PAGE  F  61 – 64   /D  40 – 43/

 

A/ /?/.15.9.1.3                                                          The Mayan date value is undeterminable.

B/ 9 Kan 12 Kayab                                                  A cyclic date repeating every 18,980 days.

                                                                                   The Mayan date final value in the chronology system is undeterminable.

 

C/ 8.16.15.16.1                                                        1,272,921 days

     -         1.4.16                                                          -        456 days

D/ /8.16.14.11.5/      3 Chicchan                            1,272,465 days

   

E/ 8.16.14.15.4                                                        1,272,544 days

    -               6.1                                                          -         121 days

F/ /8.16.14.9.3/       13 Akbal                                  1,272,423 days

 

G/ 8.11.8.7.0                                                            1,234,220 days

    -       11.15                                                             -         235 days

H/ /8.11.7.13.5/       3 Chicchan                              1,233,985 days

 

I/ 8.16.3.13.0                                                            1,268,540 days

    -         0.17                                                              -           17 days

J/ /8.16.3.12.3/      13 Akbal                                    1,268,523 days

 

K/ 10.8.3.16.4                                                          1,499,004 days

 

L/ 10.13.13.3.2                                                         1,538,342 days

     -    7.2.14.19                                                         -    51,419 days

M/ /10.6.10.6.3/     13 Akbal                                    1,486,923 days

 

N/ /8/.19.0.4.4                                                           1,288,884 days

 

 

C/   J.D.          1,895,182                  September 22, 476 

D/   J.D.          1,894,726                  June 24, 475

E/   J.D.          1,894,805                  September 11, 475

F/   J.D.          1,894,684                  May 13, 475

G/   J.D.          1,856,481                  October 8, 370

H/   J.D.          1,856,246                  February 15, 370

I/    J.D.           1,890,801                  September 24, 464

J/   J.D.           1,890,784                  September 7, 464

K/   J.D.          2,121,265                  September 16, 1095

L/   J.D.          2,160,603                  May 30, 1203

M/  J.D.          2,109,184                  August 19, 1062

N/   J.D.          1,911,145                  June 6, 520

 

 

   Behind the set of the Mayan dates follow the tables containing multiplies of (1 to 20)x91 days, 15x364, 20x364, 40x364, 40x364, 60x364 and 80x364 days. The record of higher dates is damaged.

 

   The Mayan dates C, E, G, I and N are concerning Jupiter heliactic sets, i.e. the moments of the last short visibility over the western horizon shortly after the sunset.  The planet was invisible for the next few tens of days because of its conjunction with the Sun. Jupiter synodic circulation length multiplies are contained between the dates E, G, I and N. It moves between 395 and 404 days. The average is        398.884 070 days.

 

E/ September 11, 475

            38,324 days = 96 Jupiter synodic circulation length

 

G/ October 8, 370

            34,320 days = 86 Jupiter synodic circulation length

 

I/ September 24, 464

            20,344 days = 51 Jupiter synodic circulation length

 

N/ June 6, 520

 

C/ September 22, 476                    Jupiter is 41 days before conjunction with the Sun.

The heliactic set of the planet.

                                                           The Sun set at 5.56 p.m.

                                                           The Jupiter set at 7.47 p.m.

                                                           The autumn equinox.

 

E/ September 11, 475                     Jupiter is 23 days before conjunction with the Sun.

                                                           The heliactic set of the planet.

                                                           The Sun set at 6.05 p.m.

                                                           The Jupiter set at 7.06 p.m.

                                                           11 days before the autumn equinox.

 

G/ October 8, 370                            Jupiter is 49 days before conjunction with the Sun.

                                                           The heliactic set of the planet.

                                                           The Sun set at 5.45 p.m.

                                                           The Jupiter set at 8.03 p.m.

                                                           16 days after the autumn equinox.

 

I/ September 24, 464                       Jupiter is 35 days before conjunction with the Sun.

                                                           The heliactic set of the planet.

                                                           The Sun set at 5.54 p.m.

                                                           The Jupiter set at 7.29 p.m.

                                                           2 days after the autumn equinox.

 

N/ June 6, 520                                  Jupiter is 44 days before conjunction with the Sun.

                                                           The heliactic set of the planet.

                                                           The Sun set at 6.27 p.m.

                                                           The Jupiter set at 8.50 p.m.

                                                           14 days before the summer solstice.

 

   The results of observed, or into past calculated heliactic sets of Jupiter can be summarized into following conclusion:

 

1/ The heliactic sets set in on average 39 days before conjunction with the Sun. This corresponds to the time, when the planet is for the last time shortly visible after the sunset over the western horizon, before it gets into conjunction with the Sun.

 

2/ Jupiter heliactic sets always happened approximately in the prominent parts of the tropical year. Four times around the autumn equinox and once around the summer solstice.

 

3/ The Sun set in a very short time interval of 20 minutes, since 5.45 till 6.05 p.m. in cases C, E, G and I. Jupiter set some 57 minutes, since 7.06 till 8.03 p.m.

 

   The Mayan dates   C, E, H, L and M are concerning the Saturn heliactic rises, i.e. the moments, when the planet was visible for the first time in the morning sky before the sunrise.  It was unobservable for few tens of days before, because of its conjunction with the Sun. The Saturn synodic circulation length multiples are contained in all these data. With a slight scatter the circulation makes 378.091 900 days.

 

C/ September 22, 476

            377 days                   = 1x the Saturn synodic circulation length

 

E/ September 11, 475

            38,559 days              = 102x the Saturn synodic circulation length

 

H/ February 15, 370

            304,357 days            = 805x the Saturn synodic circulation length

 

L/ May 30, 1203

            51,419 days              = 136x the Saturn synodic circulation length

 

M/ August 19, 1062

 

C/ September 22, 476                    The Saturn is 43 days after conjunction with the Sun.

                                                           The heliactic rise of the planet.

                                                           The Saturn rose at 3.23 a.m.

                                                           The Sun rose at 5.49 a.m.

 

E/ September 11, 475                     The Saturn is 45 days after conjunction with the Sun.

                                                           The heliactic rise of the planet.

                                                           The Saturn rose at 3.13 a.m.

                                                           The Sun rose at 5.47 a.m.

 

 

H/ February 15, 370                         The Saturn is 63 days after conjunction with the Sun.

                                                           The heliactic rise of the planet.

                                                           The Saturn rose at 2.53 a.m.

                                                           The Sun rose at 6.29 a.m.

 

L/ May 30, 1203                               The Saturn is 61 days after conjunction with the Sun.

                                                           The heliactic rise of the planet.

                                                           The Saturn rose at 2.30 a.m.

                                                           The Sun rose at 5.26 a.m.

 

M/ August 19, 1062                         The Saturn is 51 days after conjunction with the Sun.

                                                           The heliactic rise of the planet.

                                                           The Saturn rose at 2.44 a.m.

                                                           The Sun rose at 5.45 a.m.

 

 

   Two files of following Mayan dates are concerning the Mercury positions close to its maximal western or eastern elongations. The G, J, C, K, H and D dates are concerning the western elongations, when the planet was rising in the eastern sky before the sunrise.  The F, N and E dates are concerning the eastern elongations. The Mercury set in the evening sky after the sunset. The planet was practically observable only in those positions, when it got into the maximal angle distances from the Sun. The Mercury synodic circulation length multiples are contained between the dates, incidentally the synodic and siderial circulations and the approximate tropical year conformities.

 

G/ October 8, 370

            34,303 days              = 296x the Mercury synodic circulation length

                                                  390x the Mercury siderial circulation length

                                                    94x the tropical year length

 

J/ September 7, 464

             4, 398 days              = 38x the Mercury synodic circulation length

                                                  50x the Mercury siderial circulation length

                                                    12x the tropical year length

 

C/ September 22, 476       

226,083 days            = 1,951x the Mercury synodic circulation length

                                                  2,570x the Mercury siderial circulation length

                                                     619x the tropical year length

 

K/ September 16, 1095

            265,019 days            = 2,287x the Mercury synodic circulation length

 

H/ February 15, 370

            38,480 days              = 332x the Mercury synodic circulation length

 

D/ June 24, 475

 

 

F/ May 13, 475

16,461 days              = 142x the Mercury synodic circulation length

                                                  187x the Mercury siderial circulation length

                                                    45x the tropical year length

 

N/ June 6, 520

            16,340 days              = 141x the Mercury synodic circulation length

 

E/ September 11, 475

 

 

   If the Mercury synodic and siderial circulation length meets the tropical year approximate length, the maximal elongations of the planet are repeating in positions concerning (with little differences) the conformity of:

 

1/ the planet rises and sets time,

2/ the Sun rises and sets time,

3/ the approximate position of the planet on its ecliptics,

4/ the date of the year with difference smaller than 30 days.

 

G/ October 8, 370                The Mercury is close to the western elongation with angle distance 17.61° from the Sun.

                                               The Mercury rose at 4.44 a.m.

                                               The Sun rose at 5.52 a.m.

 

                                               The real maximal elongation of 18.83° was on October 12, 370.

                                               The difference between the estimated and real elongation is 1.22°.

 

J/ September 7, 464            The Mercury is close to the western elongation with angle distance 17.27° from the Sun.

                                               The Mercury rose at 4.37 a.m.

                                               The Sun rose at 5.46 a.m.

 

                                               The real maximal elongation of 17.92° was on September 10, 464.

                                               The difference between the estimated and real elongation is 0.65°.

 

C/ September 22, 476         The Mercury is close to the western elongation with angle distance 14.51° from the Sun.

                                               The Mercury rose at 4.55 a.m.

                                               The Sun rose at 5.49 a.m.

 

                                               The real maximal elongation of 18.33° was on September 29, 476.

                                               The difference between the estimated and real elongation is 3.82°.

 

K/ September 16, 1095       The Mercury is close to the western elongation with angle distance 17.61° from the Sun.

                                               The Mercury rose at 4.39 a.m.

                                               The Sun rose at 5.49 a.m.

 

                                               The real maximal elongation of 17.94° was on September 18, 1095.

                                               The difference between the estimated and real elongation is 0.33°.

 

H/ February 15, 370             The Mercury is close to the western elongation with angle distance 26.08° from the Sun.

                                               The Mercury rose at 4.58 a.m.

                                               The Sun rose at 6.30 a.m.

 

                                               The real maximal elongation of 27.69° was on February 22, 370.

                                               The difference between the estimated and real elongation is 1.61°.

 

D/ June 24, 475                    The Mercury is close to the western elongation with angle distance 19.25° from the Sun.

                                               The Mercury rose at 4.11 a.m.

                                               The Sun rose at 5.23 a.m.

 

                                               The real maximal elongation of 19.96° was on June 27, 475.

                                               The difference between the estimated and real elongation is 0.71°.

 

 

   The Mayan dates are determining the Mercury western elongations on average four days sooner, before the real moment of the maximal elongation. The Mayan astronomers have made an average mistake 1.39°, which was not measurable at all because of the difficulties connected with observing this planet. The biggest departure of –3.82° can be found on September 22, 476 – the date C. The Mercury synodic and siderial circulation length and the approximate tropical year meets between the dates G, J, C and K. The determined elongations are probably results of theoretical calculations. The date K into the future, the next dates into the deep past. Therefore a bigger mistake occurred by the C date, if only average values of the planet circulation length were used. The Mercury synodic circulation length vary from 104 to 132 days.

 

F/ May 13, 475                     The Mercury is close to the eastern elongation with angle distance 23.41° from the Sun.

                                               The Sun set at 6.22 p.m.

                                               The Mercury set at 8.07 p.m.

 

                                               The real maximal elongation of 23.51° was on May 10, 475.

The difference between the estimated and real elongation is 0.1°.

 

N/ June 6, 520                      The Mercury is close to the eastern elongation with angle distance 23.49° from the Sun.

                                               The Sun set at 6.30 p.m.

                                               The Mercury set at 8.10 p.m.

 

                                               The real maximal elongation of 25.15° was on May 25, 520.

The difference between the estimated and real elongation is 1.66°.

 

E/ September 11, 475         The Mercury is close to the eastern elongation with angle distance 25.21° from the Sun.

                                               The Sun set at 6.05 p.m.

                                               The Mercury set at 7.16  p.m.

 

                                               The real maximal elongation of 25.70° was on September 6, 475.

The difference between the estimated and real elongation is 0.49°.

 

   The Mayan astronomers determined the eastern elongation on average 5 days later, after the planets maximal distance from the Sun. They have made an average mistake 0.75°, which was due to their methods undiscoverable. The angle distance of the Mercury and the Sun changes only slightly for a few days around the maximal elongations. The planet seemingly stands at one place. Therefore the Mayan astronomers could not have reached bigger accuracy.

 

   The following time intervals a to h are added to the cyclic date B /9 Kan 12 Kayab/. We can not determine the real value of this date in the Mayan chronology system and therefore recalculate it into the Christian dating system.

 

a/ 4.6./1./11.3.1.       3 Chicchan                            12,395,221 days

b/ 4.6./13./13.15.1    3 Chicchan                            12,482,581 days

c/ 4.6.1.9.15.0           3 Kan                                     12,394,740 days

d/ 4.6.9.16.10.1        3 Chicchan                            12,454,761 days

e/ 4.6.7.12.4.10        3 Ix                                          12,438,810 days

f/ 4.6.11.10.7.2         3 Cimi                                     12,466,942 days

g/ 4.6.9.15.12.19      13 Akbal                                 12,454,459 days

h/ 4.6.1.9.15.0           3 Kan                                      12,394,740 days

  

   Basing on the analysis of single time sections and mutual intervals between them we found out, that they are concerning the observations of tropical year for very long time period, but it is impossible to match them with Christian calendar dates.

 

a/ 12,395,221 days              33,937 tropical years with +3 days departure

d/ 12,454,761 days              34,100 tropical years with –3 days departure

 

The interval between dates e – f contains 77 tropical years with –8 days departure.

The interval between dates g – b contains 77 tropical years with +2 days departure.

The interval between dates c – b contains 240.5 tropical years.

The interval between dates c – g contains 163.5 tropical years with -2 days    departure.

 

   The intervals between some time sections also contain some planets synodic circulations, what theoretically correspondences with their conjunctions.

  

Time interval of 87,360 days between dates a-b = Mars, Jupiter and Saturn  conjunction.

Time interval of 72,202 days between dates c-f = Jupiter and Saturn conjunction.

Time interval of 12,483 days between dates f-g = Mars and Saturn conjunction.

 

   The Mayan dates E, F, I, J, L and M are repeated on page F 31-32 /D 60-61/. Than follows the table of 91 and 364 multiplies, which are added to the dates.

  

A/ /?/ 15. 9. 4. 4                    The value of the date is undeterminable.

 

B/ 9 Kan 12 Kayab               The cyclical date repeating every 18,980 days. The final value of this date in Mayan chronological system is undeterminable.