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.