Hearthstones in a triangular configuration following the glyph YAX, which carries the meanings of 'first,' 'new,' and 'green,' also the color representing 'center.' John Justeson suggests that the hearthstone glyph itself may be YOKEHT (Schele and Looper 1996:29), and this finds further support in the common occurrence of syllabic yo- signs flanking the three stones, also found flanking Sun and Moon signs in eclipse glyphs. Looper first identified this same triadic formation of three stones depicted on the back of a celestial turtle on page 71a of the Madrid Codex, while an image of a turtle with three linear star glyphs resembling Orion's Belt appears in the Bonampak murals (Freidel et al. 1993:79-82). Ethnographic accounts from various Maya sources indicate that the stars in both Orion and Gemini have been identified as a turtle, while Orion's Belt was identified as the Az- tee fire-drill mamalhuaztli (Milbrath 1999:266-68; Thompson 1972:68). John Carlson initially pointed out to Schele that this fire-drill constellation was used to ignite the "New Fire," symbolic of a new cycle of time (Freidel et al. 1993:81). In the Aztec Historia de los mexicanos por sus pinturas, we find that this first fire was lit using three flint stones in the form of three sticks "with a heart" (Garibay 1965:32-33), while in the Postclassic Yucatec Maya Chilam Balam of Chumayel, Looper (1995:24) notes a reference to the "three cornered precious stone of creation" that closely parallels the creation accounts from hieroglyphic texts. While tentative, the hypothesis that the triadic Three Hearthstones in Classic period Maya texts is the same as the K'iche' asterism of the Three Hearthstones in Orion is supported by various threads of evidence. As Schele suggests, the Maya may have Palenque Temple of the Cross: [a 4AJAW 4Ajaw 8 BIX-OHL-la 8 Kumk'u CliW 13-PIK 13 Bak'tuns JEL-ji-ya since it was changed .. TZUTZ-yi completed k'o-ba TI'-CHAN-na the altar,* edge of the sky YAX-YOKEHT?-NAL First I New ThreeHearthstone Place * See Callaway (2011 :283-286). Quirigua Stela C: 4AJAW 4Ajaw 8 BIX-OHL-la 8 Kumk'u JEL-la-ja k'o-ba the altar* was changed u-ti-ya TI'-CHAN-na it happened [at the] edge of the sky YAX-YOKEHT?-NAL First I New Three-Hearthstone Place TZUTZ-ya 13-PIK completed 13 Bak'tuns Era base events involving the Three Hearthstones (drawings by author after Linda Schele, in Schele and Freidel 1990:Figure 6:14). FIGURE SB. VOLUME XXV 2012-2013 61 H I 1 2 3 4 5 6 7 FIGURE 6. Copan Stela 23. Initial Series 9.10.18.12.8, 8 Lamat 2 Yaxk'in (should be 1 Yaxk'in) (drawing from Morley 1920:148). E9: 8LAMAT 010: 2 YAXK'IN EIO: u-??-K'IN-ni Dll: 11 K'IN 5 WINIK-ki Ell: 1 TUN (distance number of 471 days) Ell: 12AJAW Fl: 8 KEEJ G7: 4AJAW F8: 8 BIX-OHL G8: TZUTZ-ya F9: 13?-[PIK?]. HI: YAX-YOKEHT?-NAL II: JEL-ja? k'o-ba. H4: 8LAMAT 14: 2 YAXK'IN compared the cosmos to a house on a grand scale, and these hearthstones would therefore conceivably represent the central hearth of a traditional Maya home (Freidel et al. 1993:79). Given the comparable Central Mexican mythological concept of five successive world ages, each governed by a new Sun, it is also possible that these Maya mythological accounts 62 ARCHAEOASTRONOMY of the Three Hearthstones involve the rebirth of the Sun in a cosmic hearth fire at the beginning of the current era. We may derive additional support for this idea, given that these texts frequently describe the historical era as following another prior age of 13 Bak'tuns, or 5,200 Tuns of 360 days each, though there is no definitive evidence to determine whether the Maya uniformly conceived of five such repeating cycles of 13 Bak'tuns. From Stela 23 in Copan (Figure 6), also part of Ruler 12's sculpture program, we find another reference to the Three Hearthstones in association with the era base 4 Ajaw 8 Kumk'u. Stela 23 has since been destroyed, though Morley fortunately was able to draw the text that was visible to him before it was used as cement fill (Aldana 2002:37; Morley 1920:134). The two references to the Three Hearthstones in Copan are in fact the very first monumental references to this mythological asterism known in the corpus of Maya inscriptions. Only one earlier reference to the Three Hearthstones is found on an undated Early Classic greenstone mask (Figure 7), most likely from Rfo Azul, where they are again mentioned in association with the era base 4 Ajaw (Van Stone 2010:52-53). In all of these examples, as well as in the later mythological texts in Palenque and Quirigua, the Three Hearthstones are always said to be TI'-CHAN '[at the] edge of the sky.' Furthermore, despite the prior usage of the Long Count, which uses the shared starting point of 4 Ajaw 8 Kumk'u on the era base, Stela 23 is the first known text to mention that the era base concluded a period of 13 Bak'tuns. This specific period ending is FIGURE 7. then repeated in most subsequent references to the events that took place on the era base. Barring evidence to the contrary, it is quite possible that the popularized concept of an earlier era of 13 Bak'tuns in length was specifically conceived in Copan, as no earlier evidence exists to suggest otherwise (Grofe 2011a:217, 2011b:61). The Copan Baseline and the Rising Orion Nebula The reference to the Three Hearthstones on Copan Stela 12, and the Copan baseline itself, serve as an important test of the hypothesis that this asterism is indeed related to the contemporary K'iche' Three Hearthstones in Orion. What is so unusual about the example of the Three Hearthstones on Copan Stela 12 is that it is not directly associated with the mythological era base accounts. Instead, it is the only such reference to the Three Hearthstones found in association with a known historical date. In fact, the text states that on the date of the commemoration of the K'atun ending 9.11.0.0.0, K'ahk' Uti' Witz' K'awiil witnessed the first/new Three Hearthstones at the edge of the sky, and this prompted me to investigate whether the Copan baseline may actually relate to the asterism of the Three Hearthstones 4 AJAW ??-ya Tl' CHAN-na, YAX-YOKEHT?-NAL Undated Early Classic jade mask, era base event (drawing by author after Michael Carrasco, in Van Stone 2010:53). VOLUME XXV 2012-2013 63 FIGU RE 8. View across the Copan Valley from Stela 10 looking ea t toward Stela 12 (tip of arrow). in Orion literally ri ing or etting on the horizon, as Stela 12 seems to uggest. If we predict that the Copan ba eline was u ed to observe either the ri ing or setting of the fairly large Three Hearthstone asterism, it would logically follow that it specifically targeted orne part of the Orion Nebula in the center of this asterism. Evidence from the Postclassic K'iche' site of Utatlan suggests that multiple temples at this site are aligned with the setting azimuths of stars in Orion (Freidel et al. 1993:103). However, even accounting for preces ion , no part of the K'iche' asterism of the Three Hearthstones or even the belt tars in Orion could ever have set on the 278° western azimuth of the Copan baseline. Conversely, might the baseline commemorate the rising of the Hearthstones? This would require that observations were made from the position of Stela 10 looking east toward Stela 12, even though Stela 12 does not appear directly on the horizon. From Stela 10, Stela 12 appears on a hillside, at an angle of 38' below the true horizon and less than 2° beneath the crest of Cerro La Pintada, an approximately 1,020-m hill named for Stela 12 and the paint still visible on its surface. Behind this hill, the visible skyline can be een on the slope of the much higher and more distant Cerro Montenegro, a mountain in the Sierra Gallinero range (Figure 8). This is the farthest point vi ible along the azimuth of the • 64 ARCHAEOASTRONOMY ba eline, and it is approximately 1,600 m in elevation and 23.7 km from Stela 10, thereby appearing 1°46' above the true horizon. As we have seen , from the perspective of Stela 12, Stela 10 is also not directly on the skyline, as it has another larger hill behind it, with the skyline appearing about half a degree above Stela 10. But since Stela 10 stands on a ridgeline, slightly higher than Stela 12 and pointing to a position some 34' above the true western horizon , this led Morley (1920:143) to believe that it specifically referred to a sunset azimuth when viewed from Stela 12, and all subsequent researchers have accepted this assumption. However, since hills appear behind both Stela 10 and Stela 12, is it not equally plausible that the baseline was intentionally oriented toward the eastern hori zon behind Stela 12, especially if the baseline was used to identify a stellar alignment with the aid of a signal fire at night? Indeed, since he could not clearly see Stela 10 from Stela 12 owing to the abundance of smoke from burning milpas in early April , Morley (1926) lit a large bonfire directly behind Stela 10 to create a visible marker for hi sunset observation. Baudez (1987) contends that the need to light such a fire in order to see what might otherwise be an invisible point of observation at this time of year renders less likely the proposal that these monuments were even used as an .astronomical baseline. However, the logical solution of using a signal fire may have proved to be even more effective for evening observations. Believing that Stela 10 and Stela 12 referred to positions of the planet Venus, Linda Schele (1991:4) suggested that these monuments may have been illuminated at night by fire, much like those kept by contemporary K'iche' on sacred mountains during the rituals of Waxaqib Batz'. If it was illuminated at night, Stela 12 could have been utilized as a sidereal marker for the point on the horizon directly above it. In fact, to function for either horizon-based stellar, planetary, or even solar observations, a fireilluminated stela placed beneath the horizon might prove to be more useful, since a fire on the horizon can either obscure a star or itself be obscured by the light of the Sun. Since the visible skyline is much farther away in the Sierra Gallinero, well beyond the Copan Valley, positioning Stela 12 farther beneath the skyline on a nearby hillside also enables ease of access, while providing a functional alignment. Again, using the same GPS coordinates I obtained for Stela 10 and Stela 12 together with the Vincenty formula, we find that the Copan baseline points eastward to an azimuth of 98°47'25" on the skyline directly above Stela 12. Using either of the GMT correlations, the K'atun ending on 9.11.0.0.0 occurred in AD 652. Due to the variable dynamics of lunisolar and planetary precession, the azimuth and the time of year of the rise of a given star will change slowly over time, since the axis of the north celestial pole slowly wobbles. This significantly alters the celestial coordinates of any given star over time, so that the change in declination (8), equivalent to celestial latitude, will directly impact the azimuth position of a star rise; while the right ascension (a), equivalent to celestial longitude, largely changes the time of year and the time of the night that the star rises. As a preliminary test, I observed the azimuth of 98°47 ' and an altitude of 1°50' above the horizon, simulating the vantage point of Stela 10 using Starry Night 6.2.3 astronomical software (Simulation Curriculum Corp. 2009), and I found that in AD 652, the Copan baseline pointed very closely to the azimuth of the rising position of Na'ir al Saif, the brightest star in the nebulous region of Orion's Sword in the center of the Three Hearthstones (Figure 9). While closer stars can show significant variation over time, due to their unique movements relative to other stars, in AD 652 the distant Na'ir al Saif would have risen close to an azimuth of 98°32', at an altitude of 1°50' above Stela 12 when viewed from Stela 10, only 15' FIGURE 9. Reconstruction of Na'ir al Saif rising at an azimuth of 98°32' directly above Stela 12 as viewed from Stela 10 in AD 652. Stela 12 is indicated with an asterisk to simulate illumination of the stela by fire at an azimuth of 98°47' (image made usi ng composite horizon photograph with Starry Night Pro 6.4.3 © Simulation Curriculum Corp.). VOLUME XXV 2012-2013 65 from the baseline azimuth, equivalent to half of the width of the solar disk. The declination of Na'ir al Saif at this time is given as -7°45'46.44". To confirm this, we can calculate the declination of Na'ir al Saif for a precise day in history using specific formulae that incorporate precessional quantities measured from the point of January 1, AD 2000 (12000). The declination of Na'ir al Saif for 12000 is given as -5°54'36" (Kelley et al. 2011:57, Table 3.1), while the declination of Na'ir al Saif for October 14, AD 652, would have been -7°46'3.5", essentially identical to that obtained by Starry Night 6.4.3 previously, which thus provides the same azimuth position of 98°32'. 4 Therefore, the astronomical alignment of the Copan baseline, the text on Stela 12 regarding the observation of the Three Hearthstones, and the year of the GMT correlations strongly support ,the hypothesis that this asterism is related to the contemporary K'iche' Three Hearthstones and that Stela 12 served as a celestial marker for the rising point of Na'ir al Saif as the center point of this hearth. While both of the GMT correlations generally support the evidence that the Copan baseline was used to commemorate the rising of Na'ir al Saif in the center of the Three Hearthstones, we find that this star rose precisely at the eastern end of the baseline around AD 530, over a century prior to the events surrounding the commemoration of K'atun 9.11.0.0.0 in AD 652. Curiously, we find that Na'ir al Saif continues to rise close to this same azimuth of 98°48 ' for several hundred years during the Classic period, because of the properties of precessional dynamics for stars with celestial longitudes close to those of the solstices. The azimuth rising positions of stars close to six hours of right ascension shift much more slowly over time than those closer to the zero point of right ascension where we find the vernal equinox. As a result, the azimuth of the rising point of Na'ir al Saif shifted less than a quarter of a degree per century before and after AD 652. Therefore, the use of the Copan baseline as a celestial marker for the rising point of Na'ir al Saif, as well as the adjacent Orion Nebula, would remain quite stable and would have functioned properly for the remaining duration of Copan's history until the early ninth century, when its rising azimuth shifted north 66 ARCHAEOASTRONOMY by only half a degree, the observable width of the solar disk. The Sunrise on 9.11.0.0.0 and the Copim Baseline Beyond the apparent baseline alignment to the Three Hearthstones itself, there appears to be another important rationale for why this asterism is mentioned in association with the K'atun ending 9.11.0.0.0 on Stela 12, and this evidence also supports the use of one of the GMT calendar correlations. Employing a Gregorian proleptic calendar akin to our own tropical-year positions, we find that the 584285 GMT correlation constant places 9.11.0.0.0 on October 14, AD 652 (October 11, Julian). On this date, we find that the first light of the Sun rose just 16' south of the baseline, equivalent to half the width of the solar disk at an azimuth of 99°3' and an altitude of 1°50 ', essentially matching the rising position of Na'ir al Saif in the Three Hearthstones (Figure 10). Therefore, it is possible that the Copan baseline commemorated the position of the rising Sun on the date of the completion of the eleventh K'atun. In this way, it appears that K'ahk' Uti' Witz' K'awiil was linking himself and the sunrise on K'atun 9.11.0.0.0 to the center of the Three Hearthstones as the mythological hearth fire, perhaps from which the Sun itself was thought to have emerged at the beginning of the current era on 4 Ajaw 8 K'umk'u. If the Copan baseline was designed to associate both the rising point of Na'ir al Saif in the Three Hearthstones and the sunrise on 9.11.0.0.0, which appears to be the case, this is a very strong argument for the use of the 584285 GMT correlation in this specific time and place. In the decades surrounding AD 652, it is significant that the azimuth of the sunrise on the baseline varied between October 13 and 14, where it continues to appear at present. However, the Sun never rose behind the baseline on October 12, which would be the date of 9.11.0.0.0 using the alternative 584283 GMT correlation constant. Likewise, the more recently proposed 584286 correlation (Martin and Skidmore 2012) places this date on October 15, one day after the baseline azimuth. While not definitive proof, the evidence supports the validity of the use of the 584285 GMT correlation, at least in Copan during this time in the FIGURE 10. Reconstruction of sunrise at an azimuth of 99°3' directly above Stela 12 as viewed from Stela 10 on 9.11.0.0.0, 12 Ajaw 8 Keh, October 14, AD 652 (October 11, Julian), using the 584285 GMT correlation constant. Stela 12 is indicated with an asterisk to imulate illumination of the tela by fire at an azimuth of 98°47' (image made using composite horizon photograph with Starry ight Pro 6.4.3 © Simulation Curriculum Corp.). Cla ic period. For the ake of argument, and to facilitate a clearer presentation, I will hereafter use only the 584285 GMT correlation within this discussion, although this doe not discount the possibility of the accuracy of the 584283 GMT or the 584286 correlation both in Copan and elsewhere, since we cannot assume that the Long Count remained unchanged in all times and places. In fact, as Aldana (2002:39) notes, it appears that Ruler 12 himself recorded several nonstandard Calendar Round dates that shift the Haab position forward by one day on Stela 2, Stela 3, and Stela 23. Contrary examples of Haab dates shifted backward by one day have been used to support the idea that these may have been evening observations if the Tzolk'in changes at sunset before the Haab at sunrise (Martin and Skidmore 2012; Mathews 2001 [1979]; Stuart 2004), but these Copan dates do not conform to this pattern. Sidereal Measurements Using Na 'ir a/ Saif and the Orion Nebula Na'ir al Saif rises at the eastern end of the Copan baseline, but might such an observation have been made of its heliacal rise when it becomes first visible at dawn? During the Classic period, the hel iacal rise of Na'ir al Saif would have occurred in mid-June. Using either of the two GMT correlations, we curiously do not find any significant position for a'ir al Saif for either the Initial Series date on Stela 12 of 9.10.15.0.0, 6 Ajaw13 Mak, on November 10, AD 648 (November 7, Julian), or for the K'atun ending 9.11.0.0.0, 12 Ajaw 8 Keej, on October 14, AD 652 (October 11, Julian). If either one of the GMT correlations is correct, these period ending dates do not appear to have been used for the observation of the first visibility of Na'ir al Saif. On the other hand, if we take the inscription on Stela 12 to literally refer to the first visibility of Na'ir al Saif on 9.11.0.0.0, then both of the GMT correlations would be incorrect, and the possibility remains open to explore an alternative correlation that reconciles this interpretation. Yet, as we have found, 9.11.0.0.0 does corre pond to the sunrise on the eastern end of the Copan baseline using the 584285 GMT correlation, while this same azimuth identifies the rising point of Na'ir al Saif, and this suggests that K'ahk' Uti' Witz' K'awiil intentionally compared the sunrise on the 9.11.0.0.0 K'atun ending with the rising point of the center of VOLUME XXV 2012-2013 67 Reconstruction of the first visibility of Na'ir al Saif and the Orion Nebula rising directly above Stela 12 as viewed from Stela 10 on 9.10.18.12.8, June 30, AD 651 (June 27, Julian), using the 584285 GMT correlation constant. Stela 12 is indicated with an asterisk to simulate illumination of the stela by fire at an azimuth of 98°47' (image made using composite horizon photograph with Starry Night Pro 6.4.3 © Simulation Curriculum Corp.). FIGURE 11. the Three Hearthstones. Given the predominant evidence for the GMT correlations, I take this as the more likely explanation. While the 9.11.0.0.0 K'atun ending does not appear to correspond to the first visibility of Na'ir al Saif using either of the GMT correlations, Stela 10 and Stela 23 present themselves as possible candidates. As the point of observation of the baseline looking east, Stela 10 gives the unusual Initial Series date of 9.10.19.13.00, 3 Ajaw 8 Yaxk'in, July 6, AD 652 (July 3, Julian). Non-period-ending dates such as this suggest that this specific date was chosen for another purpose. With an apparent magnitude of 2.76, Na'ir al Saif would have been first visible on the horizon about two weeks earlier. However, this later date may correspond to the time of the first visibility of the Orion Nebula immediately adjacent to Na'ir al Saif, behind Stela 12 prior to dawn when the Sun was 20° below the horizon toward the end of astronomical twilight (see Figure 9). At this time, depending on clarity, the sky would still be at its darkest, allowing for horizon observations of fainter stars. By first observing the heliacal rise of Na'ir al Saif, observers may have been able to track and predict the first appearance of the Orion Nebula on the horizon at dawn as the visible "smoke" from the Three Hearthstones. , 68 ARCHAEOASTRONOMY The actual date of the expected heliacal rise of the Orion Nebula would more likely have occurred a week or so earlier, when the Sun was within 12o16° below the horizon during nautical twilight, when magnitude 4 objects such as the Orion Nebula are still visible. However, the age of the Moon on Stela 10 is given as 21 days since new, so it is possible that the brightness of the Moon interfered with the observation of first visibility, as it was still visible at sunrise. Aveni (2001:255) notes that a visible lunar eclipse occurred several days prior to the Initial Series date on Stela 10, on June 29, AD 652 (June 26, Julian), while Stela 10 then records the first Ajaw day following this event, which may have also provided another important significance for this date, since Ajaw is used as the standardized whole multiple of the vigesimal-based system. This eclipse was perhaps all the more notable given that the lunar nodes were positioned at the point of the two solstices at the time-a phenomenon that recurs approximately every nine years. We will return to further investigate additional references within the text from Stela 10. On Stela 23, which is the second monumental text to prominently feature the Three Hearthstones, we also find an unusual Initial Series date 9.10.18.12.8, on June 30, AD 651 (June 27, Julian), that corresponds to the same time of year as the date on Stela 10, only six days earlier in the tropical year, which may have coincided with the date of the first visibility of the Orion Nebula when the Sun was 15° below the horizon at nautical twilight (Figure 11). Therefore, it is possible that the two non-periodending dates on Stela 23 and Stela 10 were used to record the first visibility of the Orion Nebula in association with Na'ir al Saif behind Stela 12 on the Copan baseline. Using the Tzolk'in and the K'atun to Calculate the Metonic Cycle Helen Alexander (1988:47) noted the appearance of pairs of dates separated by 260 days among the monuments in Copan. She found that one of the Initial Series dates on Ruler 12's Stela 3 occurred on 9.10.19.5.0, exactly 260 days prior to the period ending on 9.11.0.0.0. Alexander compared this to another pair of dates mentioned on Copan Stela A, a monument commissioned by the later Ruler 13, Waxaklajuun Ubaah K'awiil. Similarly, one date on Stela A, 9.14.19.5.0, falls exactly 260 days prior to the period ending on 9.15.0.0.0, also mentioned in this text. Alexander suggested that these intervals relate to positions of Venus at superior conjunction, while she also found that both of the texts on Stela 3 and Stela A posthumously refer to Ruler 11, whose full name is given as K'ahk' Uti' Chan Yopaat, though he was previously nicknamed "Butz' Chan" (Grube and Martin 2000:200). Yet there are additional paired dates separated by 260 days in Copan, and they do not all seem to relate to Venus. After confirming the Initial Series date on Copan Stela 12 as 9.10.15.0.0, Schele (1992) subsequently noted that Stela 2, another of Ruler 12's monuments, gives a date 260 days later as 9.10.15.13.0. Moreover, both Stela 12 and Stela 2 contain a great deal of parallel text, but they do not conform to Alexander's Venus positions, and they contain no obvious references to Butz' Chan. John Teeple (1930:71) noticed that Stela A in Copan contains the date 9.14.19.5.0, which is not only 260 days prior to the K'atun ending 9.15.0.0.0; it is also exactly 6,940 days after the previous K'atun ending on 9.14.0.0.0. This is a Metonic cycle, which can be used to commensurate an interval of 19 tropical years with 235 lunations. Significantly, Stela A appears in the Great Plaza very close to Stela C, another of Waxaklajuun Ubaah K'awiil's monuments, with the date 9.14.0.0.0 for comparison. In effect, the position of the tropical year and the phase of the Moon-significantly, the full Moon-are equivalent on 9.14.0.0.0 and 9.14.19.5.0, and Teeple suggests that this Metonic cycle was surely noticed and intentionally recorded. Metonic cycles were evidently calculated on both K'atun and Hotun endings. As Schele found on Stela 2, we find the date 9.10.15.13.0, July 27, AD 648 (July 24, Julian). This is 260 days after the Hotun date on Stela 12, 9.10.15.0.0, and it would also be one Metonic cycle prior to the Hotun on 9.11.15.0.0, exactly one K'atun after the date on Stela 12. Indeed, K'ahk' Uti' Witz' K'awiil commemorated this later date on the south side of Stela 5. Combined with the 260-day Tzolk'in, the K'atun could be used to calculate the tropical-year position and the phase of the Moon and to predict exactly where the Sun will rise on future K'atuns. We can now examine how K'ahk' Uti' Witz' K'awiil may have utilized the Metonic cycle to calculate positions in the tropical year and lunar phases over multiple K'atuns, and how he may have utilized the Copan baseline as a means of predicting and celebrating the K'atun ending 9.11.0.0.0, when the Sun rose at the same azimuth as Na'ir al Saif in the Three Hearthstones. Ruler 12's monuments evidently contain multiple such Metonic K'atun predictions within a host of other specific calculations of the tropical year. Table 1 provides an inventory of these monuments and their associated dates. Metonic Cycles and the Death of Butz' Chan: The Symbolic Tropical Year Alexander (1988) noted that the east side of Ruler 12's Stela 3 records the date 9.10.19.5.0, January 28, AD 652 (January 25, Julian), exactly 260 days prior to the K'atun ending on 9.11.0.0.0. Associated with this date on Stela 3, we find the name of Ruler 12's predecessor, Butz' Chan. This date is also one Metonic cycle after the previous K'atun ending on 9.10.0.0.0, January 27, AD 633 (January 24, Julian), VOLUME XXV 2012-2013 69 Table 1. The Monuments of Copan Ruler 12 (GMT 584285) StelaE 9.5.0.0.0, 11 Ajaw 18 Sek July 5, 534 (July 3, J) Commemoration of K'atun Sun in identical sidereal position as Stela 10: 9.10.19.13.0, July 6, 652 (July 3, J) StelaE 9.5.18.10.0, 9 Ajaw 8 Sak Oct. 18, 552 (Oct. 16, J) Blackened Ajaw, four days before lunar eclipse 260 days before July 5, date of 9.5.0.0.0 Sun in identical position as it was on 9.4.0.0.0 Stela 5 9.9.14.17.5, 6 Chikchan 18 K'ayab Feb.8,628(Feb.5,J) Accession of Ruler 12 (also mentioned on Stela 2 and Stela 12), solar nadir Stela 12 9.10.15.0.0, 6 Ajaw 13 Mak Nov. 10, 647 (Nov. 7, J) Commemoration of the Hotun Stela 2 9.10.15.13.0, 6 Ajaw 8(9) Mol .., July 27-28, 648 (July 24-25, J) Metonic: 260 days after 9.10.15.0.0 Sun in identical position as on Stela 5: 9.11.15.0.0 Stela 23 9.10.18.12.8, 8 Lamat 1(2) Yaxk'in June 30/July 1, 651 (June 27-28, J) 260 days after Oct. 14, date of 9.11.0.0.0 K'atun Sun in identical position as it will be on 9.12.0.0.0 First visibility of Orion Nebula Stela 3e 9.10.19.5.0, 12 Ajaw 13(14) K'ayab Jan.28-29,652(Jan.25-26,J) Metonic: 260 days before 9.11.0.0.0, Stela 13 Sun in identical position as it was on K'atun 9.10.0.0.0 This date also mentioned in Stela 10, with a blackened AJAW Stela 3w 9.10.19.5.10, 9 Ok 3(4) Kumk'u Feb.7-8,652(Feb.4-5,J) Sun in identical position as it was on accession (Stela 5), solar nadir Stela 10 9.10.19.13.0, 3 Ajaw 8 Yaxk'in July 6, 652 (July 3, J) Lunar eclipse 6 days earlier, nodes exactly at the solstices Exactly the same solar sidereal as Stela E: 9.5.0.0.0 11, July 5, 534 (July 3, J) Blackened Ajaw 160 days earlier on 9.10.19.5.0 (Stela 3e) Stela 19 9.10.19.15.0, 4 Ajaw 8 Ch'en Aug. 15, 652 (Aug. 12, J) Solar zenith on Aug. 13 related to 4 Ajaw 8 Kumk'u era base date? Stela 13 9.11.0.0.0, 12 Ajaw 8 Keej Oct. 14, 652 (Oct. 11, J) Sun rises on Copan baseline, same position as Orion Nebula Commemoration of K'atun, mentioned on Stelae 2, 3, 10, and 12 Stela 5 9.11.15.0.0, 4 Ajaw 13 Mol Commemoration of the Hotun Sun in identical position as on Stela 2: 9.10.15.13.0 July 28, 667 (July 25, J) 90K 90k SIH-ya-ja Was born 4BIXOHL 4 Kumk'u YAXCHIT First Companion/Father la?-ma-ja is submerged? [Title of Ruler 12] CH'ICH'-BAAK Blood and bones K'AHK-TI'-WITZ'-K'AWIIL [Ruler 12] Copan Stela 3 west (photograph by author). FIGURE 12A. which would have been the first K'atun ending during Ruler 12's reign. Significantly, on the west side of Stela 3, we find a date 10 days after the date on the east side, on 9.10.19.5.10, February 9, AD 652 (February 6, Julian). The text curiously refers to a (re)birth event involving blood and bones and what appears to be the conjured spirit of Butz' Chan, identified by the recognizable title YAX-CHIT (Figure 12a), here with the rabbit-head form of CHIT (T759) that substitutes for the more common form (T580). Following the initial reading of T580 as CHIT (Stuart et al. 1999:56), Barbara MacLeod translates this term as a cognate of the Yucatec ke:t as 'one of a pair' and 'companion,' while Sven Gronemeyer reads it as 'patron god,' following a suggestion by Pierre Colas (Gronemeyer and MacLeod 2010:13). The term chit also appears in many male parentage statements. However, MacLeod identifies the use of this term in a rare female parentage statement, suggesting that it refers to 'her co-creation' (Gronemeyer and MacLeod 2010:53). As 'first companion/pair,' yax chit is an interesting title that often appears in the name of so-called vision serpents involved in conjuring the spirits of departed ancestors. In the context of Maya conjuring in Copan, it would seem that the kings pair themselves with their departed ancestors as their "first companions." In so doing, they may provide a means for the spirit of their ancestors to be reborn in their bodies, thereby paralleling the archetype of the Maize God, who dies and is reborn with the help of his own children, the Hero Twins (Taube 1985). Aldana (2002:39) noticed that the date 9.10.19.5.10 on Stela 3 is a tropical-year anniversary of the accession of Ruler 12, precisely 24 years (3 synodic cycles of Venus) earlier on 9.9.14.17.5, February 8, AD 628 (February 5, Julian), as stated on the west side of Stela 2, the north side of Stela 12, and the south side of,Stela 5. Here on Stela 3, associated on one monument, it seems that K'ahk' Uti' Witz' K'awiil was intentionally measuring the tropical-year anniversary of his accession, as well as one Metonic cycle following his first K'atun ending on 9.10.0.0.0. Curiously, we find that his accession occurs precisely on the February 8-9 solar nadir, or the anti-zenith at Copan, and such an intentionally chosen date appears to have served as an important anchor in the tropical year. Indeed, the date of the solar nadir at Copan's latitude of 14.8° N was used repeatedly in Copan, as well as at various sites at a number of different latitudes during the Classic and Postclassic periods (Grofe 2011a, 2011b:225-226). I propose that the reference to Butz' Chan on the east side of Stela 3, in association with the date VOLUME XXV 2012-2013 71 K'AHK' Tl' CHAN ma[m]-AJAW-wa 9-i-pi-la-ja BAAK-CH'ICH' Butz Chan' [Ruler 11] Grandfather? Lord many times strengthened bones and blood K'IN-ni su-sa-ja ba-ki u-CHAM-ya-li [of] the Sun. Were cut bones of the dead OCH-bi-ji u-me-k'e-ji-ya the banner stone u la-ka-ma TUN-ni Entered the road [died]. He had embraced u-bah AN-nu K'AHK' TI'?-K'IN CHAN-na YAX CHIT-ta ta-o-CHIT-ta NAH-K'UH He impersonates [sqlar? Ruledl] First Companion/Father at the Companion God House place? 18-b'a K'AWIIL-la K'UH [BAT]-piAJAW-wa ba-ka-ba 18 Ubaah K'awiil [Ruler 13] Holy Copan Lord, Bakab FIGURE 12B. Copan Stela A west (drawing by author after Schele 2000:Number 1003). 9.10.19.5.0, January 26, AD 652 (January 23, Julian), most likely derives from a close proximity to the tropical-year anniversary of the date of his death, which was recorded on Step 8 of the Copan Hieroglyphic Stairway as 9.9.14.16.9, January 21, AD 628 (January 18, Julian). Sixteen days after the death of Butz' Chan, K'ahk' Uti' Witz' K'awiil acceded as Ruler 12. Thus, on Stela 3, Ruler 12 appears to be commemorating the death of his predecessor, along with the anniversaries of both his own accession and his first K'atun in office on 9.10.0.0.0. Similarly, as Alexander found, Waxaklajuun Ubaah K'awiil, the successor to Ruler 12, also directly refers to Butz' Chan on Stela A, twice mentioning his name, including the same title found on Stela 3, YAX-CHIT. Rather than its being a result from the Metonic calculation mentioned on Stela A, I propose that this reference appears because the Initial Series date of Stela A, 9.14.19.8.0, February 3, AD 731 (January 30, Julian), is also close to the tropical-year anniversary of the death of Butz' Chan, • 72 ARCHAEOASTRONOMY much as we find in Stela 3. Furthermore, the text on Stela A (Figure 12b) directly mentions the death of Butz' Chan twice, along with the "strengthening of the blood and bones of the sun" compared with some kind of ritual or symbolic exhumation and cutting or "scraping of the bones of his deceased" (Biro and Reents-Budet 2010; MacLeod, personal communication 2014) that seems to parallel the events mentioned on Stela 3, though here we are told that Waxaklajuun Ubaah K'awiil commemorates this event by impersonating Butz' Chan himself as the Maize God. These repeating commemorations of the death of Butz' Chan make sense, given that they occur very close to the tropical-year anniversary of his death. Thus, these observed anniversaries provide a significant insight into the ritual importance of the tropical year, suggesting the symbolic parallel of the yearly rebirth of the Sun and maize with the death and rebirth of ancestral kings. Stela A also contains the Metonic calculation that Teeple (1930:71) first noted, but this is actually a ref- erence to the commemoration of the nearby Stela H, 60 days earlier on 9.14.19.5.0, December 5, AD 730 (December 1, Julian). Here, Waxaklajuun Ubaah K'awiil is depicted impersonating his grandfather as the Precious Maize God-the very symbol of agricultural rebirth itself. Stela H thus repeats the same position of the Sun and full Moon that occurred one Metonic cycle earlier on the adjacent Stela C, on 9.14.0.0.0, December 5, AD 711 (December 1, Julian). On both of these dates, the Sun was (invisibly) in conjunction with the center of the widest part of the Milky Way between Sagittarius and Scorpio, while, significantly, the full Moon appeared at the opposite position in the Milky Way near Orion. The Copan Baseline and the Metonic Cycle The text of Stela 10, the western monument on the Copan baseline, counts back 160 days to the Metonic interval from the east side of Stela 3, 9.10.19.5.0, January 28, AD 652 (January 25, Julian). This date is exactly 260 days prior to the K'atun ending on 9.11.0.0.0, and it also would have been the tropicalyear position of the previous K'atun on 9.10.0.0.0. Given that the Copan baseline marks the precise position of the sunrise on 9.11.0.0.0 as viewed from Stela 10, it would have been relatively straightforward to predict this position by observing the sunrise azimuth 260 days after K'atun 9.10.0.0.0, here commemorated one Metonic cycle later on both Stela 3 and Stela 10. Similarly, we might expect to find predictions for the following K'atun on 9.12.0.0.0. In fact, on the unusual date from Stela 23 of 9.10.18.12.8, June 30, AD 651 (June 27, Julian), we find that the tropical-year position of this date is equivalent to the same position exactly 260 days after K'atun 9.11.0.0.0. This suggests that, even though it was dedicated over one year prior to the K'atun ending on 9.11.0.0.0, Stela 23 may have predicted the tropical-year position of the following K'atun ending on 9.12.0.0.0, July 1, AD 672 (June 28, Julian). Like the 24-tropical-year anniversary of Ruler 12, this prediction suggests a break from the strict Metonic cycle, and it is likely that this particular date was chosen for other reasons. As we have seen, the date on Stela 23 may have coincided with the first heliacal appear- ance of the Orion Nebula and Na'ir al Saif rising r the eastern end of the Copan baseline. Therefore. Stela 23 may have also predicted that this central star in the Three Hearthstones would become first visible on the precise date of the K'atun ending on 9.12.0.0.0, exactly 21 tropical years later. Solar, Lunar, and Eclipse Intervals The unusual date on Stela 23 may also be the result of recording lunar information. The Metonic cycle is also only 7.6 days longer than 20 eclipse years of 346.62 days. Therefore, one Metonic cycle can predict a repeating eclipse on the same day of the tropical year, precisely 19 tropical years later. However, this eclipse interval breaks down after three successive Metonic cycles, and a more refined measurement is necessary over longer periods of time. A further analysis of the date on Stela 23 demonstrates that it coincides with the day on which the Sun crosses a lunar node. Though an invisible lunar eclipse occurred 11 days after this date on July 11, AD 651 (July 8, Julian), it is possible that the Maya were closely tracking and predicting the eclipse year and the eclipse half-year, as I have proposed elsewhere (Grofe 2007:140-150, 212-219). Further support for the proposal that the Maya were capable of tracking these intervals is evident in the recently excavated astronomical inscriptions from Xultun (Bricker et al. 2014:162). Although K'atun endings rarely coincide with eclipse events, the intervals between specific eclipses and K'atun endings could have been recorded to facilitate the prediction of eclipses in future K'atuns. This is precisely what the unusual non-periodending date on Stela 10 suggests, on 9.10.19.13.0, July 6, AD 652 (July 3, Julian), since a lunar eclipse occurred just six days prior to this date, as noted by Aveni (2001:255). Here, it is interesting that the tropical-year position of this lunar eclipse is within one day of the tropical-year position of both Stela 23 and the future K'atun ending on 9.12.0.0.0. Furthermore, the lunar nodes on this date are located precisely in the sidereal position of the two solstices, and this may have been of interest to astronomers seeking to anchor eclipse events to positions in the tropical year. VOLUME XXV 2012-2013 73 (a) (b) FIGURE 13: Blackened AJAW in Ruler 12's monuments. (a) Detail from CPN StelaE: 9.5.18.10.0, 9 Ajaw 8 Sak (drawing by author after Schele 2000:Number 1007). (b) Detail from CPN Stela 10, Gl-H2 (drawing by author after Barbara Fash, in Schele 1989:34). It appears that the measurements of Metonic cycles were particularly associated with K'atun endings and associated eclipse events, despite their rare co-occurrence. The Metonic cycle is thus quite useful and easy to use together with the cycle of K'atuns for the purposes of tracking the tropical year, the lunar cycle, and eclipses. Stela E and the Blackened Ajaw Dates Stela E in Copan can be found on the western edge of the Great Plaza. While its text is difficult to read, StelaE was apparently dedicated by Ruler 12 (Grube and Martin 2000:197, 201). The text on StelaE appears to describe events in the life of the much earlier Ruler 7, Bahlam Nen, with the Initial Series corresponding to 9.5.18.10.0, October 19, AD 552 (October 16, Julian). The Calendar Round date corresponds to 9 Ajaw 8 Sak, and the face of the Ajaw glyph is unusually darkened with cross-hatching (Figure 13a). Interestingly, we find the very same type of blackened Ajaw glyph on Stela 10 (Figure 13b), corresponding to the Metonic interval found on Stela 3, 9.10.19.5.0, January 28, AD 652 (January 25, Julian), 260 days prior to the K'atun • 74 ARCHAEOASTRONOMY ending on 9.11.0.0.0 and equivalent to the same tropical-year position as the previous K'atun ending on 9.10.0.0.0. The second date mentioned on Stela E is the previous K'atun ending 9.5.0.0.0, 11 Ajaw 18 Sek, July 5, AD 534 (July 3, Julian). It is fascinating that this is exactly the same sidereal position of the Sun that we find in the Initial Series date from Stela 10, on 9.10.19.13.0, 3 Ajaw 8 Yaxk'in, July 6, AD 652 (July 3, Julian), while the tropical year has shifted nearly two days due to precession in the intervening 118 years. This type of paired sidereal positions of the Sun is quite interesting, and such paired dates suggest intentional calculations of the sidereal year. Given the unusual non-period-ending date on Stela 10, and the fact that Stela 10 and Stela E were both commissioned by Ruler 12, it is possible that Ruler 12 was using Stela 10 to commemorate the sidereal-year anniversary of the K'atun ending on 9.5.0.0.0, nearly six K'atuns earlier during the reign of Bahlam Nehn. Recalling that the Initial Series date on Stela 10 fell close to the time of the first visibility of the Orion Nebula in association with Na'ir al Saif on the Copan baseline, it is conceivable that these observations were used to calculate the sidereal year and that the slowly accumulating difference between the sidereal year and the tropical year was noticeable, using data collected over hundreds of years. Perhaps significantly, in AD 534, the retrospective year of K'atun 9.5.0.0.0 referenced on Stela E, Na'ir al Saif itself would have risen exactly above the eastern azimuth of the Copan baseline, suggesting that the preliminary observations for the baseline itself may have first originated at this early date. The sidereal year is an independent measurement, separate from the rate of the precession of the equinoxes, which changes slowly with the variable length of the tropical year. Nevertheless, comparing the accumulated difference between a calculated tropical-year value and the sidereal year yields a calculation for precessional drift. The sidereal year of approximately 365.25636 days remains quite constant over thousands of years, reflecting the orbital period of the Earth relative to the stars (Capitaine et al. 2003). Therefore, I maintain that it is possible to find supporting evidence for the intentionality of sidereal-year calculations by the presence of paired dates on either a single text or related texts that place the Sun in approximately the same sidereal position over intervals greater than 100 years in length (Grofe 2011b). These shorter intervals then can be compared with longer deep-time intervals, often in the same texts, to determine if they also provide whole multiples of the resulting sidereal-year value, as calculated by the Maya. Evidence for sidereal-year calculations can be found in deep-time intervals from Palenque and multiple other sites in the Classic period. These texts include Naranjo Altar 1, Tikal Stela 10, Tortuguero Monument 6, and Copan Stela J, each of which I have described and analyzed (Grofe 2011a, 2011b). Elsewhere (Grofe 2007, 2011b), I have demonstrated that several deep-time intervals in the Dresden Codex appear to correspond to precise calculations of the sidereal year, placing the Sun in the same sidereal position over thousands of years using a sidereal-year value very similar to the currently measured interval. In addition, both Barbara MacLeod (2008) and I (2003) independently noticed that the 3-11 Pik interval of 25,980 days, mentioned in multiple texts throughout the Classic period, closely corresponds to one day of precessional drift between the sidereal year and the tropical year. Calculations of the sidereal year may have been facilitated by the use of celestial star risings, such as the first appearance of Na'ir al Saif or the Orion Nebula, in tandem with specific days in the tropical year. Therefore, long-term usage of the Copan baseline could have enabled precise measurements of the sidereal year. Additionally, the blackened Ajaw Initial Series date from Stela E, on 9.5.18.10.0, October 19, AD 552 (October 16, Julian), is exactly equivalent to a tropical-year position 260 days earlier from the tropical-year position of the K'atun ending on 9.5.0.0.0. This implies yet another commemoration of the tropical-year anniversary of the previous K'atun ending on 9.4.0.0.0, October 16, AD 514 (October 14, Julian). While it is not a Metonic cycle, the interval between 9.5.0.0.0 and 9.5.18.10.0 is exactly 260 days less than a Metonic cycle, and this specific date may have been chosen due to both its being a tropical-year anniversary of the earlier K'atun and its proximity to a partial lunar eclipse, which occurred four days after the Initial Series date of Stela E, on October 22, AD 552 (October 20, Julian). Similarly, Stela 23 coordinates a non-Metonic pre-anniversary prediction of the K'atun ending on 9.12.0.0.0, while also placing the Sun at a lunar eclipse node. It is tempting to suggest that the blackened Ajaw on Stela E refers to this lunar eclipse coordinated with the Metonic cycle, whereas the blackened Ajaw on Stela 10 similarly coordinates another lunar eclipse with the Metonic cycle. The blackened Ajaw dates on Stela 10 and Stela E both reference a tropical-year position 260 days prior to a K'atun ending, equivalent to the tropical-year position of the previous K'atun. Since K'ahk' Uti' Witz' K'awiil dedicated both Stela E and Stela 10, it appears that he was also calculating lunar eclipse cycles using data that spanned multiple centuries. Conclusion: Stela 19, the Solar Zenith, and the Era Base of the long Count Finally, in his extensive commemoration of the K'atun ending on 9.11.0.0.0, K'ahk' Uti' Witz' VOLUME XXV 2012-2013 75 K'awiil erected Stela 19 and Stela 13 at the extreme western and eastern boundaries of the Copan Valley. In the northeast, Stela 13 is the last of the valley stelae, with the Initial Series of the K'atun ending itself on 12 Ajaw 8 Keej, October 14, AD 652 (October 11, Julian). Located in a small valley to the west of Stela 10, Stela 19 is curiously nearly aligned on the baseline, but apparently not visible from Stela 10. However, an observer high on the hill to the west of Stela 19 conceivably would be able to view an illuminated Stela 19 aligned with Stela 10. In the far distance, it would be possible to see Stela 12 behind Stela 10 from this same vantage point. Using the 584285 GMT correlation, Stela 19 gives an Initial Series date of 9.10.19.15.00, 4 Ajaw 8 Ch'en, August 15, AD 652 (August 12, Julian). As we have seen, non-period-ending dates such as this may, on further examination, encode intentional astronomical information. In this case, Stela 19's date falls just two days after the August 13 solar zenith in Copan, perhaps serving as an important anchor in the tropical year only 60 days prior to the K'atun ending. The alternative 584283 GMT correlation would place the date of Stela 19 exactly on this August 13 solar zenith, possibly suggesting contrary evidence for this correlation. Indeed, if the 584285 GMT correlation was being used here in Copan in AD 652, as the baseline azimuth suggests, it is unclear why Stela 19 would not have been placed two days earlier on the exact date of the solar zenith. While precise observations of the zenith can be difficult to measure directly with great specificity, the Ajaw date on Stela 19 may have been of primary importance. As the first Ajaw date following two days after the zenith, this pattern would seem to parallel what Aveni (2001:255) proposed for Stela 10, which commemorates the first Ajaw date six days after a lunar eclipse. The 584285 GMT correlation constant takes its name from Julian Day Number 584285, which curiously places the back-calculated era base of the Long Count, 4 Ajaw 8 Kumk'u, on August 13, 3114 BC (September 8, Julian), the same date of the solar zenith in Copan. Whether placing the era base on the August 13 zenith was an intentional calculation of the originators of the Long Count is diffi• 76 ARCHAEOASTRONOMY cult to prove, though several scholars have suggested that the Long· Count was invented at the latitude of Copan at 14.8° N for the very reason that the era base is identical to the second solar zenith at this latitude, using the 584285 GMT correlation. In addition, the two solar zeniths at this particular latitude are precisely 260 days apart-another fortuitous harmony with the pan-Mesoamerican Tzolk'in, suggesting either a great coincidence or an intentional calculation. Vincent Malmstrom (1997:104, 179) has also noted multiple building alignments to the August 13 (Gregorian) sunset throughout Mesoamerica, including Chichen Itza, Teotihuacan, and Tikal. Most of these sites are far north of 14.8° N latitude; therefore, the days on which their local solar zenith passages occur are not equivalent to those in Copan. Nevertheless, it appears that the two dates of August 13 and April 30/May 1 were recognized throughout Mesoamerica. Ivan Sprajc (2000, 2009) has since demonstrated that these same architectural alignments to the sunset on these two days are common in Central Mexico, along with the corresponding sunrises on February 12 and October 30, precisely half a year from the August 13 and April 30/May 1 positions. Multiple Early Classic sites in the Maya Lowlands of southeastern Campeche appear to focus on these same sunrises on February 12 and October 30, suggesting that they have been observed throughout Mesoamerica for some time, splitting the year into fixed agricultural periods of 260 days and 105 days. If we use the alternative 584283 GMT correlation, the era base would have fallen two days earlier on August 11, 3114 BC (September 6, Julian). Nevertheless, if the 584283 correlation was used at the time the Long Count was inaugurated, and if the August 13 zenith was intentionally targeted, a two-day error is certainly within the realm of possibility or even probability among early astronomers endeavoring to back-calculate dates thousands of years in the past. However, without additional evidence, it is difficult to firmly establish the possible intentions of the creators of the Long Count, and we are left to speculate regarding the specificity of the era base date, albeit with great interest. If the originators of the Long Count intended to back-calculate the era base on the August 13 so- lar zenith at the latitude of Copan, then this would have required quite an accurate measurement of the length of the tropical year as early as the first century BC, at the time of the earliest evidence for the use of the Long Count. Certainly, the unique phenomenon of the zenith passage in tropical latitudes could fortuitously enable some degree of accuracy in such measurements, and it is possible that Mesoamerican peoples noted and recorded these measurements quite early. Furthermore, ethnographic evidence demonstrates that Maya peoples continue to recognize the two solar zeniths (B. Tedlock 1982; Girard 1948). It is worth mentioning here that the verb associated with the 'altar/pedestal' of the Three Hearthstones and the events that took place on the era base is spelled JEL-ja, which Barbara MacLeod first read as jelaj, meaning 'was changed' (Callaway 2011:45-46, 283-286; Freidel and MacLeod 2000). Similarly, the K'iche' name for solar zeniths contains the cognate jal-bal 'place of change' (B. Tedlock 1982:180), suggesting that these texts may indeed refer to the intended solar zenith using nearly identical terminology. Given the specific ways in which K'ahk' Uti' Witz' K'awiil appears to have measured the Metonic cycle using the K'atun and the Tzolk'in together, it is possible that such measurements were similarly employed by the originators of the Long Count and that they attempted to place the era base at the point of the August 13 zenith at 14.8° N latitude. We find additional support for this in noting that the latitude of Copan produces a very unique result when a K'atun count begins precisely on the August 13 solar zenith. A count of one K'atun that begins on this solar zenith will conclude precisely on the April 30/ May 1 solar zenith, 260 days later. As we have seen, the Metonic cycle of 19 tropical years is precisely 260 days less than one K'atun. Therefore, an idealized K'atun count that begins on August 13 seems to suggest this very measurement of the tropical year using the two solar zenith passages. The results of this investigation provide specific evidence that the contemporary K'iche' asterism of the Three Hearthstones is directly related to the triadic First Three Hearthstones mentioned in Maya hieroglyphic texts from the Classic period. Specif- ically, the text on Stela 12 and its relationship with Stela 10 provide evidence that K'ahk' Uti' Witz' K'awiil used the Copan baseline as both a sidereal alignment to the rising azimuth of Na'ir al Saif at the center of the Three Hearthstones and an alignment to the sunrise on the K'atun ending 9.11.0.0.0. Since it takes more than 71 years to accumulate only one day of difference between the tropical year and the slightly longer sidereal year, we might assume that Maya astronomers would not have initially distinguished between them. Early astronomers in both Mesopotamia and Egypt used heliacal star risings as a primary measurement of the length of the year (North 2008:28-30, 51). Ancient Egyptians observed the heliacal rise of Sirius as a herald of the annual flooding of the Nile, while Babylonian astronomers kept track of the sidereal year as the only measurement of their year (Neugebauer 1969:140). Is it possible that the Maya eventually distinguished between the sidereal and tropical years? By recording the first appearance of the Orion Nebula and Na'ir al Saif in comparison with the tropical year over several generations, Maya astronomers could have observed the slowly accumulating difference between the tropical year and the sidereal year. Given the relatively stable azimuth position of the rising of Na'ir al Saif over several hundred years, the Copan baseline could have remained useful for this purpose for the duration of the Copan dynasty in the Classic period. The Three Hearthstones are mentioned almost exclusively in statements describing the events on the era base, where they are said to have appeared "at the edge of the sky" in association with the verb jelaj, which suggests the solar zenith. The earliest text to mention the Three Hearthstones in association with the era base is on the undated greenstone mask from the Early Classic (see Figure 7). However, K'ahk' Uti' Witz' K'awiil was the first to codify this association in monumental texts, and his initial reference to the Three Hearthstones is curiously found on Stela 12, describing his witnessing the Hearthstones "at the edge of the sky" in historical time on the K'atun ending on 9.11.0.0.0. However, if K'ahk' Uti' Witz' K'awiil and his predecessors were measuring the sidereal year through observations of the heliacal rise of the Orion Nebula and Na'ir al Saif, it is VOLUME XXV 2012-2013 77 possible that the statements about the Three Hearthstones on the era base involved a precessional calculation of the accumulated difference between the tropical year and the sidereal year since the time of the era base in 3114 BC. If the originators of the Long Count themselves intended to place the era base on the August 13 solar zenith, using a fairly accurate measurement of the tropical year, might they also have had an equally accurate estimation of the sidereal year? We are left to wonder whether the specific, and rather remote, back-calculated year of 3114 BC might have been chosen using some calculation of the sidereal year. If not, is it possible that there was an awareness of the sidereal year and precessional drift by the time K'ahk' Uti' Witz' K'awiil dedicated his monuments? Indeed, Alonso Mendez and Carol " Karasik (2014:99-101) have proposed that the Maya of Palenque were aware that one of the belt stars of Orion crossed the nadir at the time of the era base zenith in 3114 BC. Thus, inscribed in the cosmological texts from the Tablet of the Cross (see Figure 5b), we find an even more detailed, local account of creation involving the Three Hearthstones and the completion of 13 Bak'tuns. Clearly, this is another version of the story that we first see mentioned in the monuments of Copan. Was K'ahk' Uti' Witz' K'awiil somehow back-calculating the changing celestial declination of the Three Hearthstones? This would require a sophisticated knowledge of both the tropical year and the sidereal year. Curiously, using astronomical software to determine the sidereal position of where the Sun would have been on the era base, we can see that the Sun was within six days of the sidereal position where it appears on the K'atun ending on 9.11.0.0.0. Depending on the value of his estimation of the length of the sidereal year compared to the tropical year, perhaps K'ahk' Uti' Witz' K'awiil was aware of this close equivalence. Indeed, the evidence from Stela E and Stela 10 suggests that the Copan baseline itself was being used to calculate the sidereal year over shorter intervals of time. Regardless of the calendar correlation used, the sidereal equivalence of the Sun's position between 9.11.0.0.0 and the era base is interesting, if not exact. It is important to note that if both of the GMT cor• 78 ARCHAEOASTRONOMY relations are inaccurate and Na'ir al Saif was instead literally first visible rising on 9.11.0.0.0, then it also would have been very close to being first visible rising on the era base. However, as we have seen, if we use the 584285 GMT correlation, the Sun rose at the azimuth of the Copan baseline on 9.11.0.0.0, but the Orion Nebula next to Na'ir al Saif would have been first visible at this azimuth exactly one K'atun later, on 9.12.0.0.0. Likewise, if the era base was intentionally chosen to begin a count on the August 13 solar zenith in 3114 BC, one K'atun forward would arrive exactly on the other April 30/May 1 solar zenith, close to the day when the Orion Nebula would have become first visible in that year. This harmonious commensuration of the first appearance of the Orion Nebula and the April 30/May 1 zenith at what would have been the conclusion of the measurement of the first K'atun of the era may have made for an idealized triangulation for the era base, when these three measurements would have coincided. While there is no evidence to suggest that the originators of the Long Count necessarily incorporated the rising of the Orion Nebula into their choice of era base, such an organized measurement involving the two solar zeniths and a sidereal marker may have had a similar precedent in the origination of the Long Count. Elsewhere (Grofe 2007:92, 2009, 2011b:217), I have proposed that the Pleiades may have been involved with the original formulation of the era base. Assuming that the era base was intentionally chosen to be placed on the August 13 solar zenith at 14.8° N, the question remains why the era base was placed in the specific, remote year 3114 BC, thousands of years prior to the initial use of the Long Count in the first century BC. One proposal that may help to explain this choice is that the originators of the Long Count had developed some understanding of the difference between the length of the tropical year and the slightly longer sidereal year. Indeed, the Pleiades precisely crossed the zenith at 14.8° N latitude between the first and second centuries BC, during the time immediately preceding the earliest attested Long Count date from Chiapa de Corzo, given as 7.16.3.2.13, December 8, 36 BC (December 10, Julian) (Coe 1994:76). In addition, the Pleiades would have been first visible, heliacally rising at dawn after close conjunction with the Sun at this time on the very day of the April 30/May 1 solar zenith passage, thereby announcing the day of the solar zenith. Given that these two events were simultaneously paired during the very window of time, and conceivably the place, in which the Long Count was inaugurated, it is possible that the slowly accumulating difference between the recorded day of the April 30/May 1 solar zenith and the increasingly later heliacal rise of the Pleiades on the horizon allowed for the originators of the Long Count to backcalculate the era base to a time when the Pleiades would have risen at a very different time of year. In fact, in 3114 BC, the Pleiades would have risen heliacally due east, announcing the precise day of the vernal equinox. During the first two centuries BC, if a K'atun count began on the August 13 solar zenith, the first K'atun would conclude on the April 30/May 1 solar zenith, on the same day that the Pleiades first appeared rising at dawn. This type of pairing may have been used at the end of the K'atun, and the changing results recorded over time would provide astute observers with a measurement of both the tropical year and the sidereal year, thereby yielding an observation of accumulated precession. Given the usefulness of the K'atun and the Tzolk'in for measuring the Metonic year, the 260-day interval between the two solar zeniths at the latitude of 14.8° N may have served as a useful measuring tool when combined with sidereal observations of the rise of the Pleiades. Indeed, observations of the first and last appearance of the Pleiades continue to be an important component of the agricultural year for contemporary Maya people (Milbrath 1999:258). If the Pleiades were an important sidereal marker in the formative years of the Long Count, announcing the arrival of the April 30/May 1 solar zenith and the beginning of the rains and the planting season for many Maya people, later authors of mythological narratives may have similarly attempted to determine what analogous celestial marker would have been first visible during the April 30/May 1 solar zenith at the time of the era base in 3114 BC. Little evidence exists to suggest that the originators of the Long Count considered the Three Hearthstones important. Instead, the specific involvement of the Three Hearthstones within era base texts-as well as the shared concept of a previous era ending after completing 13 Bak'tuns-may have been cosmological concepts that evolved later in Classic period Copan, based on earlier principles of astronomical measurement using the K'atun, the Tzolk'in, the two solar zeniths, and sidereal observations of stars like Na'ir al Saif. Such solar, lunar, and sidereal observations as we find in the monuments of K'ahk' Uti' Witz' K'awiil suggest that Maya astronomers were capable of making precise astronomical measurements over time involving calculations of the tropical year, the sidereal year, and the eclipse year. Where possible, further research on the inscriptions of these various monuments will undoubtedly help to clarify their context and meaning and their intended historical, mythological, and astronomical references. Acknowledgments I would like to thank Barb MacLeod for her ongoing support and feedback and her willingness to collaborate and entertain new ideas and to generously share her years of experience. Special thanks to Ed Barnhart and the Maya Exploration Center for providing the funding for my research and travel to Copan, without which this article would not have been possible. Thanks to John Carlson, Shannon Kring Buset, Flavia Cueva, Bob Benfer, Stanislaw Iwaniszewski, Carl Callaway, Hal Greene, and Gerardo Aldana for their support, invitations, and collaboration during the research and development of this article. I am likewise grateful to Martha Macri and Matthew Looper for their sustained support and feedback. Thanks to the Carnegie Foundation for the generous usage of Sylvanus Morley's original drawings. Finally, I would like to thank my Copan field students and colleagues who helped with measurements and photographs, and from whom I derive much of my inspiration: Isabel Araujo, Satish Bhatnagar, Denise Brown, Gopal Elluru, Krystan Felt, Karlee Finch, Desislava Pavlova, Jonathan Rushing, Jim Sievers, Liz Sivell, Mirabel Wigon, Amanda Wright, Gary Young, and the Ch'orti' children of La Pintada. Any errors contained within this article are solely those of the author. VOLUME XXV 2012-2013 79 e = atan2[sin(-0.001051229). cos(0.259058243), Notes l. The Long Count is a vigesimal positional system of repeating cycles of 360 days that reckons from an era base several thousand years prior to the first evidence of the use of the system in the first century BC. The two widely accepted Goodman-Martinez-Thompson (GMT) correlations are given by the varying Julian Day Numbers associated with the era base. The 584283 GMT correlation constant places the era base on August 11 , 3114 BC (September 6, Julian), whereas the 584285 GMT correlation constant places the era base on August 13, 3114 BC (September 8, Julian). Long Count notation is transcribed with the largest period first , typically beginning with the Bak'tun (400 X 360 days), followed by the K'atun (20 X 360 days), the 360-day Tun, the Winal (20 days), and the K'in (I day). Therefore, the Long Count date 9.11.0.0.0 commemorates K'atun 11 of Bak'tun 9 after the era base, and it fell on the day 12 Ajaw 8 Keh, with 12 Ajaw being the name of the day in the Tzolk'in, a concurrent 260-day cycle composed of 20 named days and a cycle of 13 numerals. The date 8 Keh follows as the Haab position, a canonical solar cycle of 365 days composed of 18 periods of 20 numbered days with an additional 5-day period. 2. The formula for the calculation of an initial forward azimuth bearing between two coordinates, point A and point B, can be stated in radians as: e= · cos(cp 2) , cos(cp 1) • sin(cp2) sin( cp 1) • cos( cp 2) • e = degrees mod 360° = difference in longitude between points A and B cp 1 = latitude of point A cp 2 = latitude of point B Coordinates for point A, Stela 12 = 14°50'34.6" N = 14.833783° = 0.258898354 rad 89°11'3.53" w = 89.124083° = 1.5555087 rad Coordinates for point B, Stela 10 = 14°50'1.62" N = 14.842944° = 0.259058243 rad 89°7'26.7" w = 89.184314° = 1.5565599 rad • 80 ARCHAEOASTRONOMY cos"(0.258898354) · sin(0.259058243) - sin(0.258898354) · cos(0.259058243) · cos(-0.001051229)] = atan2(-0.001016151 , 0.247632843 - 0.247472817) = atan2(-0.00101615l , 0.000160026) = - 1.414597 radians= -81.0504° = 278.9496° 278°56'58.56" from Stela 12 to Stela 10 = The Haversine formula (Sinnott 1984) can be used with the above to determine distances using a spherical model of the Earth, where R = mean radius of the earth = 6,371 km : c = 2 · atan2(Va, V(l - a)) d= R·c This provides a distance of 6,551 m between Stela 12 and Stela 10. Recognizing the ellipsoidal oblateness of the actual shape of the Earth, the Vincenty formu la (Vincenty 1975) can be used to determine a much more accurate bearing, as well as a more accurate distance between two coordinates. Using a JavaScript calculator for the Vincenty formu la (Veness 2014) provides a slightly different bearing from Stela 12 to Stela 10 of 278°48'20.47", and a distance of 6,558.97 m between them. 3. I obtained these estimates using Starry Night Pro Plus 6.2.3 (Simulation Curriculum Corp. 2009), which has programmed within it current 12000 measurements for the variability in the obliquity of the ecliptic, the elliptical orbit of the Earth, and the Earth's precessional rotation, which together affect the velocity of the Earth and the azimuth position of the Sun on a given date over the past several thousand years. 4. The formula for calculating the declination and right ascension of any star through time is stated in David H. Kelley and colleagues (2011:67): sin( a - z)cos 8 = sin( a 0 + i;;)cos 80 cos( a - z)cos 8 = cos( a 0 + I;;) cos e cos 80 - sin e sin 80 sin 8 = cos( a 0 + i;;)sin e cos 80 + cos e sin 80 z = [(0.0000051 · T + 0.0003041) · T + 0.6406161] · T e= [( -0.0000116 · T -0.0001185) · T + 0.5567530] · T = [(0.0000050 · T + 0.0000839) · T + 0.6406161] · T T = number of centuries, measured negatively before 12000 sin o = cos( a 0 + e cos o0 + cos e sin o0 sin 8 = cos(83.85833334° - 8.627293925) · sin(-7.493647658) · cos(-5.91 °) + cos(-7.493647658) · sin(-5.9JO) sino= cos(75.23103942) · sin(-7.493647656) · cos( -5.91 °) + cos( -7.493647658) · sin(-5.91 °) sino= (0.254921954)(-0.130416271 )(0.994684861 ) + (0.991459327) . (-0.102966144) t = calendar date of interest JDN = Julian Day Number T = (t- 2000.0)/100 = (JDN - 2451545.0)/36525 a 0 = right ascension of star in 12000 00 = declination of star in 12000 a = right ascension of star in target date 8 = declination of star in target date To determine the declination of Na'ir al Saif on 9.11.0.0.0: 9 .11.0.0.0 = October 14, AD 652 = JDN 1959485: T = -492060/36525 = -13.47186858 z = {[0.0000051 ( - 13.47186858) + 0.0003041] ( -13.47186858) + 0.6406161} . ( -13.47186858) z = -8.587574056 e= {[ -o.oooo116 c-13.47186858) -0.0001185] ( - 13.47186858) + 0.5567530} . ( -13.47186858) e= -7.493647656 = {[0.0000050 (-13.47186858) + 0.0000839] ( -13.47186858) + 0.6406161} . ( -13.47186858) = -8.627293925 For Na'ir al Saif (Kelley et al. 2011:56): a 0 = 5h35'26" = 5.590555556h = 83.85833334° sino= -0.033069264- 0.102086743 sino= -0.135156007 0 = -7.767641109° = -7°46'3.5" References Aldana, Gerardo V. 2002 Solar Stelae and a Venus Window. 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