PETIN M.I.
PETIN - METON calendar
Contents - http://Petin1Mikhail.narod.ru/index.htm Brief description
Structure of calendar
The PETIN-METON Calendar contains two basic calendars: a lunar calendar (19-year Meton cycles) and a solar calendar (the annual continuous numbering of days from the Southern solstice date - December, 21).
The each 19-year Meton cycle of lunar calendar contains 235 lunar months (125 months with 30 days and 110 months with 29 days).
Lunar months with 30 days consist of 4 weeks (with 7 days) plus 2 additional days off (for example, dates 15 and 30); lunar months with 29 days consist accordingly of 4 weeks (with 7 days) plus 1 additional day off (for example, date 15).
For simplicity lunar months are designated by ordinal numbers. Duration of months, their consecutive alternation in a year, provisional conformity to months of solar (Gregorian) year are shown in Tables 1 - 3 of Enclosure 1 ( http://Petin12Mikhail.narod.ru/index.htm , http://Petin11Mikhail.narod.ru/index.htm , http://Petin10Mikhail.narod.ru/index.htm and also below in the text.
1996.. 1 year of Meton's cycle =12 lunar months = 6 x 30 + 6 x 29 = 354 days,
1997.. 2 « =12 « = 6 x 30 + 6 x 29 = 354 « ,
1998.. 3 « =13 « = 7 х 30 + 6 х 29 = 384 « ,
1999.. 4 « =13 « = 7 х 30 + 6 х 29 = 384 « ,
2000.. 5 « =12 « = 7 х 30 + 5 х 29 = 355 « ,
2001.. 6 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2002.. 7 « =13 « = 7 х 30 + 6 х 29 = 384 « ,
2003.. 8 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2004.. 9 « =12 « = 7 х 30 + 5 х 29 = 355 « ,
2005..10 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2006..11 « =13 « = 7 х 30 + 6 х 29 = 384 « ,
2007..12 « =13 « = 7 х 30 + 6 х 29 = 384 « ,
2008..13 « =12 « = 7 х 30 + 5 х 29 = 355 « ,
2009..14 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2010..15 « =13 « = 7 х 30 + 6 х 29 = 384 « ,
2011..16 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2012..17 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2013..18 « =12 « = 6 х 30 + 6 х 29 = 354 « ,
2014..19 « =13 « = 7 х 30 + 6 х 29 = 384 «.
----------------------------------------------------------------------------------------------
235 lunar months = 29,5305885 x 235 = 6939,6883 days ~ 124 x 30 + 11 x 29 =
6939 days,
19 solar years = 365,242195 x 19 = 6939,6017 days ~ 365 x 19 + 4 leap days =
6939 days.
Lunar months of each year are designated in a calendar in the chronological order as «Month 1», «Month 2 »..... «Month 12». The additional thirteenth month is named «Month 13». It is the last month of a lunar year.
Month 13 is inserted between Months 12 and 1 in the next years of each Meton’s cycle: 3, 7, 11, 15, 17, 18 and 19.
The duration of odd lunar months (1, 3, 5, 7, 9, 11) of any year and Month 13 equals 30 days, the duration of even months (2, 4, 6, 8, 10) of any year – 29 days. Month 12 has duration 30 days only in 1, 5, 9, 13 years of 19-year Meton’s cycle, in other years of Meton’s cycle it has duration 29 days.
The first day of each month in lunar year is date 1, the other days of month are accordingly numbered as date 2, date 3...., date 29, date 30 (Table 2 - http://Petin11Mikhail.narod.ru/index.htm , Months 1 - 12 http://Petin27Mikhail.narod.ru/index.htm ). Thus date 1 of each lunar month always falls on Monday and coincides with a lunar phase - the New Moon.
The additional day off (Lunaday) of each month - date 15 is inserted between the Sunday (date 14) and Monday (date 16). Date 15 always coincides with a lunar phase - the Full Moon.
The second additional day off (Lunaday) - date 30 is inserted between the Sunday (date 29) and Monday (date 1 of the next month).
Note. It is also possible to make the date 1 of each month falling on Sunday, and accordingly additional days off (Sundays) will be dates 16 and 30. However, in this case each Friday of any month will fall on date 13, which is undesirable as superstitious people badly perceive a similar combination.
Industrial monthly cycles (the beginning - the end of the monthly plan) are synchronized in the calendar with a natural lunar cycles.
The calendar is developed in such a manner that each date of any lunar month always corresponds to the same phase of the Moon and besides always falls on the same day of week. For example, date 1 of any lunar month always coincides with a New Moon and always falls on Monday, and date 15 of any lunar months always coincides with the Full Moon and always falls on Sunday.
Besides each date of any lunar month has a coordinate concerning day of the Southern solstice as the date of a solar year (tropical).
The account of days of a solar year in the given calendar (memorials, national and religious holidays, terms of seasonal works etc.) is conducted by the continuous numbering from the date of passage by the Earth through a point of the Southern solstice on the Earth orbit around the Sun (December, 21).
In a calendar the opportunity of displaying the local (national or religious) calendar is foreseen as an auxiliary third calendar.
Table 1 - http://Petin10Mikhail.narod.ru/index.htm - illustrates the transition from a solar calendar (continuous numbering of dates) to a solar Gregorian calendar. The continuous numbering of dates in the solar calendar concerning the date of the Southern solstice provides connection of the given World calendar with any former or existing calendars.
According to the solar calendar:
- date 1 - a point of the Southern (winter) solstice;
- « 91 - « the Eastern (spring) equinox;
- « 183 - « the Northern (summer) solstice;
- « 275 - « the Western (autumn) equinox,
- « 366 - a Leap Day (February, 29).
Calendar 2004 - http://Petin27Mikhail.narod.ru/index.htm - show the variant of the embodiment of the PETIN-METON Calendar as tables.
Each line in the table of the PETIN-METON Calendar represents a day of a week - Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday and Lunaday, accordingly. Columns in the table represent weeks of a lunar month. Each box on the crossing of a line and a column is the appropriate date of a lunar month.
On lines: Monday - Lunaday inside each box there are three indicators. The first indicator located in the top right corner, shows the date the solar year. The second indicator located in middle, shows the date of a lunar month. The third indicator (at the bottom) shows the date of an auxiliary (any local) calendar.
The offered calendar can be realized by various ways. For example, it can be made up as the tangible device with written indication of months, weeks and dates of year, shown on web-site - http://Petin27Mikhail.narod.ru/index.htm . The calendar can be executed as a computer or the special device with digital indication and the information stored in the electronic memory etc.
Natural cycles:
- sutki (day + night) - mean duration of a revolution of the Earth about the axis,
- solar year (tropical) = 365,242195 sutki - mean duration of the time interval
between two consecutive passages of the centre of the Sun through the
Eastern equinox point,
- solar Meton cycle = 19 solar years = 6939,6017 sutki - the period of time, after which
the sequences of solar eclipses practically repeat themselves,
- solar Grand Meton cycle = 341 solar Meton cycles = 6479 solar years =
2 366 404,2 sutki - the period of time, after which the Earth and the Moon (in
the Southern solstice day) come back to the initial position concerning the Sun,
- lunation (lunar sinodic month) = 29,5305888531 sutki - mean value of the time interval
between two consecutive identical phases of the Moon,
- lunar year = 12 (13) lunations - time intervals according to Table-calendars (types
ÌÀ, ÌÂ, Ìcorr) – http://CalendarPetin-Meton.narod.ru/table-calendars.htm
- lunar Meton cycle = 235 lunations = 6939,6883 sutki - mean value of a time interval
after which sequences of solar eclipses repeat themselves,
- lunar Grand Meton cycle = (341 õ 235 – 1) lunations = 2 366 404,2 sutki - time interval,
after which the Earth and the Moon (in the Southern solstice day) come back to the
initial position concerning the Sun.
- 1 precession cycle = 25 796,178 solar years (tropical) is the period of movement the
Earth axis on the cycle cone about stars (precession). In the PETIN – METON
Calendar the influence of precession is taken into account by means of the solar years
(tropical).
- d - the drift of the lunar cycle relatively the solar cycle.
(6939,6883 – 6939,6017) sutki sutki sutki
velocity of drift d = ------------------------------------------- = 0,00456 ------ (or 0, 0866 ---------------- )
19 solar years year Meton cycle
Calendar cycles:
à) solar calendar:
- sutki - the period of time equal to the mean duration of natural sutki,
- solar month - a time interval determined, for example, by the Gregorian
solar calendar,
- solar year = 365 sutki,
- leap-year = 366 sutki,
- an intercalary day = 1 sutki,
- solar Meton cycle ÌÀ = 19 solar years = 6940 sutki –
http://CalendarPetin-Meton.narod.ru/typeMA.htm ,
- solar Meton cycle ÌÂ = ÌÀ - 1 sutki = 6939 sutki ,
- solar Grand Meton cycle GMet = 6479 solar years = 2 366 404 sutki.
A note. In the PETIN-METON Calendar the rules of the solar (seasonal) calendar
correspond to the rules of the Gregorian Calendar .
á) lunar-solar calendar (a calendar of eclipses):
- sutki - the period of time equal to the mean duration of natural sutki,
- lunation LA = 30 sutki - a time interval between two consecutive
identical phases of the Moon, approximated to an integer to the greater side,
http://CalendarPetin-Meton.narod.ru/typeMB.htm ,
- lunation LB = 29 sutki - a time interval between two consecutive
identical phases of the Moon, approximated to an integer to the smaller side,
- lunar year LYA = LA+LB+LA+LB+LA+LB+LA+LB+LA+LB+LA+LB = 354 sutki,
- lunar year LYB = LA+LB+LA+LB+LA+LB+LA+LB+LA+LB+LA+LA = 355 sutki,
- lunar year LYC = LYA + LA = 384 sutki,
- lunar Meton cycle ÌÀ = 235 lunations = 8 LYA + 4 LYB + 7 LYC = 6940 sutki,
- lunar Meton cycle ÌÂ = 235 lunations = 9 LYA + 3 LYB + 7 LYC = 6939 sutki,
- correcting Meton cycle Ìcorr = (235-1) lunations = 10 LYA+3 LYB+6 LYC = 6909 sutki,
- base lunar cycle MetÀÂÀ = MA+MB+MA = 20 819 sutki,
- lunar Hipparh cycle HA = 5 MetÀÂÀ + MA = 111 035 sutki,
- lunar Hipparh cycle HÂ = HA + MA + MetÀÂÀ = 138 794 sutki,
- lunar Petin cycle PA = 4 [5 (MA+MB+MA)+MA]+2MA+MB+MA = 471 899 sutki,
- lunar Grand Meton cycle GMet = 3 PA + Mcorr + 2 PA= 2 366 404 sutki.
In section « Table - calendars » ( http://CalendarPetin-Meton.narod.ru/table-calendars.htm ) are shown the alternation and the durations of the cycles of the PETIN-METON calendar within the limits of an interval of time - 6479 solar years:
- Ìåtîn-cycles:
- 19-year Ìåton-cycle ÌÀ (6 940 sutki),
- 19-year Ìåton-cycle ÌÂ (6 939 sutki),
- 19-year Ìåton-cycle Ìcorr (6 909 sutki),
- a base Ìåton-cycle:
- 57-year Ìåton-cycle (20 819 sutki),
- Hipparch-cycles:
- 304-year Hipparch-cycle HA (111 035 sutki),
- 380-year Hipparch-cycle ÍÂ (138 794 sutki),
- Petin-cycles:
- 1292-year Petin-cycle ÐÀ (471 899 sutki),
- 1311-year Petin-cycle ÐÂ (478 808 sutki),
- Great Ìåton-cycle:
- 6479-year cycle GMet (2 366 404 sutki).
The beginning of nearest next the Great Ìåton-cycle (i.e.GMet-2 ) is December 21, 1786 CE.
------------------------------------------------------------------------------
Contents - http://Petin1Mikhail.narod.ru/index.htm Brief description
