PETIN M.I.
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)
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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
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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 .
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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
( Nyears, BC – 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 )
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16 437 days
11. 1 721 426 , i.e. JD of January 01, 1 AD
- 16 437
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1 704 989 , i.e. JD of January 01, 45 BC ( proleptic Gregorian calendar).
12. 1 704 989
- 1 704 958
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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
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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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