PAGE  F 69 – 73, / D 48 – 52/


A/  /?/.15.9.4.4                                  The Mayan date value is undeterminable.

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

 

    The cyclic date is mentioned twice, its’ final value is undeterminable.

 

C/ 9.13.12.10.0                                                 1,394,120 days

    -         1.12.6                                                   -         606 days

D/ /9.13.10.15.14/   9 Ix                                    1,393,514 days

 

E/ 9.19.11.13.0                                                 1,437,020 days

    -         4.10.6                                                   -      1,646 days

F/ /9.19.7.2.14/        9 Ix                                    1,435,374 days

 

G/ 10.17.13.12.12    4 /Eb/                              1,567,332 days

 

H/  10.11.3.18.14     9 Ix                                   1,520,654 days

 

I/  8.6.16.12.0                                                    1,201,200 days

    -            4.6                                                      -           86 days

J/ /8.6.16.7.14/         9 Ix                                   1,201,114 days

 

K/  8.16.19.10.0                                                1,274,240 days

     -            /9/.8                                                   -         188 days

L/ /8.16.19.0.12/       4 Eb                                1,274,052 days

 

M/ /10/.14.2.16.12    4 Eb                                1,541,852 days

 

N/ /9/.15.9.15.14    9 Ix                                     1,407,554 days

 

O/ /9/.11.11.15.14  9 Ix                                     1,379,474 days

 

P/ /9/.4.16.8.12     /4/ Eb                                  1,330,732 days

 

C/        J.D. 2,016,381                                 July 20, 808                         

D/        J.D. 2,015,775                                 November 22, 806

E/        J.D. 2,059,281                                 January 2, 926

F/        J.D. 2,057,635                                 July 1, 921

G/        J.D. 2,189,593                                 October 12, 1282

H/        J.D. 2,142,915                                 December 25, 1154

I/          J.D. 1,823,461                                 May 13, 280

J/         J.D. 1,823,375                                 February 17, 280

K/        J.D. 1,896,501                                 May 3, 480

L/         J.D. 1,896,313                                 October 28, 479

M/        J.D. 2,164,113                                 January 7, 1213

N/        J.D. 2,029,815                                 May 1, 845

O/        J.D. 2,001,735                                 June 14, 768

P/        J.D. 1,952,993                                 January 2, 635

 

 

   The multiplies of number 54 are added to the Mayan dates ended by 9 Ix day: 1-13, 26, 39,  52, 65, 78, 91, 104, 117, 130, 520, 780, 1,040, 1,300, 1,560, 1,820, 2,080, 2,340 and 2,600 times.

  

 The multiplies of number 65 are added to the Mayan dates ended by 4 Eb day: 1-28, 56, 84, 224, 336, 448, 560, 672, 784, 1,008, /1,232 ?/, 1,456, 1,680, /1,904 ?/ and /2,128 ?/ times.

 

O/ June14, 768                     4 days before the summer solstice.

                                               All the visible planets were rising or setting close to the maximal northern declination of the Sun, i.e. in the place, where the Sun rises and sets during the summer solstice.

                                               Declinations:  Sun                23.40°

                                                                        Mercury          24.41°

                                                                        Venus           18.54°

                                                                        Mars              23.56°

                                                                       Jupiter            23.47°

                                                                        Saturn            23.32°

 

   The Mayan dates C, N and M are concerning the dates of Venus last visibility in the western sky before its lower conjunction with the Sun. Venus synodic circulation lengths (583.92139 days) are contained between those dates.

 

C/ July 20, 808         

 

    13,434 days = 23 Venus synodic circulation lengths.

 

N/ May 1, 845

 

    134,298 days = 230 Venus synodic circulation lengths.

 

M/ January 7, 1213             

 

C/ July 20, 808                     Venus 8 days before the lower conjunction with the Sun.

                                               Seen for the last time as an evening star in the western sky.

                                               The Sun set at 6.32 p.m.

Venus set at 7.06 p.m.

 

N/ May 1, 845                       Venus 6 days before the lower conjunction with the Sun.

                                      Seen for the last time as an evening star in the western sky.

                                               The Sun set at 6.18 p.m.

Venus set at 7.09 p.m.

 

M/ January 7, 1213              Venus 12 days before the lower conjunction with the Sun.

                                               Seen for the last time as an evening star in the western sky.

                                               The Sun set at 5.49 p.m.

Venus set at 7.15 p.m.

 

   All the Mayan dates, except the date O /June 14, 768/, are concerning the Mercury circulations. The basic positions of Mercury – Sun and Mercury – Earth during one synodic circulation /115.877 484 days/ are following: 

The upper conjunction with the Sun

36 days

The maximal eastern elongation   

22 days

The lower conjunction with the Sun

22 days

The maximal western elongation  

36 days

The upper conjunction with the Sun

    The intervals between the Mercury positions are only approximate and can differ a few days after every finished synodic circulation with length varying between 104 to 132 days. This is caused by a great eccentricity of the Mercury trajectory around the Sun.

 

   The Mayan dates are recording the Mercury positions close to the four basic positions that occur during its circulation around the Sun. They can be divided into four files:

 

File 1 – the maximal eastern elongation – dates L, D and G.

File 2 – the maximal western elongation – dates I and E.

File 3 – the lower conjunction with the Sun – dates C, F, P, H, M and N.

File 4 – the upper conjunction with the Sun – dates J and K.

 

   The Maximal elongations are observable when the planet sets in the longest time interval after the sunset during the eastern elongation, or rises before the sunrise during the western elongation. The lower and upper conjunction (the planet is unobservable) was probably counted by the Mayan astronomers as the middle of time intervals between two following maximal elongations. In the tables concerning Venus visibility they also counted 8 and 90 days, when the planet was unobservable, because it was around the lower or upper conjunction with the Sun – pages F 24, 46-50, /D 24-29/.

 

   The Mercury synodic circulation lengths are contained between all the dates in each file. Between some multiplies of synodic and siderial circulation meetings (87.9693 days) with approximate tropical year length (365.242 199 days). That means approximately same mutual positions of the Mercury, Sun and Earth were held after some time.

 

File 1 – the maximal eastern elongation - dates L,D and G

 

L/ October 28, 479

    119,462 days =    1,031 Mercury synodic circulation lengths.

                                   1,358 Mercury siderial circulation lengths.

                                      327 tropical year lengths.

 

D/ November 22, 806

    173,818 days =    1,500 Mercury synodic circulation lengths.

                                   1,976 Mercury siderial circulation lengths.

                                      476 tropical year lengths.

 

G/ October 12, 1282

  

L/ October28, 479               The Mercury is close to the eastern elongation with angle distance 21.34° from the Sun.

                                               The Sun set at 5.34 p.m.

                                               The Mercury set at 6.46  p.m.

 

                                               The real maximal elongation of 22.40° was on October 22, 479.

The difference between the estimated and real elongation is 1.06°.

 

D/ November 22, 806          The Mercury is close to the eastern elongation with angle distance 20.21° from the Sun.

                                               The Sun set at 5.28 p.m.

                                               The Mercury set at 6.48  p.m.

 

                                               The real maximal elongation of 20.30° was on November 23, 806.

The difference between the estimated and real elongation is 0.09°.

 

G/ October 12, 1282            The Mercury is in the eastern elongation with angle distance 23.61° from the Sun.

                                               The Sun set at 5.37 p.m.

                                               The Mercury set at 6.52  p.m.

 

   The Mayan astronomers have made an average mistake of 0.38° in those three elongations – for them an undiscoverable mistake.

 

File 2 – the maximal western elongation - dates I and E

 

I/ May 13, 280

    235,820 days =    2,035 Mercury synodic circulation lengths.

 

E/ January 2, 926

 

I/ May 13, 280                       The Mercury is close to the western elongation with angle distance 23.06° from the Sun.

                                               The Mercury rose at 4.19 a.m.

                                               The Sun rose at 5.29 a.m.

 

                                               The real maximal elongation of 23.33° was on May 15, 280.

The difference between the estimated and real elongation is 0.27°.

 

E/ January 2, 926                 The Mercury is close to the western elongation with angle distance 21.54° from the Sun.

                                               The Mercury rose at 5 a.m.

                                               The Sun rose at  6.33 a.m.

                                                

The real maximal elongation of 23.55° was on

December 22, 925.

The difference between the estimated and real elongation is 2.01°.

 

   The Mayan astronomers have made an average mistake of 1.14° in those two elongations – for them an undiscoverable mistake.

 

File 3 – the lower conjunction with the Sun – dates C, F, P, H, M and N.

 

C/ July 20, 808

    41,254 days =      356 Mercury synodic circulation lengths.

                                   469 Mercury siderial circulation lengths.

                                   113 tropical year lengths.

 

F/ July 1, 921

    104,642 days =    903 Mercury synodic circulation lengths.

 

P/ January 2, 635

    189,922 days =    1,639 Mercury synodic circulation lengths.

                                   2,159 Mercury siderial circulation lengths.

                                   520 tropical year lengths.

 

H/ December 25, 1154

    21,198 days =      183 Mercury synodic circulation lengths.

                                   241 Mercury siderial circulation lengths.

                                   58 tropical year lengths.

 

M/ January 7, 1213

    134,298 days =    1,159 Mercury synodic circulation lengths.

 

N/ May 1, 845

 

   The dates are concerning the Mercury positions around the lower conjunction with the Sun. The Mayan astronomers have probably determined this position with help of the visible eastern and western elongations, when the Mercury is best visible. They set an approximate middle of the time the Mercury was unobservable (between two following maximal elongations and around the lower conjunction with the Sun). 

 

C/ July 20, 808                     The Mercury 2 days before the lower conjunction.

                                               26 days after the eastern elongation.

                                               19 days before the western elongation.

 

F/ July 1, 921                        The Mercury 1 day after the lower conjunction.

                                               29 days after the eastern elongation.

                                               18 days before the western elongation.

 

P/ January 2, 635                 The Mercury 7 days after the lower conjunction.

                                               23 days after the eastern elongation.

                                               17 days before the western elongation.

 

H/ December 25, 1154       The Mercury 5 days after the lower conjunction.

                                               21 days after the eastern elongation.

                                               19 days before the western elongation.

 

M/ January 7, 1213              The Mercury 1 day before the lower conjunction.

                                               14 days after the eastern elongation.

                                               26 days before the western elongation.

 

N/ May 1, 845                       The Mercury 1 day before the lower conjunction.

                                               22 days after the eastern elongation.

                                               26 days before the western elongation.

 

   The results of the Mayan astronomers calculations could be using a statistical average method simplified into following conclusion, that is concerning the Mercury position close to the lower conjunction with the Sun: 

1/ 1.3 days before the lower conjunction.

2/ 4.3 days after the lower conjunction.

3/ 22.5 days after the eastern elongation.

4/ 20.8 days before the western elongation.

    The average length of time to the dated position of the Mercury after eastern elongation and before western elongation is 21.7 days. This precisely corresponds with the real average time length from position - eastern elongation to lower conjunction and from lower conjunction to western elongation, which lasts for 22 days on average, as shown before.

 

File 4 – the upper conjunction with the Sun – dates J and K.

 

J/ February 17, 280

    73.126 days =       631 Mercury synodic circulation lengths.

 

K/ May 3, 480

 

   The dates are concerning the Mercury positions around the upper conjunction with the Sun. In a similar way as with the lower conjunction, the Mayan astronomers have set an approximate middle of the time the Mercury was unobservable between both the maximal elongations and around the upper conjunction with the Sun.

 

J/ February 17, 280             The Mercury 14 day before the upper conjunction.

                                               31 days after the western elongation.

                                               40 days before the eastern elongation.

 

K/ May 3, 480                       The Mercury 1 day before the upper conjunction.

                                               38 days after the western elongation.

                                               36 days before the eastern elongation.

 

We can gather the results of dated positions of the Mercury around lower conjunction with the Sun in a statistical average: 

1/ 7.5 days before the upper conjunction.

2/ 34.5 days after the western elongation.

3/ 38 days before the eastern elongation.

   The time lengths average, when the Mercury was accordingly to the Mayan dating in position after the western elongation and before eastern elongation, is 36.25 days. This precisely correspondences with the real time length average from western elongation to upper conjunction and from upper conjunction to eastern elongation, which is on average 36 days, as shown before.

 

   Following time interval a is added to the cyclical date B and time interval b is probably added to date A. Because we can not reliably determine the value of dates A-B in the Mayan calendar system, it is impossible to match their total with time intervals to particular dates of the Christian calendar.

 

a/ 4.5.19.13.12.8                  4 Eb                           12,381,728 days

b/ 4.6.19.0./12./ 10               9 Ix                              12,521,050 days

 

   The time intervals are probably concerning the tropical year observations for very long time intervals.

 

a/ 12,381,728 days = 33,900 tropical years with –18 days mistake.

b/ 12,521,050 days = 34,281.5 tropical years.