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Vladimir Ladma

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Correlation of Mayan and Julian calendar

Long count
Congruences
Serpent numbers
Symmetric configurations and period tzolkin
Test of correlations
Correlation 650302
Examples of correlations

Long count

Mayan syntax of dates makes possible to observe accuracy of conjunctions of Earth (E) with Mars (R) and lunar line of nodes (Ln). These conjunctions E-Ln-R frame certain raster with period 12 tzolkin, i.e. 3120 days (8.542 years).

In the following schema the rows step with period of conjunctions Earth-Mars. Period 13 tun (18 tzolkin) is highlighted (bold).

Beginning of long count:
 -------------------------
 0. 0. 0. 0. 0 (      0) 
 0. 0. 2. 3. 0 (    780)
 0. 0. 4. 6. 0 (   1560)
 0. 0. 6. 9. 0 (   2340)
--------------------------
 0. 0. 8.12. 0 (   3120)
 0. 0.10.15. 0 (   3900)
 0. 0.13. 0. 0 (   4680) 
 0. 0.15. 3. 0 (   5460)
--------------------------
 0. 0.17. 6. 0 (   6240)
 0. 0.19. 9. 0 (   7020)
 0. 1. 1.12. 0 (   7800)
 0. 1. 3.15. 0 (   8580)
--------------------------
 0. 1. 6. 0. 0 (   9360) 
.....

End of long count:
-----------------------
12.19. 2.12. 0 (1865760)
12.19. 4.15. 0 (1866540)
12.19. 7. 0. 0 (1867320) 
12.19. 9. 3. 0 (1868100)
-----------------------
12.19.11. 6. 0 (1868880)
12.19.13. 9. 0 (1869660)
12.19.15.12. 0 (1870440)
12.19.17.15. 0 (1871220)
-----------------------
13. 0. 0. 0. 0 (1872000)

Congruences

We test connections of Mayan dates with help of congruences (remainder classes).
E.g. the following dates are congruent according to module 260 days (tzolkin):

 Mayan date          D [days]      D/260   [D mod 260]
 -----------------------------------------------------
 9.16. 0.13.17       1411477      5428.7577   197
 9.16. 4. 6.17       1412777      5433.7577   197
 9.16.12. 5.17       1415637      5444.7577   197
 9.17.19.13.16       1425516      5482.7538   196

Serpent numbers

Group of 10 (2*4+2) numbers in Dresden codex.

 Mayan date          D [days]      D/3120  [D mod 3120]
 -----------------------------------------------------
 1/ 9.17.8. 8.5        1421445      455.5913  [1845]
 2/ 10.11.5.14.5       1521285      487.5913  [1845]
 3/ 10. 7.4. 3.5       1491905      478.1746  [ 545]
 4/ 9.18.5.16.4        1427724      457.6038  [1884]
 ------------------
 5/ 10. 8.5. 0.6       1499406      480.5788  [1806]
 6/ 10. 4.6.15.4(14)   1471264(74)  471.5590  [1744(54)]
 7/ 9.18.4. 8.4        1427204      457.4372  [1364]
 8/ 10. 6.10.6.3       1486923      476.5779  [1803]
 -----------------------------------------------------
 9/ 9.16. 8.5.12       1414192      453.2667  [ 832]
10/ 9.17.15.6.14       1423934      456.3891  [1214]

Rates to period Y = 3120 days (12 tzolkin) are on right.
Dates 1,2,(4) and 5,(6),8 seems to be congruent according to 3120 days.

Difference of date 1 and 2 is 99840 days (273.3 years).
After this period lunar line of nodes points not only to Mars, but also to Venus. It concerns exact interval of conjunctions V-E-R (V-E-Ln-R) or (rather) straight line alignment of E-V-R (E-Ln-V-R).
99840 = 9 *19 *583.85965 days = 2^7 *3 tzolkin = 2^5 *Y

Symmetric configurations and period tzolkin

Some synodic and resonant periods of outer planets are nearly exact multiples of period tzolkin (z).
E.g.

Period of stable resonance (J,-S/3,N/2) is c. 185.1 years= 67600 days= 260*z.
We know period 9*z= 2340 days= 6.4 years of motion of inner planets. It corresponds also to stable resonance (J,S/3,-U,-N/3)= 2340.8 days =6.41 years.
Period 18*z= 4680 days= 12.81 years offers more posibilities:
- ([J,N],U)= 12.74 years,
- (J,N)= 4668.7 days= 12.78 years,
- (U/2,S/3)= 12.81 years,...
Period 28z= 7280 days= 19.93 years does not correspond to synodic period (J,S)= 7253.5 days= 19.86 years. Period of mutual motion of axis J-S and U-N is ([J,S],[U,N]) = (16.9132418,111.2908942) = 19.94423 years = 7284.6 days.
Not even period 50*z= 13000 days= 35.59 years is equal to synodic period (S,N)= 13101.5 days = 35.87 years. But ([J,U],[S,N]) = 13001 days = 35.59 years. Also 3*J = 12997.8 days = 35.59 years.

See Symetric configurations.

From ([J,U],[S,N]) = 50z and ([J,S],[U,N]) = 28z it follows: (J,N) = 700z/39 and (S,U) = 700z/11 (but 13 tun= 18z = 702z/39). If 3*J = 50z then N = 13*(J,N) = 700z/3.
Period 700z = 700*260 days = 182000 days = 498.29 years is one of periods of multiple conjunctions.

Let (J,S/3,-U,-N/3)= P/25 (9*z), ([J,S],[U,N])/2= P/16 (14z) and ([J,U],[S,N])/2 = P/9 (25*z). Period P is common multiple of mentioned periods and is equal to 224 (14*16) or 225 (9*25) tzolkin, c. 160 years.
See Stable resonance J-S-U.

Test of correlations

Each correlation is a result of a set of conditions. To determine right correlation it is necessary to establish right set of conditions.

Let us have e.g. the following conditions:

8.16.14.15.4 (1272544) 	conjunction J-S   (|Lj-Ls|<90°)
9.15.9.15.10 (1407550) 	conjunction V-E   (|Lv-Le|<10°)
9.15.9.15.14 (1407554) 	conjunction M-E   (|Lm-Le|<10°)
9.15.9.15.14 (1407554) 	conjunction M-E   (|Lm-Le|<10°)
9.16.4.11.18 (1412878)  Moon at node      (|Ln-L |<10°)
9.17.8.8.5   (1421445)  E-V-R in line     (|Li-Lj|<10°)

On interval (-4000,-2000) for begining of long count we get these correlations:
322720, 325047, 336748, 517737, 622258 , 650301 , 757150, 887387, 889714, 982534.

Number 622258 coresponds to correlation Bohm&Bohm (622261).
Below we will follow correlation 650301-650302.

Correlation 650302

Origin c. -2931.631.
568.484, 8.17.11.1.10 (1278390) full moon (E:291°, L:294°) and 21.6.568 solstice.
568.567: 8.17.11.3.0 (1278420)
Raster of conjunctions E-R (E 320°, R 341°) coincide with instant of alignment J-S and U-N.
(J 155°,S 203°,U 305°,N 57° ; 155°+203°)/2=179° (305°+57°)/2=181°);
Axes J-S and U-N coincide with coordinate axis x (determined by vernal point).
(Exact symmetry [J,S][U,N] according to Bretagnon data follows 40 days later, on 568.672.)
570.702, 8.17.13.6.0 (1279200) fits to the raster of Y (E-Ln-R) (E 8°, Ln 41°, R 37°).
936.659, 9.16. 4.11. 3 (1412863) is not an eclipse, but it is continuation of sequence of eclipses (with period 46 tzolkin): 707.5, 740.2, 772.9, 805.8, 838.5 , 871.2, 903.9, ...

In view of Thompson correlation (584283):

It starts 66019 days (180.75 years) after Thomson origin.
Conjunctions J-S are compatible (180.75 years is c. 9*(J,S)), but they act behind the Sun (heliactic rises - sets).
Solstices are moved by 0.75 year.

In view of correlation Bohm&Bohm (622261):

It starts 28041 days (76.77 years) after Bohm&Bohm origin.
Conjunctions M-V-E are compatible
(76.77 years is c. 48*(V,E) and 242*(M,E)).
1.and 2. serpent numbers are compatible, straight line alignment of E-V-R.

Symmetry of planets at the beginnings of particular baktuns
([A,B][C,D] denote, that axis A-B align with axis C-D).

 baktun  configuration deviation
 --------------------------------------
  13.    [J,S][U,N]     1°
   1.    [J,N][S,U]    15°
   2.    [J,S][U,N]    10°
   3.    [J,N][S,U]    11°
   4.    [J,S][U,N]    26°
   5.    [J,N][S,U]    19°
   6.    [J,S][U,N]    31°
   7.    [S,N][J,U]    13°
   8.    [S,N][J,U]    26°
   9.    [J,S][U,N]    36°
  10.    [J,N][S,U]    23°
  11.    [J,S][U,N]    30°
  12.    [J,N][S,U]     1°
  13.    [J,S][U,N]     5°

Origin of baktuns:

-----------------------------------------------------------
                                             13.  6.6.
   1.   6.9.     2.   6.12.     3.   8.3.     4.  7.6.
   5.   7.9.     6.   7.12.     7.   8.3.     8.  8.6.
   9.   7.9.    10.   8.12.    11.   9.3.    12. 20.6
-----------------------------------------------------------
  13.  22.9.

Mayan cycles