PETIN M.I.
The PETIN - METON calendar
Contents - http://Petin1Mikhail.narod.ru/index.htm
The accuracy of the PETIN-METON Calendar
2. Compensation of the calendar lunar cycles drift.
2.1. The beginning of the count of Meton cycles [Date 1, Lunar month (Lunation) 1-LA, Lunar year 1-LYB, Meton cycle 1-MA, Grand Meton cycle 1-GMet] is date of the Gregorian proleptic calendar - December 21, 4694 BCE or Date 1, Lunation 1-LA, 4694 BCE.
2.2. The mean value of the period of the Moon rotation around of the Earth (Lunation) - 29,5305888531 days.
2.3. The sequence and duration of the calendar lunar months and years in Meton simple cycles should correspond to Table 3 (http://Petin12Mikhail.narod.ru/index.htm).
Table 3. The alternation and the duration of the lunations
in the Meton-cycle MB 12 (1996 Ц 2014 Gregorian calendar).
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Count of ! Lunations, sutki ! Total, sutki
calendar years ! !---------------------------------
-----------------------------------!---------------------------------------------------------------------------------------------------------------------! Cycles !
Meton !Gregorian! 1-LA 2-LB 3-LA 4-LB 5-LA 6-LB 7-LA 8-LB 9-LA 10-LB 11-LA 12-LB 13-LA !----------------------!Misalign-
! ! 12-LA !Calendar! Natural ! ment
-----------------------!-----------!---------------------------------------------------------------------------------------------------------------------------------------------!----------
1-LY└ 22.12.95 ! 1996 ! 30 29 30 29 30 29 30 29 30 29 30 29 -- ! 354 ! 354, 367 ! +0, 367
2-LYA 10.12.96 ! ! л л л л л л л л л л л 29 -- ! 354 ! 354, 367 ! +0, 367
3-LYC 29.11.97 ! ! л л л л л л л л л л л л 30 ! 384 ! 383, 898 ! -0, 102
4-LYA 18.12.98 ! 1999 ! л л л л л л л л л л л л 30 ! 384 ! 383, 898 ! -0, 102
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5-LYB 06.01.00 ! 2000 ! л л л л л л л л л л л 30 -- ! 355 ! 354, 367 ! -0, 633
6-LYA 26.12.00 ! ! л л л л л л л л л л л 29 -- ! 354 ! 354, 367 ! +0, 367
7-LYC 15.12..01 ! ! л л л л л л л л л л л л 30 ! 384 ! 383, 898 ! -0, 102
8-LYA 03.01.03 ! 2003 ! л л л л л л л л л л л л -- ! 354 ! 354, 367 ! +0, 367
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
9-LYB 23.12.03 ! 2004 ! л л л л л л л л л л л 30 -- ! 355 ! 354, 367 ! -0, 633
10-LYA 12.12.04 ! ! л л л л л л л л л л л 29 -- ! 354 ! 354, 367 ! +0, 367
11-LYC 01.12.05 ! ! л л л л л л л л л л л л 30 ! 384 ! 383, 898 ! -0, 102
12-LYA 20.12.06 ! 2007 ! л л л л л л л л л л л л 30 ! 384 ! 383, 898 ! -0, 102
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13-LYB 08.01.08 ! 2008 ! л л л л л л л л л л л 30 -- ! 355 ! 354, 367 ! -0, 633
14-LYA 28.12.08 ! ! л л л л л л л л л л л 29 -- ! 354 ! 354, 367 ! +0, 367
15-LYC 17.12.09 ! ! л л л л л л л л л л л л 30 ! 384 ! 383, 898 ! -0, 102
16-LYA 05.01.11 ! 2011 ! л л л л л л л л л л л л -- ! 354 ! 354, 367 ! +0, 367
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
17-LYC 25.12.11 ! 2012 ! л л л л л л л л л л л 29 -- ! 354 ! 354, 367 !+-0, 367
18-LYC 13.12.12 ! ! л л л л л л л л л л л 29 -- ! 354 ! 354, 367 ! +0, 367
19-LYC 02.12.13 ! 2014 ! л л л л л л л л л л л 29 30 ! 384 ! 383, 898 ! -0, 102
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Total ! 6939 ! 6939, 688 ! +0, 688
Note. 1. The 1996 Ц 2014 period is the (341+12) Meton cycle.
2. Date 1, Lunation LA 1, Lunar year LYB 1, Meton-cycle MB 12, Grand Meton-cycle GMet 2
means - December 22, 1995 or Date 1 Lunation 1, 1996 ╤┼.
2.4. The base cycle M1 compensation:
M1 = 57 lunar years = 3 Meton cycles = Meton simple + Meton leap + Meton simple.
2.5. The order of following in time of Meton cycles determines a sign, a value and the shape of the bending curve in the misalignment ranges.
Therefore for achievement of the best results of compensation while using a calendar during long time intervals (about hundreds thousand years) it is expedient to pack the Meton cycles in certain groups of summands..
In calculations the following combinations of these groups of summands were considered:
1) M1 = b = L + s + L = 57 lunar years (a base cycle M1 of the compensation),
where:
L = Meton simple = 19 lunar years = 235 lunations = 6940 days,
s = Meton leap = 19 lunar years = 235 lunations = 6939 days.
M2 = 6b+L = 361 lunar years (PetinM2 cycle),
M3 = 2 (6b+L) + L = 741 lunar years (PetinM3 cycle),
M4 = 2 (6b+L) + L + 2 (6b+L) = 1463 lunar years (PetinM4 cycle),
M5 = 260 x 1463 = 380 380 lunar years (PetinM5 cycle),
2) H2 = 5b+L = 304 lunar years (Hipparh2 cycle),
3) P3 = 24 x H2 + L= 7 315 lunar years (Petin3 cycle),
P4 = 52 ( 24 x H2 + L) = 380 380 lunar years (Petin4 cycle),
and also:
4) (L+5 b) + (L+5 b) + (L+4 b) = 855 lunar years,
5) (5 b + L) + (5 b + L) + (4 b + L) = 855 lunar years,
6) (2 b + L + 3 b) + (2 b + La + 3 b) + (2 b + L + 2 b) = 855 lunar years,
7) (7 b + L) + (7 b + L) + L = 855 lunar years,
8) 7 b+ 3 L + 7 b = 855 lunar years,
9) ╨2 = 38 [(7 b + L) + (7 b + L) + L] = 32 490 lunar years,
etc.
The calculations are fulfiled on the basis of tables 6B, 7, 8 - http://Petin49Mikhail.narod.ru/index.htm
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