dating of mayan calendar using long-periodic astronomical ...

DATING OF MAYAN CALENDARTable 1. A set of 52 values of τ [days], in ascendingorder, authors’ names and dates of publication.No. τ Author year1 394483 Bowditch 19102 438906 Willson 19243 449817 Bunge 19404 482699 Smiley 1 19605 482914 Smiley 2 19606 487410 Owen 19757 489138 Makemson 19468 489383 Spinden 1 19309 489384 Spinden 2 192410 489484 Ludendorff 193011 492622 Teeple 192612 497878 Dinsmoor 196513 500210 Smiley 3 196014 507994 Hochleitner 197415 508362 Hochleitner 197416 525698 Hochleitner 197417 550279 Kelley 218 553279 Kelley 1 197619 563334 Martin20 577264 Hochleitner 197221 578585 Hochleitner 197022 583919 Suchtelen 195723 584280 Goodman 190524 584281 Martinez 191825 584283 Thompson 195026 584284 Beyer 193727 584285 Thompson 193528 584286 Lounsbury 197829 584314 Calderon 198230 585789 Cook 197331 588466 Mukerji 193632 588626 Pogo 193733 594250 Schove 1 197634 609417 Hochleitner 197435 615824 Schove 2 197736 622261 B&B (Böhms) 199137 626660 Kaucher 198038 626927 Kreichgauer 192739 660205 Hochleitner 197440 660208 Wells & Fuls 200041 663310 Kelley 2 198342 674265 Hochleitner 197443 674927 Hochleitner 197444 677723 Schulz 195545 679108 Escalona 194046 679183 Vaillant 1 193547 698163 Dittrich 193648 739601 Verbelen 199149 774078 Weitzel 194750 774079 Vollemaere 1 198251 774080 Vollemaere 2 198452 774083 Vaillant 2 1935Additional tests made below will bring newindependent arguments to support the B&B correlation.It is important to note that all phenomenadiscussed here were used neither in deriving the correlation(Böhm and Böhm, 1991, 1996, 1999), norin subsequent tests (Klokočník et al. 2008). This iscompletely new, never and nowhere published. Notefinally that the analyzes presented here are all donefor Palenque (latitude 17 ◦ 29 ′ N, longitude 92 ◦ 03 ′ W).The differences for other Mayan localities are negligiblefor our purpose.It is important to note that in the DC theglyphs for the solar eclipses or Venus are shown togetherwith the data (intervals for the relevant phenomenaon the same relevant pages of the DC).It provides a confidence that the glyphs and thedata belong together. We show the known glyphsin Figs. 1 and 2. But nothing similar was discoveredand confirmed yet for the other planets and theMoon, so one has still to rely only upon possible astronomicalmeaning of the time intervals read fromthe DC. When referring to pages in the DC below,D is numbering according to Knorozov (1963), F accordingto Förstemann (1880).D 34a (F 55a) D 35a (F 56a) D 36a (F 57a) D 31b (F 52b)D 33b (F 54b) D 35b (F 56b) D 36b (F 57b) D 37b (F 58b)D 32a (F 53a) D 32b (F 53b)Ah Puch,Ixtab,God of Decease Goddess of Self-MurderFig. 1. Glyphs for the solar eclipses, according toDresden Codex, tables of the eclipses.Fig. 2. Glyphs for Venus, according to Dresden Codex,pp. D 24–D 29 (F 24, 46–50), left and middle,and the glyph for Venus on the altar R in Copán,right.55

V. BÖHM et al.2. TESTS WITH SOLAR ECLIPSESThere is a list of predicted solar eclipsesrecorded on pp. D 30 – D 37 (F 51 – F 58) of the DC;the initial Mayan date of the solar eclipse 9.16.4.10.812 Lamat (LC=1 412 848) is followed by 69 cycles(each comprising 177, 178 or 148 days), reflecting thedates of the next expected eclipses. Quite naturally,only some of them were observable in Yucatan, mostrefer to the ones occurring at other places on theEarth. The table begins and ends by the same Mayandate, 12 Lamat, and covers altogether 11 960 days(i.e., 405 synodic months, 439.5 draconic months and46 tzolkin cycles of 260 days). The uncertainty of theprediction (±1 day) is expressed by three consecutivedates in each case. The list of all these 70 eclipsesis reproduced in Table 4. We tested them againstall eclipses that really occurred somewhere on theEarth and found that there is a group of correlationswith 59 or more successful predictions: Teeple(66), Vollemaere 1 (66), Weitzel (66), Kelley 1 (65),Wells and Fuls (60), Escalone (60), B&B (59), Vollemaere2 (59). Out of these, Weitzel, Vollemaere 1and Vollemaere 2 correlations are practically identical(they agree within two days). On the otherhand, GMT predicted only 4 of them. It is notzero just by a chance due to the fact that we workwith the short-periodic phenomenon (typical periodicityof the eclipses is 177 days, the range is 148–178days). When similar tests were made against theeclipses visible only in Yucatan, the best scored oneswere: B&B (8), Pogo and Hochleitner (7), Willsonand Teeple (6). Thus the B&B correlation seems toyield the best agreement.3. TESTS WITH LONG-PERIODICASTRONOMICAL PHENOMENAFor a unique determination of τ we need anon-periodic phenomenon, but there is nothing likethat in the DC or another Maya source. But there isa synchrony of the dates of heliacal risings/settingsof Venus with the Sun’s eclipses, or between conjunctionsof two planets and the solar eclipses – coincidencebetween two short-periodic phenomena whichis itself of long- periodic character. By synchronywe mean here the situation when there exists in theDC a time interval between two recorded dates thatcontains integer numbers of periods of different astronomicalphenomena. Such synchronies are rareand can simulate long-periodic phenomena. Fortunately,we were able to decode such data from theDC so that we will utilize them now.3.1 Synchrony in the DC of Venusian heliacalrisings with solar eclipsesLet us use the date 9.16.4.10.8 12 Lamat, correspondingto LC = 1 412 848. It points to the firstsolar eclipse in the series of eclipses in the DC, whichis accepted by nearly all investigators; see pages D 30– 37 (F 51 – 58), e.g. Klokočník et al. (2008). Nowwe look for the second useful date. Page D 24 (F 24)of DC contains the date 9.9.9.16.0 1 Ahau 18 Kayab,which corresponds to LC = 1 364 360. On that dayVenus was first seen, according to the Maya, as theMorning Star after its inferior conjunction with theSun. This was also the first date for determinationof further heliacal risings of Venus (added to thisdate are various multiples of the cycle of 2 920 days).This interval is the basic periodicity of overlappingVenusian synodic and sidereal orbits with the tropicalyear after which Venus rises or sets every 8 yearsin approximately the same place in the sky.Thus we have two LC dates, 1 412 848 and1 364 360, marking two different astronomical phenomenavisible in the Mayan sky. It is evidentthat the time interval between these two phenomena,∆ = 48 488 days, must be the same as the timeinterval actually existing “in the nature”. If we takeboth these Mayan dates and attempt to apply theindividual correlations, then the correct correlationmust yield the same time interval ∆ as was actuallyobserved between the heliacal rising of Venus and thesolar eclipse.We tested all the correlations from Table 1.For 39 correlations, we have got no solar eclipse forLC = 1 412 848, while 12 correlations did correspondto solar eclipses but none was visible in the Mayanregion. Apart from B&B, only Teeple’s correlation(τ = 492 622) gave a date when there was a solareclipse visible to the Maya (November 22, 504) butat the maximum of this eclipse, only 12% of the solardisc was obscured. However, for the second date(LC = 1 364 360), the heliacal rising of Venus did notoccur; the date corresponding to Teeple’s correlationfell on February 21, 372 when Venus was at inferiorconjunction and so not visible at all.We took into account all eclipses that were observablein the Mayan region in the period from June428 to August 1011; just 207 solar eclipses occurred.For each date of an eclipse, we subtracted the value∆ and checked if the date found coincided with aheliacal rising of Venus (there were 365 of them betweenMay 295 and December 878). Only the pronouncedsolar eclipse (85%) of October 29, 859 andonly the heliacal rising of Venus 48 488 days beforeit (January 27, 727) fulfil the condition of the synchrony.These dates coincide with LC dating only ifthe B&B correlation is used, from all τ’s in Table 1.So, the analysis of the synchrony of the solareclipses with heliacal rises of Venus speaks clearly:none but one of today known 52 correlations (accordingto Table 1), including the GMT, can be used toconvert the Maya dates to our calendar. The onlyexception is the B&B correlation. With it, the resultlooks like this:9.9.9.16.0 1 Ahau 18 Kayab = 1 364 360 +622 261 = 1 986 621 JD = January 27, 727.Heliacal rising of Venus occurred, eight daysafter inferior conjunction with the Sun.9.16.4.10.8 12 Lamat = 1 412 848 + 622 261 =2 035 109 JD = October 29, 859.The solar eclipse occurred in the Maya area,maximum magnitude was 85%.56

DATING OF MAYAN CALENDAR3.2 Synchrony of Venus and Marsconjunctions with solar eclipsesSimilarly to the Venusian heliacal aspects,there is a synchrony between Venus and Mars conjunctionswith the solar eclipses. By this, we meanthe situation when the solar eclipse is followed by aconjunction of Venus with Mars after 13 512 days.This occurred in Mayan history only once. It is necessaryto say that the average time interval betweenthe conjunctions is 234 days, but in reality the individualintervals can vary between 200 and 300 days,and sometimes they can even exceed 700 days (whentwo conjunctions do not really occur, and the twoplanets move in parallel several degrees apart).We start again with the same ‘initial’ solareclipse date 9.16.4.10.8 12 Lamat, LC = 1 412 848,recorded on p. D 31 (F 52) of DC. Other importantdates can be found on p. D 37 (F 58):9.18.2.2.0 4 Ahau (LC = 1 426 360), with the timedifference from the preceding one equal to 13 512days, that is accompanied by 9.12.11.11.0 4 Ahau(LC = 1 386 580), and also by a time interval 12.11(251 days), in which the number 11 is surrounded bya frame (a glyph of minus sign). The difference betweenthe two dates is equal to 39 780 days, i.e. 170times the average interval between two conjunctionsof Venus with Mars. If we subtract 251 days (againclose to the interval between the two conjunctions)from the first above mentioned date, we get 9.18.1.7.913 Muluc (whose last part, 13 Muluc, is also recordedthere), corresponding to LC = 1 426 109. So, we canassume that all three LC dates (1 386 580, 1 426 109and 1 426 360) recorded on this page refer to the samephenomenon, conjunction of Venus with Mars.Next we tested all correlations from Table 1 tofind which ones are capable of identifying all four LCdates (one for the eclipse, three for the conjunctions)with real phenomena. The only one that can assurethis with sufficient accuracy is the B&B correlation:phenom. LC B&B date Comp. dateconj. 1 386 580 Nov 28, 787 Nov 25, 787ecl. 1 412 848 Oct 29, 859 Oct 29, 859conj. 1 426 109 Feb 18, 896 Feb 16, 896conj. 1 426 360 Oct 26, 896 Oct 24, 896Small differences in the dates of conjunctions arefully acceptable, since these phenomena proceed veryslowly and the Mayan observations with naked eyecould not achieve better accuracy than a few days.3.3 Repeated conjunctions of Jupiter andSaturnConjunctions of Jupiter and Saturn repeat onthe average approximately every 19.6 years. At leastafter 40 years a situation occurs when two conjunctionscome shortly one after the other. This is the‘synchronization’ that is interesting from our point ofview. Consequently, we were looking for two dates inDC differing by a multiple of 40 years (14 560 days).We found interesting complex information, consistingof two Mayan dates and an accompanying table,on page D 74 (F 45) of the DC. This allows to beinterpreted as referring to repeated conjunctions ofJupiter and Saturn.On page D 74, there are two Mayan dates inthe system of Long Count (LC) which correspond,after corresponding re-calculation, to the followingnumber of days in decimal expression:A) 8.17.11.3.0 4 Ahau 1 278 420−1.10 −30B) (8.17.11.1.10) 13 Oc 1 278 390The date B is not given directly in LC, but only bythe date 13 Oc of 260-day tzolkin cycle; missing digitsof LC are given in parentheses. It can be calculatedby subtracting 30 days (accompanied by a minus signhieroglyph) from the date A. This way of calculatingthe next date by subtracting certain number of daysfrom the initial date is quite usual in DC. New dateis sometimes not expressed by all digits of LC, butonly by the final date of 260-day cycle (in this case13 Oc). On the same page of DC below the date B,there is an accompanying table, containing time intervals.The text in DC is partly damaged, but it ispossible to reconstruct it and prove that the individualitems represent multiples of 364 and 260 days, asexplained in Table 2.Table 2. Mayan table of page D 74 (F 45) of DresdenCodexMayan record Analysis of the tableof time interval days ×364d ×260d?.?.8 13 Etznab 728 23.0.12 13 Ik 1092 34.0.15 13 Cimi 1456 45.1.0 13 Oc 1820 5 710.2.0 13 Oc 3640 10 1415.3.0 13 Oc 5460 15 21?.?.8.0 13 Oc 14560 40 56?.0.12.0 13 Oc 21840 60 844.0.16.0 13 Oc 29120 80 112The first column contains the original Mayaninscription; the missing numbers are replaced byquestion marks. Reconstructed time intervals in daysare shown in column two, columns three and fourgive multiples of 364 (that appears often in the tablesof DC) and 260, respectively. Especially importantis the 80-year cycle (29 120 days) in the last rowof Table 3. It contains 73 synodic periods of Jupiter(398.884 days), 77 synodic periods of Saturn (378.091days) and 112 tzolkin cycles (260 days). We can assumethat it is also the average interval between twoconjunctions of both planets. The initial point is thedate B, to which we should add the interval of 29 120days to obtain the next conjunction date C:B) (8.17.11.1.10) 13 Oc 1 278 390+4.0.16.0 13 Oc +29 120C) (9.1.11.17.10) 13 Oc 1 307 51057

V. BÖHM et al.during the two years 491 and 571 are given in Table3. First column describes the mutual positionsof both planets (1st or 2nd conjunction, their oppositionwith the Sun and the Mayan dates B and Cdescribed above). The second column gives the JDand calendar date, computed with the B&B correlation.The positions (geocentric mean ecliptical longitudeλ and latitude β) of both planets in degreesare given in columns 3 and 4 calculated for the datesgiven in column 2, only for the cases of conjunctions.For the oppositions, their computed JD and calendardates are given instead, for Jupiter and Saturn,respectively. Last column then shows the angulardistances of both planets at the moments of theirconjunctions and also for the Mayan dates given inDC. The situation of the table is graphically depictedNow it is necessary to find such shift between thedating in Julian Days and Long Count for which thedates B and C (in LC) fall into a close vicinity ofcomputed times of conjunctions of Jupiter and Saturn(in JD). We found that this can be achieved onlywhen using the B&B correlation (τ=622 261 days),the others failed. Using this value, we arrive to dateB being equivalent to JD = 1 900 651 (i.e., September13, 491) and date C corresponding to JD = 1 929 771(June 5, 571).Both Mayan dates B, C fall into the periodwhen Jupiter and Saturn were very close to their oppositionwith the Sun (only three days apart, respectively),and they stayed close to each other for manymonths, describing wobbles with direct and reversemotions, and showing unique situation when twoconjunctions repeated during the same year. Mayandates then reflect encounters of Jupiter with Sat-in Figs. 3 and 4, for better illustration. The angularCALENDARdistance between the two planets changed duringDATING OF MAYANurn in the moments when they were close to stationarypoints (change from retrograde to direct mo-the years 491 and 571 only a little and very slowly,DATING OF MAYAN soCALENDARthat for a terrestrial observer they both stayed formany weeks in a very close vicinity, describing thetion). The mutual positions of Jupiter and Saturn apparent wobbles almost in parallel.β [deg] β [deg]0 .00 .0-0 .52 3 M a r-0 .51 J a n2 3 M a r-1 .01 J a n1 3 S ep-1 .02 5 S ep1 0 D ec1 3 S ep-1 .52 5 S ep1 0 D ecJ u p iter-1 .5S a tu rn-2 .0J u p iterS a tu rn2 9 5-2 .03 0 0 3 0 5 3 1 0 3 1 5 3 2 02 9 5 3 0 0 3 0 5 λ [deg] 3 1 0 3 1 5 3 2 0λ [deg]Fig. 3. Ecliptical longitude λ and latitude β of Jupiter and Saturn, during the year 491 AD, covering theirrepeated conjunctions.Fig. 3. Ecliptical longitude λ and latitude β of Jupiter and Saturn, during the year 491 AD, covering theirrepeated conjunctions.β [deg] β [deg]3 .023 .5 .02 .0 .55 J u n1 J a n 2 5 F eb12 .5 .05 J u n2 9 A u g1 J a n 2 5 F eb2 7 O c t1 .0 .52 9 A u g2 7 O c t01 .5 .0J u p iter0 .0 .5S a tu rnJ u p iter2 0 60 .02 0 8 2 1 0 2 1 2 2 1 4 2 1 6 2 1 8 2 2 0 2 2 2 2 2 4 2 2 6 S a tu rn2 2 82 0 6 2 0 8 2 1 0 2 1 2 2 1 4 2 1 6λ [deg] 2 1 8 2 2 0 2 2 2 2 2 4 2 2 6 2 2 8λ [deg]Fig. 4. Ecliptical longitude λ and latitude βof of Jupiter and Saturn, during the year 571 AD, covering theirrepeated conjunctions.Fig. 4. Ecliptical longitude λ and latitude β of Jupiter and Saturn, during the year 571 AD, covering theirrepeated conjunctions.583.4 S yn ch ron ization of syn od ic an d sid eric p e- minus glyph (Fig. 5). This interval is equal to multiplesof synodic and sideric period of Mercury andriod s of M ercu ry w ith trop ical year3.4 S yn ch ron ization of syn od ic an d sid eric p e- tropical minus glyph year. (Fig. After5). this This interval, interval Mercury is equal rises to multiplesof synodic and sideric period of Mercury andandriod s of M ercu ry w ith trop ical yearSimilarly to the preceding section, we were sets at the same place in the sky. The interval contains:tropical year. After this interval, Mercury rises andlooking in the DC for two dates differing by 2 200Similarly to the preceding section, we were sets at 19 the synodic same place periods in of the Mercury sky. The (115.877484d),interval contains:25 sideric periods of Mercurydays, the interval after which the synodic and sidericlooking in the DC for two dates differing by 2 200(87.968581d),

DATING OF MAYAN CALENDARTable 3. Mutual positions of Jupiter and Saturn close to their repeated conjunctions.Mutual position JD, Jupiter’s position Saturn’s position Angularcalendar date λ β λ β distance1st conjunction 1 900 477 309.632 −0.724 309.569 −0.996 0.279March 23, 491opposition 1 900 610 1 900 607August 3, 491 July 31, 491(8.17.11.1.10) 1 900 651 307.846 −1.266 306.125 −1.371 1.72413 Oc September 13, 4912nd conjunction 1 900 663 307.352 −1.243 305.746 −1.363 1.611September 25, 4911st conjunction 1 929 671 217.046 1.318 217.532 2.500 1.280February 25, 571opposition 1 929 725 1 929 728April 20, 571 April 23, 571(9.1.11.17.10) 1 929 771 207.674 1.229 211.652 2.496 4.17213 Oc June 5, 5712nd conjunction 1 929 856 213.532 0.871 213.528 2.147 1.276August 29, 5713.4 Synchrony of synodic and sideric periodsof Mercury with tropical yearSimilarly to the preceding section, we werelooking in the DC for two dates differing by 2 200days, the interval after which the synodic and sidericperiods of Mercury and tropical year are again it thesame phase. We found such occurrence on page D 24(F 24). Two introductory Mayan dates on page D 24and the form of the inscription is the following:A) 9.9.16.0.0 4 Ahau 8 Cumku 1 366 560−6.2.0 −2 200B) 9.9.9.16.0 1 Ahau 18 Kayab l 364 360The interval of 2 200 days between the two dates Aand B is expressed directly and accompanied by aminus glyph (Fig. 5). This interval is equal to multiplesof synodic and sideric period of Mercury andtropical year. After this interval, Mercury rises andsets at the same place in the sky. The interval contains:19 synodic periods of Mercury (115.877484d),25 sideric periods of Mercury (87.968581d),6 tropical years (365.242199d).When using the B&B correlation, both Mayandates refer to the positions of Mercury when close tomaximum west elongations. In addition, they assurethat the planet was close to the aphelion of its eccentricorbit, when maximum elongation was 27 ◦ 49 ′ .The conditions to observe Mercury were thus extremelyfavorable; for a terrestrial observer, Mercurywas not only near the maximum elongation, but alsonear its maximum distance from the Sun, so that itwas more than 19 degrees above the horizon beforesunrise (Fig. 6).9 99 916 90 160 01 366 560 days1 364 360 days62200 days 2Ahau 8 Cumku01 Ahau 18 Kayab1 Ahau18 Uo9. 9. 16. 0. 0 4 Ahau 8 Cumku 1 366 560 days- 6. 2. 0 - 2 200 days9. 9. 9. 16. 0 1 Ahau 18 Kayab 1 364 360 days(9. 14. 2. 6. 0) 1 Ahau 18 Uo 1 397640 daysFig. 5. Dresden Codex, p. D 24 (F 24), data forMercury. The newly discovered interval of 2 200 daysmeans a synchrony of synodic and sideric periods ofthe planet with the tropical year. The minus glyphis represented by a frame around ‘glyph zero’(see leftcolumn 6.2.0).59

V. BÖHM et al.a)when the B&B correlation was used. The 2 200-dayinterval means a synchrony of synodic and sidericperiods of Mercury with the tropical year, (Fig. 6).4. DISCUSSIONb)Fig. 6. The positions of Mercury (Dresden Codexp. D 24 (F 24)) in the morning sky shortly beforesunrise between a) December 29, 726 and March 5,727, b) January 7, 733 and March 15, 733, closeto its maximum elongations on January 27, 727 andFebruary 4, 733, respectively (corresponding Mayadates are 9.9.9.16.0.1 Ahau 18 Kayab and 9.9.16.0.04 Ahau 8 Cumku, using the B&B correlation).a) January 27, 727 Mercury close to maximumwest elongation (26 degrees), altitude before sunrise19 degrees. Maximum west elongation occurred January21, 727.b) February 4, 733 Mercury close to maximumwest elongation (26 degrees), altitude before sunrise20 degrees. Maximum west elongation occurred January31, 733.In the DC there are dates to which time intervalsare added that are typical of some repeated astronomicalphenomena, or typical intervals betweentwo dates. Some of them were explained in the past.They are as follows:a) 2 920 days and their multiples, when synodicand sideric periods of Venus are in a synchronywith tropical year and heliacal rising of this planetoccurs (Teeple 1926).b) 11 960 days of repeated solar eclipses (Meinshausen1913, Guthe 1921).Here we found the new interval (2 200 days)and tested it via all the correlations in Table 1. Thereal astronomical meaning has been confirmed onlyAll tests described above show that the B&Bcorrelation yields the best agreement with the astronomicalphenomena recorded by the Maya in theDC. The dates of these events fall into the classicalperiod of the Maya history, when Long Count (LC)was in general use. On the other hand, the GMTcorrelation, mostly accepted by historians, is basedonly on comparing historical events with no directLC dating. We can only speculate why the historicalevents used by the GMT lead to a correlation differentby about +104 years (precisely 37 978 days)from the one based on astronomical events recordedin the DC. This difference is almost precisely equalto double interval of 18 980 days (about 52 years) inwhich tzolkin and haab cycles are in the same phase.Maybe, it is just a mere random coincidence, but itis also possible that it might be caused by an errorin the backward reconstitution of the LC, made byGMT to obtain the dating of historical events in theLC from the sixteen century sources (when the LChad been abandoned for several centuries).5. CONCLUSIONSIn addition to our previous test of validityof different correlation coefficients (Klokočník et al.2008), we made another one, quite independent.This time we rather use long-periodic astronomicalphenomena whose records we succeeded to find inthe Dresden Codex – a synchrony of Venusian heliacalrisings with solar eclipses (interval of about132 years), synchrony of conjunctions of Venus withMars and solar eclipses (interval of about 37 years),repeated conjunctions of Jupiter with Saturn (intervalof about 80 years), and synchrony of synodic andsideric period of Mercury and tropical year (intervalof 6 years, after which Mercury rises and setsat the same place in the sky). All these events, asrecorded by the Maya, coincide with reality only ifthe B&B correlation is used; all others fail. Thusthe B&B correlation is confirmed again, using differentastronomical phenomena from those used inderiving it (Böhm and Böhm 1991) and by testingdifferent correlations (Klokočník et al. 2008). So, wemust state that, from the astronomical point of view,the most frequently used GMT correlation is wrongand should be abandoned, at least for the classicalperiod of the Maya history. The possible explanationwhy the GMT and B&B correlations differ by +104years, suggested in Discussion, certainly deserves furtherinvestigation.60

DATING OF MAYAN CALENDARTable 4. Full list of the solar eclipses from the DresdenCodex: Col. 1 the ordering number; Col. 2 sumof lengths of cycles in days; Col. 3 tzolkin date; Col.4 length of cycle in days; Col. 5 LC date. * The initialdate No. 1 (9.16.4.10.8 12 Lamat) corresponds to1 412 848 days in the LC dating. Data in parentheses –script reconstructed from damaged text.1 2 3 4 51 0 12 Lamat * 1 412 8486 Kan2 177 7 Chicchan 177 1 413 0258 Cimi1 Imix3 354 2 Ik 177 1 413 2023 Akbal6 Muluc4 502 7 Oc 148 1 413 3508 Chuen1 Cimi5 (679) 2 Manik 177 1 413 5273 Lamat9 Akbal6 856 10 Kan 177 1 413 704(11) Chicchan4 (Ahau)7 1 033 5 Imix 177 1 413 8816 Ik(13) Etznab8 1 211 1 Cauac (178) 1 414 059(2) Ahau8 Men9 1 388 9 Cib 177 1 414 23610 Caban3 Eb10 1 565 4 Ben 177 1 414 4135 Ix11 Muluc11 (1 742) 12 Oc 177 1 414 59013 Chuen6 (Cimi)12 1 919 7 (Manik) 177 1 414 7678 Lamat1 Akbal13 (2 096) 2 Kan 177 1 414 9443 Chicchan6 Chuen14 2 244 7 Eb 148 1 415 0928 Ben2 Muluk15 2 422 3 Oc (178) 1 415 2704 Chuen10 Cimi16 (2 599) 11 Manik 177 1 415 44712 Lamat5 Akbal17 2 776 6 Kan 177 1 415 6247 ChicchanTable 4. continued.1 2 3 4 513 Ahau18 2 953 1 Imix 177 1 415 801(2) Ik8 (Caban)19 3 130 9 (Etznab) 177 1 415 97810 (Cauac)(13 Chicchan)20 3 278 (1) Cimi 148 1 416 126(2) Manik8 Ik21 3 455 9 Akbal 177 1 416 30310 Kan3 Cauac22 3 632 4 Ahau 177 1 416 4805 Imix11 Cib23 3 809 12 Caban 177 1 416 65713 Etznab24 3 986 7 Ix (177) 1 416 8348 Men9 Cib25 4 163 2 Chuen 177 1 417 0113 Eb4 Ben26 4 340 10 Lamat 177 1 417 18811 Muluc12 Oc27 4 488 2 Cib (148) 1 417 3363 Caban4 Etznab28 4 665 10 Ben 177 1 417 513(11) Ix12 Men29 4 842 5 Oc 177 1 417 6906 Chuen7 Eb30 5 020 1 Lamat (178) 1 417 8682 Muluc3 Oc31 5 197 9 Chicchan 177 1 418 04510 Cimi11 Manik32 5 374 4 Ik 177 1 418 2225 Akbal6 Kan33 5 551 12 Cauac 177 1 418 39913 Ahau1 Imix34 5 728 7 Cib 177 1 418 5768 Caban9 Etznab35 5 905 2 Ben 177 1 418 7533 Ix4 Men61

V. BÖHM et al.Table 4. continued.1 2 3 4 536 6 082 10 Oc 177 1 418 93011 Chuen12 Eb37 6 230 2 Etznab 148 1 419 0783 Cauac4 (Ahau)38 6 408 11 Cib (178) 1 419 25612 Caban13 Etznab39 6 585 6 Ben 177 1 419 4337 Ix8 Men40 6 762 1 Oc 177 1 419 6102 Chuen3 Eb41 6 939 9 Manik 177 1 419 78710 Lamat11 Muluc42 7 116 4 Kan 177 1 419 9645 Chicchan(6) Cimi43 7 264 9 Eb 148 1 420 11210 Ben11 Ix44 7 441 4 Muluc 177 1 420 2895 Oc6 Chuen45 7 618 12 Cimi 177 1 420 46613 Manik1 Lamat46 7 795 7 Akbal 177 1 420 6438 Kan9 Chicchan47 7 972 2 Ahau 177 1 420 8203 Imix4 Ik48 8 149 10 Caban 177 1 420 997(11) Etznab12 Cauac49 8 326 5 Ix 177 1 421 1746 Men7 Cib50 8 474 10 Ik 148 1 421 32211 Akbal12 Kan51 8 651 5 Cauac 177 1 421 4996 Ahau7 Imix52 8 828 13 Cib 177 1 421 6761 Caban2 Etznab53 9 006 9 Ix (178) 1 421 85410 Men11 CibTable 4. continued.1 2 3 4 554 9 183 4 Chuen 177 1 422 0315 Eb(6) Ben55 9 360 12 Lamat 177 1 422 20813 Muluc1 Oc56 9 537 7 Chicchan 177 1 422 3858 Cimi9 Manik57 9 714 2 Ik 177 1 422 5623 Akbal4 Kan58 9 891 10 Cauac 177 1 422 73911 Ahau12 Imix59 10 039 2 Manik 148 1 422 8873 Lamat4 Muluc60 10 216 10 Kan 177 1 423 06411 Chicchan12 Cimi61 10 394 6 Ik (178) 1 423 2427 Akbal8 Kan62 10 571 1 Cauac 177 1 423 4192 Ahau3 Imix63 10 748 9 Cib 177 1 423 59610 Caban11 Etznab64 10 925 (4) Ben 177 1 423 7735 Ix6 Men65 11 102 12 Oc 177 1 423 95013 Chuen1 Eb66 11 250 4 Etznab 148 1 424 0985 Cauac6 Ahau67 11 427 12 Men 177 1 424 27513 Cib1 Caban68 11 604 7 Eb 177 1 424 4528 Ben9 Ix69 11 781 (2) Muluc 177 1 424 6293 Oc4 Chuen70 11 958 10 Cimi 177 1 424 80611 Manik12 Lamat 1 424 80862

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V. BÖHM et al.DATIRANjE KALENDARA MAJA KORIXENjEM DUGOPERIODIQNIHASTRONOMSKIH POJAVA U DREZDENSKOM KODEKSUV. Böhm 1 , B. Böhm 1 , J. Klokočník 2 , J. Vondrák 3 and J. Kostelecký 41 The University for Political and Social Sciences,Ovčárecká 312, 280 02 Kolín, Czech RepublicE–mail: bohm@izapa.cz, paib2@upcmail.cz2 Astronomical Institute, Academy of Sciences of the Czech Republic,251 65 Ondřejov, Czech RepublicE–mail: jklokocn@asu.cas.cz3 Astronomical Institute, Academy of Sciences of the Czech Republic,Boční II, 141 00 Prague, Czech RepublicE–mail: vondrak@ig.cas.cz4 Research Institute for Geodesy, 250 66 Zdiby 98, Czech RepublicE–mail: kost@fsv.cvut.czUDK 529.31 (972.6)Originalni nauqni radOdnos između kalendara Maja i naxegkalendara dat je koeficijentom poznatim podnazivom ”korelacija”, koji predstavlja brojdana koji treba da se doda na datum u sistemuDugog brojanja dana kod Maja da se dobijeJulijanski Datum (broj dana) koji se koristiu astronomiji. Iznenađujue je koliko je velikaneodređenost u vrednosti korelacije (atime i između istorije Maja i istorije naxegsveta) koja među ovim kalendarima dostiжenajqexe nekoliko stotina godina. Postojivixe od 50 razliqitih vrednosti korelacije,od kojih neke proistiqu iz istorijskih, a nekeiz astronomskih podataka. Mi smo ovde testirali(između ostalog) najvixe upotrebljavanuGMT korelaciju (dobijenu iz istorijskih podataka)i korelaciju Bemovih (B & B), dobijenuiz astronomskih podataka dekodiranih izDrezdenskog kodeksa (DC), koja se razlikujeod GMT za oko +104 godine. U prethodnimradovima za proveru smo koristili nekolikoastronomskih pojava koje su zabeleжeneu DC. Jasno smo pokazali da: (i) GMT korelacijanije bila u stanju da predvidi ovepojave koje su se stvarno desile u prirodii (ii) GMT predviđa te pojave u dane kadanisu zabeleжene. Pojave koje smo koristilido sada za testiranje su, međutim, kratkoperiodiqnei rezultat testa ne mora da budejednoznaqan. Stoga smo za dalje testiranjeizabrali dugoperiodiqne astronomske pojave,koje su uspexno dekodirane iz DC. Te pojavesu (i) sinhronost heliaqkih izlaza Venere ipomraqenja Sunca, (ii) sinhronost konjunkcijaVenere i Marsa sa pomraqenjima, (iii) retkoponovljive konjunkcije Jupitera i Saturna, i(iv) sinhronost sinodiqkog i sideriqkog periodaMerkura sa tropskom godinom. Iz naxeanalize sledi da B & B korelacija daje najboljeslaganje sa astronomskim pojavama kojesu zabeleжile Maje. Zato predlaжemo da seodbaci GMT i prihvati B & B korelacija.64