PETIN M.I.

                        PETIN - METON calendar

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3. The results of calculations (Part 1). 

 

3.1. The misalignment value dT concerning the beginning of a lunar calendar count - Date 1, Lunation 1-LA, Lunar year 1-LYB, Meton cycle 1-MA, Grand Meton cycle 1-GMet  ( or December 21, 4694 BCE Gregorian calendar) is determined by the expression 

                                                           

                             dT = N x 29,5305885 dDJD ,  day,  

       where:

                    N the number of lunar cycles concerning the beginning of the lunar calendar count

                                  before the chosen date,  day,

                    dDJD the number of days (Julian calendar) concerning the beginning of the lunar

                                  calendar count before the chosen date,  day.

 

3.2. The misalignment values dT at the end of each lunar month, lunar year (for initial Meton simple cycle or Meton leap cycle) are given in Tables 6B, 7 and  8  accordingly. 

 

                          Table 6B.             

             The misalignments at the end of the month, days

 

1 month       -0,4694115        -0,4694115      -0,4694115      

2                 +0,0611770        +0,0611770     +0,0611770    

3                  -0,4082345         -0,4082345     -0,4082345

4                 +0,1223540        +0,1223540     +0,1223540

5                  -0,3470575        -0,3470575      -0,3470575

6                 +0,1835310        +0,1835310     +0,1835310

7                  -0,2858805         -0,2858805      -0,2858805

8                 +0,2447080        +0,2447080     +0,2447080

9                  -0,2247035         -0,2247035      -0,2247035

10               +0,3058850        +0,3058850     +0,3058850

11                -0,1635265         -0,1635265      -0,1635265

12               +0,3670620        +0,3670620      -0,6329380

13                -0,1023495                 --                    --

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                      384 days             354 days           355 days  

 

 

                           Table 7.  Meton simple  cycle
 
          SimpleM (Meton lunar years)
 
                       Misalignment                 Duration of
    year                     on the end                      lunar year
                               of lunar year 
                
                   0            0.0000000                         -        -   355

    SimpleM1           -0.6329380                       354     -      -

   Etc.         2            -0.2658754                         -     384    -  

                  3            -0.3682243                        354    -       -     

                  4            -0.0011617                          -       -   355 

                  5            -0.6340997                        354    -       -  

                  6            -0.2670371                          -    384     - 

                  7            -0.3693860                        354    -       - 

                  8            -0.0023234                           -      -   355 

                  9            -0.6352614                        354    -      - 

                10            -0.2681988                          -   384     -  

                11            -0.3705477                        354   -       - 

                12            -0.0034851                           -     -    355 

                13            -0.6364231                        354   -       - 

                14            -0.2693605                          -   384     - 

                15            -0.3717094                        354   -       - 

                16            -0.0046468                          -   384     -       

                17            -0.1069857                          -   384     -  

                18            -0.2093446                          -   384     -  

 SimpleM19            -0.3116935                          -      -       -  

                            Table 8.  Meton leap cycle 

                             LeapM (Meton lunar years)
 
                          Misalignment                       Duration of
  year                           on the end                            lunar year
                                  of lunar year 
                
                0                     0.0000000                       -       -      355 -1 (leap) 
    LeapM1                   +0.3670626                     354     -        - 
 SimpleM2                   +0.7341253                       -    384       -   
    Etc.      3                   +0.6317763                     354    -        -  
                4                   +0.9988389                       -       -      355
                5                   +0.3659009                     354    -        -
                 6                  +0.7329635                       -     384     - 
                 7                  +0.6306146                     354    -        -
                 8                  +0.9976772                       -       -     355     
                 9                  +0.3647392                     354    -        -
                10                 +0.7318019                       -     384     -
                11                 +0.6294529                     354    -        -
                12                 +0.9965155                       -       -      355
                13                 +0.3635775                     354    -       -
                14                 +0.7306401                       -     384    -
                15                 +0.6282912                     354    -       -
                16                 +0.9953538                       -     384    -
                17                 +0.8930049                       -     384    -
                18                 +0.7906560                       -     384    -
 SimpleM19                 +0.6883071                       -       -       - 
 

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