PETIN M.I.

       The World PETIN - METON calendar

 

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Example  XII. The definition of New Moon day for January, 45 BC. 

 

            Initial data:          Date 01, Month 1, 1 AD (lunar calendar)  -  1 721 436 JD

                                          January 01,             1 AD (solar calendar)  -  1 721 426 JD ( proleptic Gregorian calendar)

                                 ---------------------------------------------------------------------------------

                                          What is a solar date X, which according to the New Moon Day

                                           for   January,  45  BC  ( proleptic Gregorian calendar)?

 

1.  The passing from Date 01, Month 1,   1 AD (coinciding with January 11, 1 AD,  1 721 436 JD)

                                  to Date 01, Month 1,   57 BC ( proleptic lunar calendar ).  

        As it is known the rule of the proleptic calendars:  2 BC,   1 BC,   1AD,   2 AD etc.,  therefore  

            there are   57   lunar years between Date 01, Month 01,  57 BC and  Date 01, Month 1,  1 AD

 

2.            57 : R1 = 1,00    where:  R1 = 57 from the table 6  - http://Petin22Mikhail.narod.ru/index.htm

                                                 for interval of (57 –   <  285 years).     

              We take 1 instead of  1,00 and

                             1 x R1  =  57  years

                             1 x R2  = 20 819 days,  where:  R2  = 20 819 from the table 6

                                                                                 for interval  of  (57 –   <  285 years).  

 3.            20 819 days are  the quantity  JD between Date 01,  Month 1,  57 BC   and

                                                                                           Date 01,  Month 1,    1 AD.

4.        1 721 436  ,  i.e.  JD of  Date 01, Month 1,  1 AD 

         -      20 819

       --------------------

           1 700 617 ,   i.e.  JD of  Date 01, Month 1,  57 BC 

5.   To find  JD of  Date 01, Month 1,  45 BC  it is necessary:

            57 -  45 = 12  lunar years.

 

6.       1 700 617

         +      4 341 ,  where 4 341 days are  the quantity  JD between Date 01,  Month 1,  57 BC

                               and  Date 01,  Month 1,  45 BC  from the table 5  ,

                               column  Quantity lunar years - 1+2+...+12

                               http://Petin21Mikhail.narod.ru/index.htm .  

          ----------------------------- 

          1 704 958,   i.e.  JD of  Date 01, Month 1,  45 BC,  New Moon Day proleptic lunar calendar ). 

 

7.         45  solar years between January 01, 45 BC and  January 01, 1 AD

        To find  dNJD  , i.e the quantity JD between   January 01, 45 BC and  January 01, 1 AD we use the expression

                    ( NyearsBC – 1) x Ndays  (table 2)  + 366 = dNJD ,   days  (see points 8 - 10 below)

 

8.         45 – 1 = 44  solar years. 

9.         44 : K1 = 11,00    where:   K1 = 4  from the table 2 - ( http://Petin20Mikhail.narod.ru/index.htm    )

                                                       for interval  4 –  < 96 years.

         We take  11 instead of   11,00

                     11 x K1 = 11 x 4 = 44 solar  years

                     11 x K2  = 11 x 1461 = 16 071  days,   where:  K2 = 1461 from the table 2

                                                                          for interval of  4 –  <96 years.

10..      16 071  days

            +   366  days ,     i.e. 1 BC solar  year  ( leap year )

       ---------------------

             16 437  days

 

11.       1 721 426    ,  i.e.  JD of  January 01, 1 AD      

         -       16 437

       -----------------------------------           

             1 704 989   ,  i.e.  JD of  January 01, 45 BC  ( proleptic Gregorian calendar).

 

12.     1 704 989

      -  1 704 958

       ----------------------

                      31  days,  i.e. the quantity  JD between Date 01, Month 1,  45 BC and  January 01, 45 BC.

 

13.     1 704 958 ,   i.e.  JD of  Date 01, Month 1,  45 BC,  New Moon Day. 

         +           30

      -----------------------------------

          1 704 988 ,   i.e.  JD of  Date 01, Month 2,  45 BC,  New Moon Day proleptic lunar calendar ). 

    

14.     1 704 989  days are JD of  January  01, 45 BC,  therefore 1 704 988 ( Date 01,  Month 2,  45 BC,  New Moon Day -           proleptic lunar calendar  is  JD of  December 31, 46 BC, 

        

The date (JD 1 704 988) is December 31, -45 ( Astronomical calendar ) =  
= December 31, 46 BC in the proleptic Gregorian calendar, which is 
January 02, 45 BC in the proleptic Julian calendar.

       

15.     Finally   December 31, 46 BC   ( proleptic Gregorian calendar)  coincide with New Moon Day ( Date 01,   Month 2,  45 BC    proleptic lunar calendar ) .

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